Conditions for nonnegative independent component analysis

Author

Plumbley, Mark

Author_Institution

Dept. of Electron. Eng., Queen Mary Univ. of London, UK

Volume

9

Issue

6

fYear

2002

fDate

6/1/2002 12:00:00 AM

Firstpage

177

Lastpage

180

Abstract

We consider the noiseless linear independent component analysis problem, in the case where the hidden sources s are nonnegative. We assume that the random variables si are well grounded in that they have a nonvanishing probability density function (PDF) in the (positive) neighborhood of zero. For an orthonormal rotation y=Wx of prewhitened observations x=QAs, under certain reasonable conditions we show that y is a permutation of the s (apart from a scaling factor) if and only if y is nonnegative with probability 1. We suggest that this may enable the construction of practical learning algorithms, particularly for sparse nonnegative sources.

Keywords

learning systems; matrix decomposition; probability; random processes; signal processing; PDF; hidden sources; learning algorithms; noiseless linear independent component analysis; nonnegative independent component analysis; nonnegative matrix factorization; orthonormal rotation; permutation; prewhitened observations; probability; probability density function; random variables; scaling factor; sparse nonnegative sources; Covariance matrix; Eigenvalues and eigenfunctions; Independent component analysis; Matrix decomposition; Probability density function; Random variables; Sparse matrices;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2002.800502

Filename

1015161