Robust Independent Component Analysis via Minimum Divergence Estimation

TL;DR

This paper introduces gamma-ICA, a robust independent component analysis method based on minimum U-divergence, which is less sensitive to outliers and contamination, with proven statistical properties and demonstrated superior robustness in experiments.

Contribution

The paper develops gamma-ICA within a minimum U-divergence framework, providing theoretical guarantees and a geometrical algorithm for robust ICA.

Findings

Gamma-ICA outperforms standard ICA in robustness against outliers.

Theoretical conditions for the consistency of gamma-ICA are established.

Experimental results show improved performance on simulated and image data.

Abstract

Independent component analysis (ICA) has been shown to be useful in many applications. However, most ICA methods are sensitive to data contamination and outliers. In this article we introduce a general minimum U-divergence framework for ICA, which covers some standard ICA methods as special cases. Within the U-family we further focus on the gamma-divergence due to its desirable property of super robustness, which gives the proposed method gamma-ICA. Statistical properties and technical conditions for the consistency of gamma-ICA are rigorously studied. In the limiting case, it leads to a necessary and sufficient condition for the consistency of MLE-ICA. This necessary and sufficient condition is weaker than the condition known in the literature. Since the parameter of interest in ICA is an orthogonal matrix, a geometrical algorithm based on gradient flows on special orthogonal group is introduced to implement gamma-ICA. Furthermore, a data-driven selection for the gamma value, which is critical to the achievement of gamma-ICA, is developed. The performance, especially the robustness, of gamma-ICA in comparison with standard ICA methods is demonstrated through experimental studies using simulated data and image data.