Independent Multiresolution Component Analysis and Matching Pursuit

Independent Multiresolution Component Analysis and Matching Pursuit

We show that decomposing a class of signals with overcomplete dictionaries of functions and combining multiresolution and independent component analysis allow for feature detection in complex non-stationary high frequency time series. Computational learning techniques are then designed through the Matching Pursuit algorithm, whose performance is monitored so to extract relevant information abou...

Centrum Voor Wiskunde En Informatica Independent Multiresolution Component Analysis and Matching Pursuit

Independent Component Analysis and Projection Pursuit: a Tutorial Introduction

Independent component analysis (ICA) and projection pursuit (PP) are two related techniques for separating mixtures of source signals into their individual components. These rapidly evolving techniques are currently nding applications in speech separation, ERP, EEG, fMRI, and low-level vision. Their power resides in the simple and realistic assumption that diierent physical processes tend to ge...

New Approximations of Diierential Entropy for Independent Component Analysis and Projection Pursuit New Approximations of Diierential Entropy for Independent Component Analysis and Projection Pursuit New Approximations of Diierential Entropy for Independent Component Analysis and Projection Pursuit

We derive a rst-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D diierential entropy is derived. The approximation...

​Rank based Least-squares Independent Component Analysis

  In this paper, we propose a nonparametric rank-based alternative to the least-squares independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of th...