Independent Component Analysis for Time-dependent Processes Using AR Source Model

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Independent component analysis is a fundamental and important task in unsupervised learning, that was studied mainly in the domain of Hebbian learning. In this paper, the temporal dependencies are explained by assuming that each source is an autoregressive (AR) process and innovations are independently and identically distributed (i.i.d). First, the likelihood of the model is derived, which takes into account both spatial and temporal information of the sources. Next, batch and on-line blind source separation algorithms are developed by maximizing likelihood function, and their local stability analysis are introduced simultaneously. Finally, computer simulations show that the algorithms achieve better separation of the mixed signals and mixed nature images which are difficult to be separated by the basic independent component analysis algorithms.

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