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Weight-value convergence of the SOM algorithm for discrete input

¹Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287, USA.

Neural Computation

|June 6, 1998

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This study shows how self-organizing map (SOM) weights converge to a stable state for discrete inputs. The Robbins-Monro algorithm ensures this convergence for any input-output map dimension.

Area of Science:

Artificial Intelligence
Machine Learning
Computational Neuroscience

Background:

Self-Organizing Maps (SOMs) are unsupervised neural networks used for dimensionality reduction and data visualization.
Understanding the convergence properties of SOMs is crucial for their reliable application.
Previous research has explored SOM convergence, but specific conditions like discrete input require further investigation.

Purpose of the Study:

To provide insights into the convergence of Self-Organizing Map (SOM) weight values to a stationary state.
To analyze this convergence specifically for discrete input scenarios.
To demonstrate the applicability of the findings across various input-output map dimensions.

Main Methods:

The study applies the Robbins-Monro algorithm to analyze SOM weight convergence.

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Theoretical analysis is used to derive convergence guarantees.

The methodology is designed to be generalizable to multi-dimensional input-output spaces.

Main Results:

The research provides a formal result on the convergence of SOM weights to a stationary state.
This convergence is demonstrated to occur under discrete input conditions.
The derived convergence properties are shown to hold for input-output maps of arbitrary dimensions.

Conclusions:

The Robbins-Monro algorithm provides a robust framework for analyzing SOM convergence with discrete inputs.
The findings confirm the stability of SOMs under specific input conditions.
This work contributes to the theoretical understanding of SOMs, enhancing their practical utility in diverse applications.