Matrix Factorization for Evolution Data

We study a matrix factorization problem, that is, to find two factor matrices and such that , where is a matrix composed of the values of the objects at consecutive time points . We first present MAFED, a constrained optimization model for this problem, which straightforwardly performs factorization on . Then based on the interplay of the data in , , and , a probabilistic graphical model using the same optimization objects is constructed, in which structural dependencies of the data in these matrices are revealed. Finally, we present a fitting algorithm to solve the proposed MAFED model, which produces the desired factorization. Empirical studies on real-world datasets demonstrate that our approach outperforms the state-of-the-art comparison algorithms.