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}
}
  • P. Pajunen
  • Published in ICANN 16 July 1996
  • Computer Science, Mathematics
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… 
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27 Citations
Highly Influential Citations
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Background Citations
5
Methods Citations
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27 Citations

On nonlinear independent component analysis using self-organizing map
  • Gang Wang, D. Hu
  • Computer Science
    Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788)
  • 2004
TLDR
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
  • L. Almeida
  • Computer Science
    Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373)
  • 2000
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
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
TLDR
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
  • L. Almeida
  • Engineering
    Nonlinear Source Separation
  • 2006
TLDR
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
TLDR
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.
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References

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Symplectic Nonlinear Component Analysis
TLDR
A novel feed-forward, information conserving, nonlinear map - the explicit symplectic transformations is proposed for this task, which solves the problem of non-Gaussian output distributions by considering single coordinate higher order statistics.
A class of neural networks for independent component analysis
TLDR
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.
Neural approaches to independent component analysis and source separation
TLDR
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.
Independent component analysis, A new concept?
  • P. Comon
  • Computer Science
    Signal Process.
  • 1994
Statistical Independence and Novelty Detection with Information Preserving Nonlinear Maps
TLDR
This work applies the criterion of minimal mutual information to the real world problem of electrical motor fault detection treated as a novelty detection task, and generalizes to nonlinear transformations by only demanding perfect transmission of information.
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TLDR
It is suggested that information maximization provides a unifying framework for problems in "blind" signal processing and dependencies of information transfer on time delays are derived.
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TLDR
A new on-line learning algorithm which minimizes a statistical dependency among outputs is derived for blind separation of mixed signals and has an equivariant property and is easily implemented on a neural network like model.
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TLDR
This book presents a detailed formulation of neural networks from the information-theoretic viewpoint, and shows how these methods may be applied to the topics of supervised and unsupervised learning, including feature extraction, linear and nonlinear independent component analysis, and Boltzmann machines.
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TLDR
This work presents an extension of the self-organizing feature map algorithm, which utilizes adaptive local learning step sizes to actually control the magnification properties of the map, and results on this new algorithm are complemented by numerical simulations.
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