Connection between self-organizing maps and metric multidimensional scaling

Hujun Yin

doi:10.1109/IJCNN.2007.4371099

Connection between self-organizing maps and metric multidimensional scaling

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The self-organizing map (SOM) and some of its variants such as visualization induced SOM (ViSOM) have been seen to yield similar results to multidimensional scaling (MDS). However the exact connection has yet been established, though similar topographic mapping results have been shown in several studies. In this paper we provide a review on the SOM and its cost function and topological measures. Then we examine its relationship with MDS from their cost functions in the aspect of data visualization. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The connection between MDS and principal manifolds is also discussed. ©2007 IEEE.

Original language	English
Title of host publication	IEEE International Conference on Neural Networks - Conference Proceedings\|IEEE Int. Conf. Neural. Netw. Conf. Proc.
Place of Publication	USA
Publisher	IEEE
Pages	1025-1030
Number of pages	5
ISBN (Print)	142441380X, 9781424413805
DOIs	https://doi.org/10.1109/IJCNN.2007.4371099
Publication status	Published - 2007
Event	2007 International Joint Conference on Neural Networks, IJCNN 2007 - Orlando, FL Duration: 1 Jul 2007 → …

Conference

Conference	2007 International Joint Conference on Neural Networks, IJCNN 2007
City	Orlando, FL
Period	1/07/07 → …

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10.1109/IJCNN.2007.4371099

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title = "Connection between self-organizing maps and metric multidimensional scaling",

abstract = "The self-organizing map (SOM) and some of its variants such as visualization induced SOM (ViSOM) have been seen to yield similar results to multidimensional scaling (MDS). However the exact connection has yet been established, though similar topographic mapping results have been shown in several studies. In this paper we provide a review on the SOM and its cost function and topological measures. Then we examine its relationship with MDS from their cost functions in the aspect of data visualization. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The connection between MDS and principal manifolds is also discussed. {\textcopyright}2007 IEEE.",

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language = "English",

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booktitle = "IEEE International Conference on Neural Networks - Conference Proceedings|IEEE Int. Conf. Neural. Netw. Conf. Proc.",

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AU - Yin, Hujun

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Y1 - 2007

N2 - The self-organizing map (SOM) and some of its variants such as visualization induced SOM (ViSOM) have been seen to yield similar results to multidimensional scaling (MDS). However the exact connection has yet been established, though similar topographic mapping results have been shown in several studies. In this paper we provide a review on the SOM and its cost function and topological measures. Then we examine its relationship with MDS from their cost functions in the aspect of data visualization. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The connection between MDS and principal manifolds is also discussed. ©2007 IEEE.

AB - The self-organizing map (SOM) and some of its variants such as visualization induced SOM (ViSOM) have been seen to yield similar results to multidimensional scaling (MDS). However the exact connection has yet been established, though similar topographic mapping results have been shown in several studies. In this paper we provide a review on the SOM and its cost function and topological measures. Then we examine its relationship with MDS from their cost functions in the aspect of data visualization. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The connection between MDS and principal manifolds is also discussed. ©2007 IEEE.

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DO - 10.1109/IJCNN.2007.4371099

M3 - Conference contribution

SN - 142441380X

SN - 9781424413805

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EP - 1030

BT - IEEE International Conference on Neural Networks - Conference Proceedings|IEEE Int. Conf. Neural. Netw. Conf. Proc.

PB - IEEE

CY - USA

T2 - 2007 International Joint Conference on Neural Networks, IJCNN 2007

Y2 - 1 July 2007

ER -

Connection between self-organizing maps and metric multidimensional scaling

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