Matrix Factorization for Evolution Data

We study a matrix factorization problem, that is, to find two factor matrices U and V such that R approximate to U-T x V, where R is a matrix composed of the values of the objects O-1, O-2, ... , O-n at consecutive time points T-1, T-2, ... , T-t. We first present MAFED, a constrained optimization model for this problem, which straightforwardly performs factorization on R. Then based on the interplay of the data in U,V, and R, 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