Quantifying identifiability in independent component analysis

​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...

Mathematics in independent component analysis

to Michaela iv Preface If we knew what we were doing, it wouldn't be called research, would it? 1 Imagine you are a robot. Imagine you are a robot visiting a cocktail party — groups of people standing around chatting with each other. Imagine you are a robot trying to understand what those people talk about. You have no problems when facing one of those humans alone. You have built-in text-to-sp...

Introduction: Independent Component Analysis

Consider a situation in which we have a number of sources emitting signals which are interfering with one another. Familiar situations in which this occurs are a crowded room with many people speaking at the same time, interfering electromagnetic waves from mobile phones or crosstalk from brain waves originating from different areas of the brain. In each of these situations the mixed signals ar...

Nonparametric Independent Component Analysis

Independent Component Analysis

The famous example to illustrate ICA method is so-called cocktail party. Imagine two people are talking in a party and two different microphones are recording. Then the two records X1(t), X2(t) from those microphones are both the mixtures of the speech signal S1(t), S2(t) from the two speakers. Let us assume that only additive mixed effect exists, at this time, we can use the following equation...