Independent Component Analysis for Spatial Stochastic Processes on a Lattice

38/2014

Independent Component Analysis for Spatial Stochastic Processes on a Lattice

Monday 13th October 2014

Shen, H.; Truong, Y.; Zanini, P.

Independent Component Analysis (ICA) is a widespread data-driven methodology used to solve Blind Source Separation problems. A lot of algorithms have been proposed to perform ICA, but few of them take into account the dependence within the mixtures and not only the dependence between the mixtures. Some algorithms deal with the temporal ICA (tICA) approach exploiting the temporal autocorrelation of the mixtures (and the sources). In particular, colored ICA (cICA), that works in the spectral domain, is an effective method to perform ICA through a Whittle likelihood procedure assuming the sources to be temporal stochastic process. However spatial ICA (sICA) approach is becoming dominant in several field, like fMRI analysis or geo-referred imaging. In this paper we present an extension of cICA algorithm, called spatial colored ICA (scICA), where sources are assumed to be spatial stochastic processes on a lattice. We exploit the Whittle likelihood and a kernel based nonparametric algorithm to estimate the spectral density of a spatial process on a lattice. We illustrate the performance of the proposed method through different simulation studies and a real application using a geo-referred dataset about mobile-phone traffic on the urban area of Milan, Italy. Simulations and the real application showed the improvements provided by scICA method due to take into account the spatial autocorrelation of the mixtures and the sources.