Binary Independent Component Analysis with OR Mixtures

TL;DR

This paper introduces binary ICA for OR mixtures, proving its identifiability, and proposes a deterministic algorithm for source separation, with validation through simulations and real-world applications.

Contribution

It extends ICA to binary OR mixtures, providing theoretical guarantees and a practical algorithm for source separation in binary data contexts.

Findings

bICA is uniquely identifiable under the disjunctive model

The proposed algorithm effectively recovers source distributions and mixing matrices

Simulation results confirm the algorithm's effectiveness in various scenarios

Abstract

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 realvalued numbers 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 concerning inferring the values of latent variables are also considered along with 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.