Non-negative multiple matrix factorization with Euclidean and kullback-leibler mixed divergences

Abstract

In this paper, we tackle the problem of extracting latent structure and patterns from multiple datasets that consist of users' rating scores and activity logs (click, view, visit, …) in order to understand the typical users' behavior. Our proposed method is based on non-negative matrix factorization, and factorizes multiple matrices simultaneously while adopting Euclidean distance and generalized KL divergence for the rating matrix and the activity matrix, respectively. We derive an optimization algorithm that offers a theoretical guarantee that it can find a locally optimal solution. Our experiments show that the proposed method outperformed existing methods when measured by mean squared error, which implies that it can extract latent structure and patterns more precisely. We also confirm that the segmentation result by the proposal helps to analyze users' behavior.