ICA: A Critical Review of Three Prominent Approaches

Table of Contents

ICA: A Critical Review of Three Prominent Approaches

Outline

The Blind Source Separation Problem

Measures of Independence

We Will Investigate Three Approaches

Pierre Comon: Setup - Minimizing MI

Comon: Approximating the MI

Comon: Simplifying the Contrast

Comon: Differentiating the Contrast

Comon: Comments

Amari: Setup

Amari: Approximating the MI

Amari: Natural Gradient

Amari: Empirical Results

Amari: Comments

Bell and Sejnowski: Infomax Framework

B & S: the Entropy is the Contrast

B & S: Taking the Gradient

B & S: What does it really mean?

B & S: Cardoso’s take

B & S: Cardoso’s Implications

B & S: Comments

Comparison of the Approaches

Extensions: Empirical Studies

Ext’s: Correlated Components Analysis

Cond. Indep. Comp. Analysis (CICA)

Cond. Indep. Comp. Anl. (continued)

ICA-based clustering

Phase-Aligned ICA

Conclusions

Email: sbasu@media.mit.edu

Home Page: http://www.media.mit.edu/~sbasu