Matrix factorization for evolution data (Q1718602)

Summary: We study a matrix factorization problem, that is, to find two factor matrices \(U\) and \(V\) such that \(R \approx U^T \times V\), where \(R\) is a matrix composed of the values of the objects \(O_1, O_2, \ldots, O_n\) at consecutive time points \(T_1, T_2, \ldots, T_t\). 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.