**Aapo Hyvärinen
Helsinki University of
Technology
Laboratory of Computer and Information Science
P.O.Box 5400, FIN-02015 HUT, Finland **

A common problem encountered
in such disciplines as statistics, data analysis, signal processing,
and neural network
research, is finding a suitable representation of multivariate
data. For computational and conceptual simplicity, such a
representation is often sought as a linear transformation
of the original data.
Well-known linear transformation methods include, for example,
principal component analysis, factor analysis, and projection pursuit.
A recently developed linear transformation
method is independent component analysis (ICA), in which the
desired representation is the one that minimizes the statistical dependence of
the components of the representation.
Such a representation seems to capture the essential structure of the
data in many applications.
In this paper, we survey the existing theory and methods for ICA.

*Neural Computing Surveys, Vol. 2, pp. 94-128, 1999.*

Keywords: Independent component analysis, blind source separation, factor analysis, data analysis, higher-order statistics, neural networks, unsupervised learning, Hebbian learning

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See also the **What is ICA **page.

- Introduction
- Classical Linear Transformations
- Independent Component Analysis
- Objective (Contrast) Functions for ICA
- Algorithms for ICA
- Introduction
- Preprocessing of the data
- Jutten-Hérault algorithm
- Non-linear decorrelation algorithms
- Algorithms for maximum likelihood or infomax estimation
- Non-linear PCA algorithms
- Neural one-unit learning rules
- Other neural (adaptive) algorithms
- The FastICA algorithm
- Tensor-based algorithms
- Weighted covariance methods
- Choice of algorithm

- Noisy ICA
- Conclusions
- Definition of Cumulants
- Nomenclature:
- Bibliography
- About this document ...