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
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
Recommended Citation
Llorin, J. D. (1998). A mathematical analysis on the distribution-preserving property of Self-Organizing Map (SOM). Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/1860