A maximum likelihood approach to temporal factor analysis in state-space model

Paper [L. Xu, Temporal BYY learning for state space approach, hidden Markov model and blind source separation, IEEE Trans. Signal Process. 48 (7) (2000) 2132–2144] has presented a temporal factor analysis (TFA) algorithm in state-space model through minimizing an approximate Kullback-divergence cost function. In this paper, we further study the TFA within the maximum-likelihood (ML) framework. Without using any approximation technique, we build a connection between TFA and a traditional filtering problem in control theory, through which a new adaptive TFA algorithm is proposed. This algorithm utilizes the Kalman filter to optimally estimate the states and its covariance matrix, meanwhile using gradient-based method to tune the other model parameters. Furthermore, without taking the measurement noise into account, we further propose a variant of the algorithm and analyze its solution properties accordingly. The numerical simulations have shown promising results.