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

Independent component analysis (ICA) is a fundamental and important task in unsupervised learning, that was studied mainly in the domain of Hebbian learning. In this paper, we consider the estimation of the data model of ICA when Gaussian noise is present and the independent components are time dependent. 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, a new noisy complexity pursuit algorithm and a novel noisy algorithm are proposed to estimate the mixing matrix and the noise covariance matrix simultaneously when the noise covariance matrix is unknown. Next, the validity and performance of our algorithms are demonstrated by computer simulations