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首页用概率矩阵分解构建音乐推荐引擎（Pytorch）

用概率矩阵分解构建音乐推荐引擎（Pytorch）

Torch

概率矩阵分解

音乐推荐

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用概率矩阵分解构建音乐推荐引擎（Pytorch）,Building a Music Recommendation Engine with Probabilistic Matrix Factorization in PyTorch, by Cameron Wolfe.

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Building a Music Recommendation

Engine with Probabilistic Matrix

Factorization inPyTorch

Recommendation systems are one of the most widespread forms of

machine learning in modern society. Whether you are looking for

your next show to watch on Netflix or listening to an automated

music playlist on Spotify, recommender systems impact almost all

aspects of the modern user experience. One of the most common

ways to build a recommendation system is with matrix factorization,

which finds ways to predict a user’s rating for a specific product based

on previous ratings and other users’ preferences. In this article, I will

use a dataset of music ratings to build a recommendation engine for

music with PyTorch in an attempt to clarify the details behind the

theory and implementation of a probabilistic matrix factorization

model.

Introduction to Recommendation

Systems

Cameron Wolfe

Mar 22

15 min read

In this section, I will attempt to provide a quick, but comprehensive

introduction to recommendation systems and matrix factorization

before introducing the actual implementation and results for the

music recommendation project.

What is a Recommendation System?

To create a recommendation system, we need a dataset that includes

users, items, and ratings. Users can be customers buying products

from a store, a family streaming a movie from home, or, in our case,

even a person listening to music. Similarly, items are the products

that a user is buying, rating, listening to, etc. Therefore, the data set

for a recommendation system generally has many entries that include

a user-item pair and a value representing the user’s rating for that

item, such as the data set seen below:

User ratings can be collected either explicitly (asking user for a 5 star

ratings, asking whether a user likes a product, etc.) or implicitly

(examining purchase history, mouse movements, listening history,

etc.). Additionally, the values for ratings could be binary (a user

buying a product), discrete (rating a product 1–5 stars), or almost

anything else. In fact, the dataset used for this project represents

ratings as the total number of minutes a user has spent listening to an

Figure 1: Simple Data Set for Recommendation Systems

artist (this is an implicit rating!). Each of the entries in the data set

represents a user-item pairing with a known rating, and, from these

known user-item pairings, a recommendation system tries to predict

user-item ratings that are not yet known. Recommendations may be

created by finding items that are similar to those a user likes (item-

based), finding similar users and recommending the stuff they like

(user-based), or finding a relationship between user-item interactions

as a whole. In this way, the model recommends different items that it

believes the user might enjoy that the user has not yet seen.

It’s pretty easy to understand the purpose and value of a good

recommender system, but here is a nice figure that I believe

summarizes recommendation systems nicely:

What is Matrix Factorization?

Matrix factorization is a common and effective way to implement a

recommendation system. Using the previously-mentioned user-item

dataset (Figure 1), matrix factorization attempts to learn ways to

quantitatively characterize both users and items in a lower-

dimensional space (as opposed to looking at every item the user has

ever rated), such that these characterizations can be used to predict

user behavior and preferences for a known set of possible items. In

recent years, matrix factorization has become increasingly popular

due to its accuracy and scalability.

Figure 2: Recommender systems aim to

ﬁ

nd items that a user enjoys, but

has not yet seen[1]

Using the data set of user-item pairings, one can create a matrix such

that all rows represent different users, all columns represent different

items, and each entry at location (i, j) in the matrix represents user i’s

rating for item j. This matrix is illustrated in the following figure:

In the above figure, each row contains a single user’s ratings for every

item in the set of possible items. However, some of these ratings

might be empty (represented by “???”). These empty spots represent

user-item pairings that are not yet known, or that the

recommendation system is trying to predict. Moreover, this partially-

filled matrix, referred to as a sparse matrix, can be thought of as the

product of two matrices. For example, the above 4x4 matrix could be

created by multiplying two 4x4 matrices with each other, a 4x10

matrix with a 10x4 matrix, a 4x2 matrix with a 2x4 matrix, etc. This

process of decomposing the original matrix into a product of two

matrices is called matrix factorization.

Matrix Factorization for Recommendation

Systems

So, we know that we can decompose a matrix by finding two matrices

that can be multiplied together to form our original matrix. But, how

does matrix factorization actually work in a recommendation system?

Figure 3: A User‑Item Recommendation Matrix

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