A Game-Incorporated Alternative Least Squares-Based Approach to Latent Factor Analysis

A latent factor analysis (LFA) model is highly efficient in a high-dimensional and sparse (HiDS) matrix from a big data-related application like a recommender system (RS). Alternating least squares (ALS) is a frequently-adopted learning algorithm when building an LFA model. However, the computational cost of an ALS model is cubic with the dimension of the latent factor (LF) space, which yields the dilemma that large LF leads to high computational cost while small LF dimension results in accuracy loss. From this point of view, this paper carefully investigates the connections between a dynamic game method and an ALS algorithm, and find that the ALS-based training process is actually playing game among LFs related to the same entity. From this point of view, this paper proposes a game-incorporated alternating least squares (GALS) algorithm for building an LFA model efficiently. Its main idea is two-fold, a) considering LFs corresponding to the same entity as players and their learning objectives as strategies, and b) making these players choose strategies to achieve highest gains based on a single LF-dependent ALS algorithm following the principle of Backward Induction widely accepted in dynamic game methods. Experimental results indicate that with a GALS algorithm, an LFA model is able to decrease its computational cost as well as maintain its prediction accuracy for missing data of an HiDS matrix.