DocumentCode :
2865482
Title :
Noisy independent component analysis, maximum likelihood estimation, and competitive learning
Author :
Hyvärinen, Aapo
Author_Institution :
Lab. of Comput. & Inf. Sci., Helsinki Univ. of Technol., Espoo, Finland
Volume :
3
fYear :
1998
fDate :
4-9 May 1998
Firstpage :
2282
Abstract :
We consider the estimation of the data model of independent component analysis when noise is present. We show that the joint maximum likelihood estimation of the independent components and the mixing matrix leads to an objective function already proposed by Olshausen and Field (1996) using a different derivation. Due to the complicated nature of the objective function, we introduce approximations that greatly simplify the optimization problem. We show that the presence of noise implies that the relation between the observed data and the estimates of the independent components is non-linear, and show how to approximate this nonlinearity. In particular, the non-linearity may be approximated by a simple shrinkage operation in the case of super-Gaussian (sparse) data. Using these approximations, we propose an efficient algorithm for approximate maximization of the likelihood. In the case of super-Gaussian components, this may be approximated by simple competitive learning, and in the case of sub-Gaussian components, by anti-competitive learning
Keywords :
matrix algebra; maximum likelihood estimation; statistical analysis; unsupervised learning; anti-competitive learning; competitive learning; maximum likelihood estimation; mixing matrix; noisy independent component analysis; objective function; shrinkage operation; sparse data; sub-Gaussian components; super-Gaussian data; Blind source separation; Data models; Independent component analysis; Information science; Laboratories; Linear approximation; Linearity; Maximum likelihood estimation; Random variables; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Neural Networks Proceedings, 1998. IEEE World Congress on Computational Intelligence. The 1998 IEEE International Joint Conference on
Conference_Location :
Anchorage, AK
ISSN :
1098-7576
Print_ISBN :
0-7803-4859-1
Type :
conf
DOI :
10.1109/IJCNN.1998.687217
Filename :
687217
Link To Document :
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