Title

A mathematical analysis on the distribution-preserving property of Self-Organizing Map (SOM)

Date of Publication

1998

Document Type

Master's Thesis

Degree Name

Master of Science in Computer Science

Subject Categories

Computer Sciences

College

College of Computer Studies

Department/Unit

Computer Science

Thesis Adviser

Arnulfo P. Azcarraga

Defense Panel Chair

Elmer Dadios

Defense Panel Member

Maria Alvarez
Eduardo Razon

Abstract/Summary

Self-organizing maps (SOM) are among the more popular neural network models first studied by Teuvo Kohonen in the early 1980's. In this model, learning is unsupervised and the units organize themselves in a way that reflects the inter-relationships of the inputs they represent. Kohonen proposed an algorithm for th SOM using a highly simplified learning rule. This work reviews the original analysis done for the simple model. Several simulations on variants of the learning rule are conducted. From these simulations, a learning rule that approximates a Mexican Hat function is chosen. This is formally analyzed using the expectation values of the units in the map. Further simulations are conducted to validate the mathematical analysis done on the variant. The distribution-preserving property of 1-dimensional SOM's is carefully analyzed and illustrated using simulations. This analysis is extended to 2-dimentional SOM's.

Abstract Format

html

Language

English

Format

Print

Accession Number

TG02707

Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

82 leaves; 28 cm.

Keywords

Mathematical analysis; Neural networks (Computer science); Self-organizing systems; Memory maps (Computer science); Algorithms

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