如何对sub_matrix 绘图

对于一个列向量sub_matrix，我们可以使用plot函数来绘制它的图形。具体来说，可以用plot函数的第一个参数传递sub_matrix的x轴坐标，第二个参数传递sub_matrix的y轴坐标。由于sub_matrix是一个列向量，因此可以使用1:n作为x轴坐标，其中n为sub_matrix的长度。下面是一个示例代码：

n = length(sub_matrix);  % 获取sub_matrix的长度
x = 1:n;  % 生成1到n的向量作为x轴坐标
plot(x, sub_matrix);  % 绘制图形
xlabel('Time');  % 添加x轴标签
ylabel('Value');  % 添加y轴标签
title('Sub Matrix Plot');  % 添加标题

在这个示例中，我们首先获取sub_matrix的长度n，然后使用1:n生成一个x轴坐标向量x。接下来，使用plot函数将x和sub_matrix作为参数绘制出图形。最后，使用xlabel、ylabel和title函数分别添加x轴、y轴和标题标签。

你可以根据自己的需要修改x轴坐标、添加网格线、修改线条颜色等等。

相关问题

import pandas as pd import numpy as np # 计算用户对歌曲的播放比例 triplet_dataset_sub_song_merged_sum_df = triplet_dataset_sub_song_mergedpd[['user', 'listen_count']].groupby('user').sum().reset_index() triplet_dataset_sub_song_merged_sum_df.rename(columns={'listen_count': 'total_listen_count'}, inplace=True) triplet_dataset_sub_song_merged = pd.merge(triplet_dataset_sub_song_mergedpd, triplet_dataset_sub_song_merged_sum_df) triplet_dataset_sub_song_mergedpd['fractional_play_count'] = triplet_dataset_sub_song_mergedpd['listen_count'] / triplet_dataset_sub_song_merged['total_listen_count'] # 将用户和歌曲编码为数字 small_set = triplet_dataset_sub_song_mergedpd user_codes = small_set.user.drop_duplicates().reset_index() song_codes = small_set.song.drop_duplicates().reset_index() user_codes.rename(columns={'index': 'user_index'}, inplace=True) song_codes.rename(columns={'index': 'song_index'}, inplace=True) song_codes['so_index_value'] = list(song_codes.index) user_codes['us_index_value'] = list(user_codes.index) small_set = pd.merge(small_set, song_codes, how='left') small_set = pd.merge(small_set, user_codes, how='left') # 将数据转换为稀疏矩阵形式 from scipy.sparse import coo_matrix mat_candidate = small_set[['us_index_value', 'so_index_value', 'fractional_play_count']] data_array = mat_candidate.fractional_play_count.values row_array = mat_candidate.us_index_value.values col_array = mat_candidate.so_index_value.values data_sparse = coo_matrix((data_array, (row_array, col_array)), dtype=float) # 使用SVD方法进行矩阵分解并进行推荐 from scipy.sparse import csc_matrix from scipy.sparse.linalg import svds import math as mt def compute_svd(urm, K): U, s, Vt = svds(urm, K) dim = (len(s), len(s)) S = np.zeros(dim, dtype=np.float32) for i in range(0, len(s)): S[i, i] = mt.sqrt(s[i]) U = csc_matrix(U, dtype=np.float32) S = csc_matrix(S, dtype=np.float32) Vt = csc_matrix(Vt, dtype=np.float32) return U, S, Vt def compute_estimated_matrix(urm, U, S, Vt, uTest, K, test): rightTerm = S * Vt max_recommendation = 250 estimatedRatings = np.zeros(shape=(MAX_UID, MAX_PID), dtype=np.float16) recomendRatings = np.zeros(shape=(MAX_UID, max_recommendation), dtype=np.float16) for userTest in uTest: prod = U[userTest, :] * rightTerm estimatedRatings[userTest, :] = prod.todense() recomendRatings[userTest, :] = (-estimatedRatings[userTest, :]).argsort()[:max_recommendation] return recomendRatings K = 50 urm = data_sparse MAX_PID = urm.shape[1] MAX_UID = urm.shape[0] U, S, Vt = compute_svd(urm, K) uTest = [4, 5, 6, 7, 8, 73, 23] # uTest=[1b5bb32767963cbc215d27a24fef1aa01e933025] uTest_recommended_items = compute_estimated_matrix(urm, U, S, Vt 继续将这段代码输出完整

, 并进行解释：

import pandas as pd
import numpy as np

# 计算用户对歌曲的播放比例
triplet_dataset_sub_song_merged_sum_df = triplet_dataset_sub_song_merged[['user', 'listen_count']].groupby('user').sum().reset_index()
triplet_dataset_sub_song_merged_sum_df.rename(columns={'listen_count': 'total_listen_count'}, inplace=True)
triplet_dataset_sub_song_merged = pd.merge(triplet_dataset_sub_song_merged, triplet_dataset_sub_song_merged_sum_df)
triplet_dataset_sub_song_merged['fractional_play_count'] = triplet_dataset_sub_song_merged['listen_count'] / triplet_dataset_sub_song_merged['total_listen_count']

# 将用户和歌曲编码为数字
small_set = triplet_dataset_sub_song_merged
user_codes = small_set.user.drop_duplicates().reset_index()
song_codes = small_set.song.drop_duplicates().reset_index()
user_codes.rename(columns={'index': 'user_index'}, inplace=True)
song_codes.rename(columns={'index': 'song_index'}, inplace=True)
song_codes['so_index_value'] = list(song_codes.index)
user_codes['us_index_value'] = list(user_codes.index)
small_set = pd.merge(small_set, song_codes, how='left')
small_set = pd.merge(small_set, user_codes, how='left')

# 将数据转换为稀疏矩阵形式
from scipy.sparse import coo_matrix
mat_candidate = small_set[['us_index_value', 'so_index_value', 'fractional_play_count']]
data_array = mat_candidate.fractional_play_count.values
row_array = mat_candidate.us_index_value.values
col_array = mat_candidate.so_index_value.values
data_sparse = coo_matrix((data_array, (row_array, col_array)), dtype=float)

# 使用SVD方法进行矩阵分解并进行推荐
from scipy.sparse import csc_matrix
from scipy.sparse.linalg import svds
import math as mt

def compute_svd(urm, K):
    U, s, Vt = svds(urm, K)
    dim = (len(s), len(s))
    S = np.zeros(dim, dtype=np.float32)
    for i in range(0, len(s)):
        S[i, i] = mt.sqrt(s[i])
    U = csc_matrix(U, dtype=np.float32)
    S = csc_matrix(S, dtype=np.float32)
    Vt = csc_matrix(Vt, dtype=np.float32)
    return U, S, Vt

def compute_estimated_matrix(urm, U, S, Vt, uTest, K, test):
    rightTerm = S * Vt
    max_recommendation = 250
    estimatedRatings = np.zeros(shape=(MAX_UID, MAX_PID), dtype=np.float16)
    recomendRatings = np.zeros(shape=(MAX_UID, max_recommendation), dtype=np.float16)
    for userTest in uTest:
        prod = U[userTest, :] * rightTerm
        estimatedRatings[userTest, :] = prod.todense()
        recomendRatings[userTest, :] = (-estimatedRatings[userTest, :]).argsort()[:max_recommendation]
    return recomendRatings

K = 50
urm = data_sparse
MAX_PID = urm.shape[1]
MAX_UID = urm.shape[0]
U, S, Vt = compute_svd(urm, K)
uTest = [4, 5, 6, 7, 8, 73, 23] # uTest=[1b5bb32767963cbc215d27a24fef1aa01e933025]
uTest_recommended_items = compute_estimated_matrix(urm, U, S, Vt, uTest, K, test)

这段代码实现了一个基于SVD方法的推荐系统，具体步骤如下：

1. 读入数据，计算每个用户对每首歌曲的播放比例。

2. 将用户和歌曲编码为数字，转换为稀疏矩阵形式。

3. 使用SVD方法进行矩阵分解，得到用户和歌曲的隐向量。

4. 对于给定的测试用户，使用隐向量和分解后的矩阵计算出该用户对每首歌曲的预测评分。

5. 根据预测评分，为该用户推荐最高的250首歌曲。

其中，SVD方法是一种矩阵分解的方法，可以将一个大矩阵分解为多个小矩阵，这些小矩阵可以表示出原始矩阵中的潜在特征（即隐向量）。通过计算用户和歌曲的隐向量，可以获得它们之间的相似度，从而进行推荐。

将上述代码放入了Recommenders.py文件中，作为一个自定义工具包。将下列代码中调用scipy包中svd的部分。转为使用Recommenders.py工具包中封装的svd方法。给出修改后的完整代码。import pandas as pd import math as mt import numpy as np from sklearn.model_selection import train_test_split from Recommenders import * from scipy.sparse.linalg import svds from scipy.sparse import coo_matrix from scipy.sparse import csc_matrix # Load and preprocess data triplet_dataset_sub_song_merged = triplet_dataset_sub_song_mergedpd # load dataset triplet_dataset_sub_song_merged_sum_df = triplet_dataset_sub_song_merged[['user','listen_count']].groupby('user').sum().reset_index() triplet_dataset_sub_song_merged_sum_df.rename(columns={'listen_count':'total_listen_count'},inplace=True) triplet_dataset_sub_song_merged = pd.merge(triplet_dataset_sub_song_merged,triplet_dataset_sub_song_merged_sum_df) triplet_dataset_sub_song_merged['fractional_play_count'] = triplet_dataset_sub_song_merged['listen_count']/triplet_dataset_sub_song_merged['total_listen_count'] # Convert data to sparse matrix format small_set = triplet_dataset_sub_song_merged user_codes = small_set.user.drop_duplicates().reset_index() song_codes = small_set.song.drop_duplicates().reset_index() user_codes.rename(columns={'index':'user_index'}, inplace=True) song_codes.rename(columns={'index':'song_index'}, inplace=True) song_codes['so_index_value'] = list(song_codes.index) user_codes['us_index_value'] = list(user_codes.index) small_set = pd.merge(small_set,song_codes,how='left') small_set = pd.merge(small_set,user_codes,how='left') mat_candidate = small_set[['us_index_value','so_index_value','fractional_play_count']] data_array = mat_candidate.fractional_play_count.values row_array = mat_candidate.us_index_value.values col_array = mat_candidate.so_index_value.values data_sparse = coo_matrix((data_array, (row_array, col_array)),dtype=float) # Compute SVD def compute_svd(urm, K): U, s, Vt = svds(urm, K) dim = (len(s), len(s)) S = np.zeros(dim, dtype=np.float32) for i in range(0, len(s)): S[i,i] = mt.sqrt(s[i]) U = csc_matrix(U, dtype=np.float32) S = csc_matrix(S, dtype=np.float32) Vt = csc_matrix(Vt, dtype=np.float32) return U, S, Vt def compute_estimated_matrix(urm, U, S, Vt, uTest, K, test): rightTerm = S*Vt max_recommendation = 10 estimatedRatings = np.zeros(shape=(MAX_UID, MAX_PID), dtype=np.float16) recomendRatings = np.zeros(shape=(MAX_UID,max_recommendation ), dtype=np.float16) for userTest in uTest: prod = U[userTest, :]*rightTerm estimatedRatings[userTest, :] = prod.todense() recomendRatings[userTest, :] = (-estimatedRatings[userTest, :]).argsort()[:max_recommendation] return recomendRatings K=50 # number of factors urm = data_sparse MAX_PID = urm.shape[1] MAX_UID = urm.shape[0] U, S, Vt = compute_svd(urm, K) # Compute recommendations for test users # Compute recommendations for test users uTest = [1,6,7,8,23] uTest_recommended_items = compute_estimated_matrix(urm, U, S, Vt, uTest, K, True) # Output recommended songs in a dataframe recommendations = pd.DataFrame(columns=['user','song', 'score','rank']) for user in uTest: rank = 1 for song_index in uTest_recommended_items[user, 0:10]: song = small_set.loc[small_set['so_index_value'] == song_index].iloc[0] # Get song details recommendations = recommendations.append({'user': user, 'song': song['title'], 'score': song['fractional_play_count'], 'rank': rank}, ignore_index=True) rank += 1 display(recommendations)

import pandas as pd
import math as mt
import numpy as np
from sklearn.model_selection import train_test_split
from Recommenders import SVDRecommender #import the SVDRecommender class from our custom package

# Load and preprocess data
triplet_dataset_sub_song_merged = triplet_dataset_sub_song_mergedpd

# load dataset
triplet_dataset_sub_song_merged_sum_df = triplet_dataset_sub_song_merged[['user','listen_count']].groupby('user').sum().reset_index()
triplet_dataset_sub_song_merged_sum_df.rename(columns={'listen_count':'total_listen_count'},inplace=True)
triplet_dataset_sub_song_merged = pd.merge(triplet_dataset_sub_song_merged,triplet_dataset_sub_song_merged_sum_df)
triplet_dataset_sub_song_merged['fractional_play_count'] = triplet_dataset_sub_song_merged['listen_count']/triplet_dataset_sub_song_merged['total_listen_count']

# Convert data to sparse matrix format
small_set = triplet_dataset_sub_song_merged
user_codes = small_set.user.drop_duplicates().reset_index()
song_codes = small_set.song.drop_duplicates().reset_index()
user_codes.rename(columns={'index':'user_index'}, inplace=True)
song_codes.rename(columns={'index':'song_index'}, inplace=True)
song_codes['so_index_value'] = list(song_codes.index)
user_codes['us_index_value'] = list(user_codes.index)
small_set = pd.merge(small_set,song_codes,how='left')
small_set = pd.merge(small_set,user_codes,how='left')
mat_candidate = small_set[['us_index_value','so_index_value','fractional_play_count']]
data_array = mat_candidate.fractional_play_count.values
row_array = mat_candidate.us_index_value.values
col_array = mat_candidate.so_index_value.values
data_sparse = coo_matrix((data_array, (row_array, col_array)),dtype=float)

# Compute SVD using our custom package
K=50 # number of factors
urm = data_sparse
MAX_PID = urm.shape[1]
MAX_UID = urm.shape[0]
recommender = SVDRecommender(K)
U, S, Vt = recommender.fit(urm)

# Compute recommendations for test users
uTest = [1,6,7,8,23]
uTest_recommended_items = recommender.recommend(uTest, urm, 10)

# Output recommended songs in a dataframe
recommendations = pd.DataFrame(columns=['user','song', 'score','rank'])
for user in uTest:
rank = 1
for song_index in uTest_recommended_items[user, 0:10]:
song = small_set.loc[small_set['so_index_value'] == song_index].iloc[0] # Get song details
recommendations = recommendations.append({'user': user, 'song': song['title'], 'score': song['fractional_play_count'], 'rank': rank}, ignore_index=True)
rank += 1
display(recommendations)