# Nonlinear Independent Component Analysis by Self-Organizing Maps

@inproceedings{Pajunen1996NonlinearIC, title={Nonlinear Independent Component Analysis by Self-Organizing Maps}, author={Petteri Pajunen}, booktitle={ICANN}, year={1996} }

Linear Independent Component Analysis considers the problem of finding a linear transformation that makes the components of the output vector statistically independent. This can be applied to blind source separation, where the input data consist of unknown linear mixtures of unknown independent source signals. The original source signals can be recovered from their mixtures using the assumption that they are statistically independent. More generally we can consider nonlinear mappings that make…

## 27 Citations

On nonlinear independent component analysis using self-organizing map

- Computer ScienceFifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788)
- 2004

Experiments show that the rough nonlinear separation ability comes mostly from the decorrelation via whitening rather than from the SOM, and the process of NICA using SOM is in essence a second-order statistical method.

Linear and nonlinear ICA based on mutual information

- Computer ScienceProceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373)
- 2000

This paper presents a method for performing linear and nonlinear ICA based on MI, with few approximations, by a single network with a specialized structure, trained with a single objective function.

Independent Component Analysis

- Computer ScienceSpringer US
- 1998

ICA is a method for solving the blind source separation problem by finding a linear coordinate system (the unmixing system) such that the resulting signals are as statistically independent from each other as possible.

NONLINEAR INDEPENDENT COMPONENT ANALYSIS(ICA) USING POWER SERIES AND APPLICATION TO BLIND SOURCE SEPARATION

- Computer Science
- 2001

The derivation of an algorithm that generalizes Bell & Sejnowski’s classic ICA to tackle nonlinear ICA and the introduction of a new and efficient form of ”natural gradient” is presented.

Nonlinear Approaches ToIndependent Component

- Computer Science
- 1999

Two approaches are presented to tackle the nonlinear mixing case, and nonlinear ICA solutions are summarized for overcomplete representation as well as additive noise problems.

Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures

- MathematicsInt. J. Neural Syst.
- 2004

This paper reviews recent advances in blind source separation and independent component analysis for nonlinear mixing models and uses Bayesian inference methods for estimating the best statistical parameters under almost unconstrained models in which priors can be easily added.

Advances in Nonlinear Blind Source Separation

- Mathematics
- 2003

In this paper, we briefly review recent advances in blind source separation (BSS) for nonlinear mixing models. After a general introduction to the nonlinear BSS and ICA (indepen- dent Component…

Extensions of Linear Independent Component Analysis: Neural and Information-theoretic Methods I Wish to Thank Prof. Erkki Oja and Doc. Juha Karhunen for Supervision and Collaboration. I Am Also Grateful for Discussions and Useful Suggestions to the following People

- Computer Science
- 2007

Nonlinear transformations are considered and some existing unsupervised techniques are interpreted as implementing nonlinear ICA, and statistical independence as a measure of redundancy is extended using algorithmic information theory.

Nonlinear Source Separation

- EngineeringNonlinear Source Separation
- 2006

This publication reviews the main nonlinear separation methods, including the separation of post-nonlinear mixtures, and the MISEP, ensemble learning and kTDSEP methods for generic mixtures.

Bayesian Ensemble Learning for Nonlinear Factor Analysis

- Computer Science
- 2000

The development of a nonlinear extension of factor analysis based on Bayesian probability theory that solves many of the problems related to overfitting and makes it possible to use a significantly larger number of factors than with the previous algorithms.

## References

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This paper proposes neural structures related to multilayer feedforward networks for performing complete independent component analysis (ICA) and modify the previous nonlinear PCA type algorithms so that their separation capabilities are greatly improved.

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Various neural approaches have recently been proposed for blind source separation and ICA and the respective learning algorithms are reviewed, and some extensions of the basic ICA model are discussed.

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