Learning Modewise Independent Components from Tensor Data Using Multilinear Mixing Model

Independent component analysis (ICA) is a popular unsupervised learning method. This paper extends it to multilinear modewise ICA (MMICA) for tensors and explores two architectures in learning and recognition. MMICA models tensor data as mixtures generated from modewise source matrices that encode statistically independent information. Its sources have more compact representations than the sources in ICA. We embed ICA into the multilinear principal component analysis framework to solve for each source matrix alternatively with a few iterations. Then we obtain mixing tensors through regularized inverses of the source matrices. Simulations on synthetic data show that MMICA can estimate hidden sources accurately from structured tensor data. Moreover, in face recognition experiments, it outperforms competing solutions with both architectures.