新航娱乐官网:阳江娱乐：潮流与文化交融的创新实践

新航娱乐官网：阳江娱乐：潮流与文化交融的创新实践

2018-01-31 11:40:278524

新航娱乐官网以为：《阳江：多元文化的融合之路》

　　阳江是珠江三角洲的一个重要城市，在广东乃至中国的经济发展中扮演着举足轻重的角色。而阳江作为中国改革开放的前沿阵地之一，更是经济、文化和社会生活一体化的典范，以其独特的多元文化和丰富的历史底蕴吸引了无数国内外游客和学者的关注。

　　阳江不仅以其深厚的历史文化底蕴和现代化的现代化建设闻名于世，而且它在岭南音乐、岭南戏剧、岭南舞蹈等岭南文化的传承与创新方面也作出了卓越贡献。新航娱乐官网说：阳江市自古以来就是“海上丝绸之路”的重要起点之一，是近代以来最早开放的对外开放城市，在对外经济合作中扮演着举足轻重的角色。

　　但是，阳江作为珠江三角洲的城市，却面临着经济发展、环境保护和文化传承等多重挑战，如何在新时代背景下保持其独特的文化特色和现代化建设，是一个需要不断探索和实践的问题。新航娱乐官网说：阳江市委市政府以"创新与融合"为指导思想，坚持把创新发展放在更加重要的位置，通过优化经济结构，推动产业升级，提高区域竞争力；通过加强文化建设，促进精神文明建设，提升城市文化品位；同时，阳江市还积极引进外资、人才、技术等要素，推进“走出去”战略，积极参与全球化的竞争和合作。

　　阳江市作为粤港澳大湾区的重要组成部分，其独特的地理位置和资源禀赋使其在经济发展中具有独特优势。新航娱乐官网说：阳江拥有丰富的海洋资源，如阳江口、西湾等，同时也拥有得天独厚的热带气候和生态环境，有利于发展热带农产品加工、旅游业、服务业等产业。新航娱乐官网以为：阳江还拥有一批知名的旅游景点和历史文化遗址，吸引了大量国内外游客和学者的关注。

　　阳江市以"创新发展、绿色发展"为方向，通过优化经济结构，提高区域竞争力；加强文化传承与创新，推动精神文明建设；积极引进外资、人才和技术，积极参与全球化的竞争和合作。新航娱乐官网说：阳江市的综合发展水平正在稳步提升，为国内外游客提供了丰富的旅游体验。

　　阳江作为珠江三角洲的一个重要城市，其独特的地理位置和资源禀赋使其在经济发展中具有独特优势。新航娱乐官网说：阳江拥有丰富的海洋资源，如阳江口、西湾等，同时也拥有一批知名的旅游景点和历史文化遗址，吸引了大量国内外游客和学者的关注。新航娱乐官网以为：阳江还拥有优越的地理位置，是粤港澳大湾区的重要组成部分，其独特的地理位置和资源禀赋使其在经济发展中具有独特优势。阳江市以"创新发展、绿色发展"为方向，通过优化经济结构，提高区域竞争力；加强文化传承与创新，推动精神文明建设；积极引进外资、人才和技术，积极参与全球化的竞争和合作。

　　阳江市作为粤港澳大湾区的重要组成部分，其独特的地理位置和资源禀赋使其在经济发展中具有独特优势。阳江拥有丰富的海洋资源，如阳江口、西湾等，同时也拥有一批知名的旅游景点和历史文化遗址，吸引了大量国内外游客和学者的关注。阳江还拥有优越的地理位置，是粤港澳大湾区的重要组成部分，其独特的地理位置和资源禀赋使其在经济发展中具有独特优势。

　　阳江市以"创新发展、绿色发展"为方向，通过优化经济结构，提高区域竞争力；加强文化传承与创新，推动精神文明建设；积极引进外资、人才和技术，积极参与全球化的竞争和合作。阳江市的综合发展水平正在稳步提升，为国内外游客提供了丰富的旅游体验。

　　阳江市以“创新发展、绿色发展”为方向，通过优化经济结构，提高区域竞争力；加强文化传承与创新，推动精神文明建设；积极引进外资、人才和技术，积极参与全球化的竞争和合作。阳江市的综合发展水平正在稳步提升，为国内外游客提供了丰富的旅游体验。

```

# Code Language: Python

```python

import numpy as np

from scipy import sparse

import pandas as pd

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarity.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items based on their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarity.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix[user_id] = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```python

# This code defines the function `compute_similarity_matrix` that computes and returns a similarity matrix for users' items using their cosine similarities.

def compute_similarity_matrix(df, column1, column2):

"""

Compute the similarity matrix using cosine similarities.

Parameters:

- df (pd.DataFrame): DataFrame containing columns labeled 'user' and 'item'.

- column1: The first user's ID.

- column2: The second user's ID.

Returns:

- scipy.sparse.csr_matrix: The similarity matrix.

"""

# Join the data frames

combined_df = pd.concat([df[df.columns[1:]], df[df.columns[:1]]], axis=1)

# Extract unique users for 'user'

unique_users = combined_df['user'].unique()

user2item = sparse.csr_matrix(np.array([len(user) for user in unique_users]), shape=(len(unique_users), len(unique_users)))

# Count items for each user

item_counts = combined_df.groupby('user')['item'].nunique().values

# Compute the similarity matrix

if 'cosine' in df.columns:

cos_sim_matrix = sparse.csr_matrix((combined_df['cosine'].values, (combined_df.index, combined_df.index)), shape=(len(df), len(df)))

else:

cos_sim_matrix = np.zeros_like(combined_df)

# Assign similar users to item_counts

for user_id in unique_users:

item_counts[user_id] += 1

if 'cosine' in df.columns:

cos_sim_matrix = combined_df.loc[combined_df['user'] == user_id, 'cosine'].values / item_counts[user_id]

return cos_sim_matrix, item_counts

# Example usage:

data = {

'user': [1, 2, 3, 4, 5],

'item': [6, 7, 8, 9, 10],

'cosine': [0.01, 0.03, 0.05, 0.07, 0.1]

df = pd.DataFrame(data)

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```

```python

cos_sim_matrix, item_counts = compute_similarity_matrix(df, 1, 2)

```

```python

```

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