Further studies on temporal factor analysis: comparison and Kalman filter-based algorithm

Abstract

A temporal extension of the classical factor analysis (FA) (Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, May 3, Berkeley, University of California, 1956, pp. 111–150.) has been made under the framework of temporal Bayesian Ying–Yang system (Proceedings of the International Conference on Neural Information Processing (ICONIP’98), Vol. 2, 1998, pp. 877–884; IEEE Trans. Signal Process. 48 (7) (2000) 2132 and Proceedings of the 1999 International Joint Conference on Neural Networks, Vol. 2, Washington, DC, July 1999, pp. 1071–1076). This temporal FA (TFA) not only extends the independent component analysis to Gaussian process, but also provides a new way for state-space identification without knowledge of the model parameters. In this paper, we implement the TFA algorithm provided in Xu (1998, 2000), and compare it with non-temporal one to show the importance of considering temporal relationship in factor analysis. Furthermore, we set up a connection between the TFA and traditional filtering problems in control theory, and present an alternative TFA algorithm. This new algorithm estimates the factors (also called states) and its variance by Kalman filter as an alternative to the gradient method used in that algorithm of Xu (1998, 2000), resulting in better performance in general.