On Evaluation of Reference Vector Density for Self-Organizing Feature Map

Toshiyuki TANAKA

On Evaluation of Reference Vector Density for Self-Organizing Feature Map

Toshiyuki TANAKA

Full Text Views

0

Cite this

Summary :

In this paper, I investigate a property of self-organizing feature map (SOFM) in terms of reference vector density q(x) when probability density function of input signal fed into SOFM is p(x). Difficulty of general analysis on this property is briefly discussed. Then, I employ an assumption (conformal map assumption) to evaluate this property, and it is shown that for equilibrium state, q(x)p(x)^s holds. By giving Lyapunov functioin for time evolution of reference vector density q(x) in SOFM, the equilibrium state is proved to be stable in terms of distribution. Comparison of the result with one which is based on different assumption reveals that there is no unique result of a simple form, such as conjectured by Kohonen. However, as there are cases in which these assumptions hold, these results suggest that we can consider a range of the property of SOFM. On the basis of it, we make comparison on this property between SOFM and fundamental adaptive vector quantization algorithm, in terms of the exponent s of the relation q(x)p(x)^s. Difference on this property between SOFM and fundamental adaptive vector quantization algorithm, and propriety of mean squared quantization error for a performance measure of SOFM, are discussed.

Publication: IEICE TRANSACTIONS on Information Vol.E77-D No.4 pp.402-408

Publication Date: 1994/04/25

Publicized

Online ISSN

DOI

Type of Manuscript: Special Section PAPER (Special Issue on Neurocomputing)

Category: Mapping

Cite this

Copy

Toshiyuki TANAKA, "On Evaluation of Reference Vector Density for Self-Organizing Feature Map" in IEICE TRANSACTIONS on Information, vol. E77-D, no. 4, pp. 402-408, April 1994, doi: .
Abstract: In this paper, I investigate a property of self-organizing feature map (SOFM) in terms of reference vector density q(x) when probability density function of input signal fed into SOFM is p(x). Difficulty of general analysis on this property is briefly discussed. Then, I employ an assumption (conformal map assumption) to evaluate this property, and it is shown that for equilibrium state, q(x)p(x)^s holds. By giving Lyapunov functioin for time evolution of reference vector density q(x) in SOFM, the equilibrium state is proved to be stable in terms of distribution. Comparison of the result with one which is based on different assumption reveals that there is no unique result of a simple form, such as conjectured by Kohonen. However, as there are cases in which these assumptions hold, these results suggest that we can consider a range of the property of SOFM. On the basis of it, we make comparison on this property between SOFM and fundamental adaptive vector quantization algorithm, in terms of the exponent s of the relation q(x)p(x)^s. Difference on this property between SOFM and fundamental adaptive vector quantization algorithm, and propriety of mean squared quantization error for a performance measure of SOFM, are discussed.
URL: https://global.ieice.org/en_transactions/information/10.1587/e77-d_4_402/_p

Copy

@ARTICLE{e77-d_4_402,
author={Toshiyuki TANAKA, },
journal={IEICE TRANSACTIONS on Information},
title={On Evaluation of Reference Vector Density for Self-Organizing Feature Map},
year={1994},
volume={E77-D},
number={4},
pages={402-408},
abstract={In this paper, I investigate a property of self-organizing feature map (SOFM) in terms of reference vector density q(x) when probability density function of input signal fed into SOFM is p(x). Difficulty of general analysis on this property is briefly discussed. Then, I employ an assumption (conformal map assumption) to evaluate this property, and it is shown that for equilibrium state, q(x)p(x)^s holds. By giving Lyapunov functioin for time evolution of reference vector density q(x) in SOFM, the equilibrium state is proved to be stable in terms of distribution. Comparison of the result with one which is based on different assumption reveals that there is no unique result of a simple form, such as conjectured by Kohonen. However, as there are cases in which these assumptions hold, these results suggest that we can consider a range of the property of SOFM. On the basis of it, we make comparison on this property between SOFM and fundamental adaptive vector quantization algorithm, in terms of the exponent s of the relation q(x)p(x)^s. Difference on this property between SOFM and fundamental adaptive vector quantization algorithm, and propriety of mean squared quantization error for a performance measure of SOFM, are discussed.},
keywords={},
doi={},
ISSN={},
month={April},}

Copy

TY - JOUR
TI - On Evaluation of Reference Vector Density for Self-Organizing Feature Map
T2 - IEICE TRANSACTIONS on Information
SP - 402
EP - 408
AU - Toshiyuki TANAKA
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E77-D
IS - 4
JA - IEICE TRANSACTIONS on Information
Y1 - April 1994
AB - In this paper, I investigate a property of self-organizing feature map (SOFM) in terms of reference vector density q(x) when probability density function of input signal fed into SOFM is p(x). Difficulty of general analysis on this property is briefly discussed. Then, I employ an assumption (conformal map assumption) to evaluate this property, and it is shown that for equilibrium state, q(x)p(x)^s holds. By giving Lyapunov functioin for time evolution of reference vector density q(x) in SOFM, the equilibrium state is proved to be stable in terms of distribution. Comparison of the result with one which is based on different assumption reveals that there is no unique result of a simple form, such as conjectured by Kohonen. However, as there are cases in which these assumptions hold, these results suggest that we can consider a range of the property of SOFM. On the basis of it, we make comparison on this property between SOFM and fundamental adaptive vector quantization algorithm, in terms of the exponent s of the relation q(x)p(x)^s. Difference on this property between SOFM and fundamental adaptive vector quantization algorithm, and propriety of mean squared quantization error for a performance measure of SOFM, are discussed.
ER -