Robust independent component analysis via minimum γ-Divergence Estimation
Journal
IEEE Journal on Selected Topics in Signal Processing
Journal Volume
7
Journal Issue
4
Pages
614-624
Date Issued
2013
Author(s)
Abstract
Independent component analysis (ICA) has been shown to be useful in many applications. However, most ICA methods are sensitive to data contamination. In this article we introduce a general minimum mbi U-divergence framework for ICA, which covers some standard ICA methods as special cases. Within the mbi U-family we further focus on the mmbγ-divergence due to its desirable property of super robustness for outliers, which gives the proposed method mmbγ-ICA. Statistical properties and technical conditions for recovery consistency of mmbγ-ICA are studied. In the limiting case, it improves the recovery condition of MLE-ICA known in the literature by giving necessary and sufficient condition. Since the parameter of interest in mmbγ-ICA is an orthogonal matrix, a geometrical algorithm based on gradient flows on special orthogonal group is introduced. Furthermore, a data-driven selection for the mmbγ value, which is critical to the achievement of mmbγ-ICA, is developed. The performance, especially the robustness, of mmbγ-ICA is demonstrated through experimental studies using simulated data and image data. © 2007-2012 IEEE.
Type
journal article