Multilinear (Tensor) ICA and dimensionality reduction

Abstract

Multiple factors related to scene structure, illumination, and imaging contribute to image formation. Independent Components Analysis (ICA) maximizes the statistical independence of the representational components of a training image ensemble, but it cannot distinguish between these different factors, or modes. To address this problem, we introduce a nonlinear, multifactor model that generalizes ICA. Our Multilinear ICA model of image ensembles learns the statistically independent components of each of the multiple factors. We present an associated dimensionality reduction algorithm for multifactor subspace analysis. As an application, we consider the multilinear analysis of ensembles of facial images that combine several modes, including different facial geometries (people), expressions, head poses, and lighting conditions. For the purposes of face recognition, we introduce a multilinear projection algorithm that simultaneously projects an unknown test image into the multiple constituent mode spaces in order to infer its mode labels. We show that multilinear ICA computes a set of factor subspaces that yield improved recognition rates. © Springer-Verlag Berlin Heidelberg 2007.