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Analysis of Multivariate and High-Dimensional Data by Inge Koch

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10

Independent Component Analysis

The truth is rarely pure and never simple (Oscar Wilde, The Importance of Being Ernest, 1854–1900).

10.1 Introduction

In the Factor Analysis model x = AF + μ + , an essential aim is to find an expression for the unknown d × k matrix of factor loadings A. Of secondary interest is the estimation of F. If x comes from a Gaussian distribution, then the principal component (PC) solution for A and F results in independent scores, but this luxury is lost in the PC solution of non-Gaussian random vectors and data. Surprisingly, it is not the search for a generalisation of Factor Analysis, but the departure from Gaussianity ...

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