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Kernel-based topographic map formation achieved with an information-theoretic approach.

Marc M Van Hulle¹

¹KU Leuven, Laboratorium voor Neuro- en Psychofysiologie, Belgium. marc@neuro.kuleuven.ac.be

Neural Networks : the Official Journal of the International Neural Network Society

|November 6, 2002

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This study introduces a novel information-theoretic learning algorithm for kernel-based topographic maps. The new method optimizes joint entropy to effectively manage overlapping kernels and reduce output redundancy.

Area of Science:

Machine Learning
Information Theory
Computational Neuroscience

Background:

Topographic maps are essential for unsupervised learning and data representation.
Existing methods like Linsker's infomax principle face challenges with overlapping kernels.
Bell and Sejnowski's generalization offers a basis for improvement but requires adaptation.

Purpose of the Study:

To develop a new information-theoretic learning algorithm for kernel-based topographic map formation.
To address the limitations of existing infomax principles when dealing with free-moving, overlapping kernels of varying ranges.
To create a learning criterion that accounts for kernel overlap and minimizes output redundancy.

Main Methods:

Introduced a novel information-theoretic learning algorithm for kernel-based topographic maps.

Related Experiment Videos

Extended Linsker's infomax principle by incorporating mutual information minimization between kernel outputs.

Developed a learning criterion based on joint entropy maximization of kernel outputs.

Main Results:

The proposed algorithm effectively handles overlapping kernels with free movement and varying ranges.
Demonstrated successful topographic map formation on both synthetic and real-world datasets.
Achieved analytical verification for a synthetic example, confirming the algorithm's efficacy.

Conclusions:

The developed joint entropy maximization criterion is a viable learning approach for kernel-based topographic maps.
The algorithm offers a robust solution for topographic map formation in the presence of complex kernel interactions.
Validated performance on diverse datasets indicates broad applicability in unsupervised learning and data representation.