Author: Zen and the Art of Computer Programming
1 Introduction
The recommender system (recommender system) is a computational model based on the behavior information given by users to past data, current interest preferences, etc., and personalizes users by analyzing the relationship between user behavior data and commodity features, product prices, and other data. personalized recommendation.
In the traditional content-based recommendation method, the user query (query) is mainly matched with the product features in the known database, and the recommendation results are sorted according to the relevance score; while in the method of collaborative filtering (collaborative filtering) , then analyze the interaction data between the user and the product, and make recommendations in combination with the historical interaction data of the recommendation engine.
However, these recommendation systems often have some defects, such as the inability to accurately describe the real feelings and preferences of users, and problems such as cold start, long tail effect, and sparse data. Therefore, with the vigorous development of the Internet industry, a variety of recommendation systems were born. The most popular of these is the matrix factorization method.
2. Explanation of basic concepts and terms
2.1 Matrix factorization
Matrix decomposition, also known as singular value decomposition (singular value decomposition), is a positive definite singular value decomposition. It can decompose an m n-dimensional data matrix A into several low-rank component matrices P Q and an m n matrix R, so that the matrix A can be approximately expressed as P Q R or Q^T R^T. When matrix A satisfies certain conditions, different decomposition methods can be selected by judging the type of matrix A. For example, some matrix A is easily decomposed into the product of two matrices, and some matrix A is difficult to be decomposed, which is not suitable for singular value decomposition etc.
In general, matrix A can be decomposed into three matrices: an m r-dimensional matrix P, an r n-dimensional matrix Q, and an r*n-dimensional matrix R, which satisfy the following relationship: A = P * Q *