Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner

TL;DR

This paper analyzes a generalized family of self-organizing maps, demonstrating that Winner Enhancing algorithms can achieve optimal information-theoretic mapping with minimal computational overhead.

Contribution

It introduces and analyzes Winner Relaxing and Winner Enhancing Kohonen algorithms, showing they can reach maximal mutual information mapping efficiently.

Findings

Winner Enhancing achieves a magnification exponent of one.

The algorithms require minimal extra computations.

Numerical verification confirms the analytical magnification law.

Abstract

The magnification behaviour of a generalized family of self-organizing feature maps, the Winner Relaxing and Winner Enhancing Kohonen algorithms is analyzed by the magnification law in the one-dimensional case, which can be obtained analytically. The Winner-Enhancing case allows to acheive a magnification exponent of one and therefore provides optimal mapping in the sense of information theory. A numerical verification of the magnification law is included, and the ordering behaviour is analyzed. Compared to the original Self-Organizing Map and some other approaches, the generalized Winner Enforcing Algorithm requires minimal extra computations per learning step and is conveniently easy to implement.