Multidimensional Independent Component Analysis. (1998)
| Venue: | In Proc. Int. Workshop on Higher-Order Stat |
| Citations: | 146 - 8 self |
BibTeX
@INPROCEEDINGS{Cardoso98multidimensionalindependent,
author = {Jean-François Cardoso},
title = {Multidimensional Independent Component Analysis.},
booktitle = {In Proc. Int. Workshop on Higher-Order Stat},
year = {1998},
pages = {111--120}
}
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Abstract
This discussion paper proposes to generalize the notion of Independent Component Analysis (ICA) to the notion of Multidimensional Independent Component Analysis (MICA). We start from the ICA or blind source separation (BSS) model and show that it can be uniquely identified provided it is properly parameterized in terms of one-dimensional subspaces. From this standpoint, the BSS/ICA model is generalized to multidimensional components. We discuss how ICA standard algorithms can be adapted to MICA decomposition. The relevance of these ideas is illustrated by a MICA decomposition of ECG signals. 1. BLIND SOURCE SEPARATION We start by considering the blind source separation (BSS) problem in the simplest model: an n\Theta1 vector of observations x is modeled as x = As; with A = [a1 ; : : : ; an ] (1) where s is a n\Theta1 vector with statistically independent components and matrix A is an n \Theta n invertible matrix. The entries of s = [s1 ; : : : ; sn ] y are referred to as the `sourc...
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