Interval-valued Matrix Factorization with Applications

In this paper, we propose the Interval-valued Matrix Factorization (IMF) framework. Matrix Factorization (MF) is a fundamental building block of data mining. MF techniques, such as Nonnegative Matrix Factorization (NMF) and Probabilistic Matrix Factorization (PMF), are widely used in applications of data mining. For example, NMF has shown its advantage in Face Analysis (FA) while PMF has been successfully applied to Collaborative Filtering (CF). In this paper, we analyze the data approximation in FA as well as CF applications and construct interval-valued matrices to capture these approximation phenomenons. We adapt basic NMF and PMF models to the interval-valued matrices and propose Interval-valued NMF (I-NMF) as well as Interval-valued PMF (I-PMF). We conduct extensive experiments to show that proposed I-NMF and I-PMF significantly outperform their single-valued counterparts in FA and CF applications.