Binary Independent Component Analysis with or Mixtures

Independent component analysis (ICA) is a computational method for separating a multivariate signal into subcomponents assuming the mutual statistical independence of the non-Gaussian source signals. The classical independent components analysis (ICA) framework usually assumes linear combinations of independent sources over the field of real-valued numbers ${\cal R}$. In this paper, we investigate binary ICA for or mixtures (bICA), which can find applications in many domains including medical diagnosis, multi-cluster assignment, Internet tomography and network resource management. We prove that bICA is uniquely identifiable under the disjunctive generation model, and propose a deterministic iterative algorithm to determine the distribution of the latent random variables and the mixing matrix. The inverse problem to infer the values of latent variables is also considered for noisy measurements. We conduct an extensive simulation study to verify the effectiveness of the propose algorithm and present examples of real-world applications where bICA can be applied.