Mátrixfactorizációtól

Mátrixfactorizációtól, often simply referred to as matrix factorization, is a technique used in linear algebra and machine learning to decompose a matrix into a product of two or more matrices. This decomposition can reveal underlying structures and latent features within the original data represented by the matrix. The goal is to find matrices whose product approximates the original matrix, often with a lower rank.

One of the most common applications of matrix factorization is in recommendation systems. In this context, a user-item interaction matrix is created, where rows represent users and columns represent items (e.g., movies, products). The entries in the matrix typically indicate a rating or preference. Matrix factorization aims to decompose this large, sparse matrix into two smaller matrices: a user-feature matrix and an item-feature matrix. These latent features represent abstract characteristics that users might like or items might possess. By learning these feature representations, it's possible to predict missing ratings for users and recommend items they are likely to enjoy.

Other applications include dimensionality reduction, where the factorization can project data into a lower-dimensional space while preserving important information. It is also used in natural language processing for tasks like topic modeling, where documents are represented as matrices and decomposed to discover underlying themes. The specific factorization method employed depends on the nature of the data and the desired outcome, with popular techniques including Singular Value Decomposition (SVD) and Non-negative Matrix Factorization (NMF).