Matrix Decomposition By Additive and Subtractive Factors

A non-negative matrix factorization (NMF) is effectively applied to analyze data in an unsupervised way. Though non-negative factors are endowed with favorable interpretability, such as part-based representation, NMF lacks flexibility, being only applicable to data composed of non-negative values. In this paper, we propose a novel approach to enhance both flexibility and interpretability of matrix factorization. While NMF approximates a matrix in an additive form of non-negative factors, the proposed method disentangles the matrix into additive and subtractive parts by exploiting non-negative factors with a center factor akin to the average of data. Thereby, the disentanglement flexibly deals with any real-valued data beyond non-negative ones while rendering clear functionality to the factors. In the experiments on several factorization tasks using real-world data, the proposed method provides effective factorization to embed well interpretability especially into factors for analyzing intrinsic characteristics of the data.