Quantitative properties of Kohonen's self-organizing maps as adaptive vector quantizers

✍ Scribed by Toshiyuki Tanaka; Masao Saito

• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 724 KB
• Volume: 24
• Category: Article
• ISSN: 0882-1666
• DOI: 10.1002/scj.4690240508

✦ Synopsis

Abstract

Kohonen's model as the self‐organizing model for the neural network can be considered as a kind of adaptive vector quantization algorithm. Numerous reports have been presented on the application of the model to practical problems. Although some results have been presented for the theoretical properties of Kohonen's model, many properties remain to be clarified.

Among various properties of Kohonen's model as an adaptive vector quantization algorithm, this paper considers the problem of how the reference vectors are placed according to the probability distribution of the input signal. Considering the limit where the number of reference vectors is increased to infinity, this problem can be discussed theoretically as the distribution of the reference vectors.

Due to the effect of the “learning by neighborhood,” which is the feature of Kohonen's model, the property of the Kohonen model differs quantitatively from the property of the ordinary vector quantization algorithm. This paper discusses quantitatively the properties of Kohonen's model using the average learning equation.