Timezone: »

 
Poster
Fast Algorithms for Gaussian Noise Invariant Independent Component Analysis
James R Voss · Luis Rademacher · Mikhail Belkin

Sat Dec 07 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor
in Poster Session »

The performance of standard algorithms for Independent Component Analysis quickly deteriorates under the addition of Gaussian noise. This is partially due to a common first step that typically consists of whitening, i.e., applying Principal Component Analysis (PCA) and rescaling the components to have identity covariance, which is not invariant under Gaussian noise. In our paper we develop the first practical algorithm for Independent Component Analysis that is provably invariant under Gaussian noise. The two main contributions of this work are as follows: 1. We develop and implement a more efficient version of a Gaussian noise invariant decorrelation (quasi-orthogonalization) algorithm using Hessians of the cumulant functions. 2. We propose a very simple and efficient fixed-point GI-ICA (Gradient Iteration ICA) algorithm, which is compatible with quasi-orthogonalization, as well as with the usual PCA-based whitening in the noiseless case. The algorithm is based on a special form of gradient iteration (different from gradient descent). We provide an analysis of our algorithm demonstrating fast convergence following from the basic properties of cumulants. We also present a number of experimental comparisons with the existing methods, showing superior results on noisy data and very competitive performance in the noiseless case.

[ PDF] 

Author Information

James R Voss
Luis Rademacher (The Ohio State University)
Mikhail Belkin (Ohio State University)

More from the Same Authors