Self-organization on a sphere with application to topological ordering of Chinese characters

Andrew P. Paplinski

doi:10.1007/978-3-319-46681-1_54

Self-organization on a sphere with application to topological ordering of Chinese characters

Andrew P. Paplinski

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

Abstract

We consider a case of self-organization in which a relatively small number N of data points is mapped on a larger number M of nodes. This is a reverse situation to a typical clustering problem when a node represents a center of the cluster of data points. In our case the objective is to have a Gaussian-like distribution of weights over nodes in the neighbourhood of the winner for a given stimulus. The fact that M > N creates some problem with using learning schemes related to Gaussian MixtureModels.We also show how the objects, Chinese characters in our case, can be topologically ordered on a surface of a 3D sphere. A Chinese character is represented by an angular integral of the Radon Transform (aniRT) which is an RTS-invariant 1-D signature function of an image.

Original language	English
Title of host publication	Neural Information Processing
Subtitle of host publication	23rd International Conference, ICONIP 2016, Kyoto, Japan, October 16-21, 2016, Proceedings, Part IV
Editors	Akira Hirose, Seiichi Ozawa, Kenji Doya, Kazushi Ikeda, Minho Lee, Derong Liu
Publisher	Springer
Pages	452-459
Number of pages	8
ISBN (Electronic)	9783319466811
ISBN (Print)	9783319466804
DOIs	https://doi.org/10.1007/978-3-319-46681-1_54
Publication status	Published - 2016
Event	International Conference on Neural Information Processing 2016 - Kyoto, Japan Duration: 16 Oct 2016 → 21 Oct 2016 Conference number: 23rd https://link.springer.com/book/10.1007/978-3-319-46687-3 (Proceedings)

Publication series

Name	Lecture Notes in Computer Science
Volume	9950
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Conference on Neural Information Processing 2016
Abbreviated title	ICONIP 2016
Country/Territory	Japan
City	Kyoto
Period	16/10/16 → 21/10/16
Internet address	https://link.springer.com/book/10.1007/978-3-319-46687-3 (Proceedings)

Keywords

Angular integral of the radon transform
Gaussian mixture models
Probabilistic self-organizing maps
Self-organization on a sphere

Access to Document

10.1007/978-3-319-46681-1_54

Cite this

Paplinski, A. P. (2016). Self-organization on a sphere with application to topological ordering of Chinese characters. In A. Hirose, S. Ozawa, K. Doya, K. Ikeda, M. Lee, & D. Liu (Eds.), Neural Information Processing: 23rd International Conference, ICONIP 2016, Kyoto, Japan, October 16-21, 2016, Proceedings, Part IV (pp. 452-459). (Lecture Notes in Computer Science; Vol. 9950). Springer. https://doi.org/10.1007/978-3-319-46681-1_54

Paplinski, Andrew P. / Self-organization on a sphere with application to topological ordering of Chinese characters. Neural Information Processing: 23rd International Conference, ICONIP 2016, Kyoto, Japan, October 16-21, 2016, Proceedings, Part IV. editor / Akira Hirose ; Seiichi Ozawa ; Kenji Doya ; Kazushi Ikeda ; Minho Lee ; Derong Liu. Springer, 2016. pp. 452-459 (Lecture Notes in Computer Science).

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abstract = "We consider a case of self-organization in which a relatively small number N of data points is mapped on a larger number M of nodes. This is a reverse situation to a typical clustering problem when a node represents a center of the cluster of data points. In our case the objective is to have a Gaussian-like distribution of weights over nodes in the neighbourhood of the winner for a given stimulus. The fact that M > N creates some problem with using learning schemes related to Gaussian MixtureModels.We also show how the objects, Chinese characters in our case, can be topologically ordered on a surface of a 3D sphere. A Chinese character is represented by an angular integral of the Radon Transform (aniRT) which is an RTS-invariant 1-D signature function of an image.",

keywords = "Angular integral of the radon transform, Gaussian mixture models, Probabilistic self-organizing maps, Self-organization on a sphere",

author = "Paplinski, {Andrew P.}",

year = "2016",

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language = "English",

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editor = "Akira Hirose and Seiichi Ozawa and Kenji Doya and Kazushi Ikeda and Minho Lee and Derong Liu",

booktitle = "Neural Information Processing",

note = "International Conference on Neural Information Processing 2016, ICONIP 2016 ; Conference date: 16-10-2016 Through 21-10-2016",

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Paplinski, AP 2016, Self-organization on a sphere with application to topological ordering of Chinese characters. in A Hirose, S Ozawa, K Doya, K Ikeda, M Lee & D Liu (eds), Neural Information Processing: 23rd International Conference, ICONIP 2016, Kyoto, Japan, October 16-21, 2016, Proceedings, Part IV. Lecture Notes in Computer Science, vol. 9950, Springer, pp. 452-459, International Conference on Neural Information Processing 2016, Kyoto, Japan, 16/10/16. https://doi.org/10.1007/978-3-319-46681-1_54

Self-organization on a sphere with application to topological ordering of Chinese characters. / Paplinski, Andrew P.
Neural Information Processing: 23rd International Conference, ICONIP 2016, Kyoto, Japan, October 16-21, 2016, Proceedings, Part IV. ed. / Akira Hirose; Seiichi Ozawa; Kenji Doya; Kazushi Ikeda; Minho Lee; Derong Liu. Springer, 2016. p. 452-459 (Lecture Notes in Computer Science; Vol. 9950).

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

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N2 - We consider a case of self-organization in which a relatively small number N of data points is mapped on a larger number M of nodes. This is a reverse situation to a typical clustering problem when a node represents a center of the cluster of data points. In our case the objective is to have a Gaussian-like distribution of weights over nodes in the neighbourhood of the winner for a given stimulus. The fact that M > N creates some problem with using learning schemes related to Gaussian MixtureModels.We also show how the objects, Chinese characters in our case, can be topologically ordered on a surface of a 3D sphere. A Chinese character is represented by an angular integral of the Radon Transform (aniRT) which is an RTS-invariant 1-D signature function of an image.

AB - We consider a case of self-organization in which a relatively small number N of data points is mapped on a larger number M of nodes. This is a reverse situation to a typical clustering problem when a node represents a center of the cluster of data points. In our case the objective is to have a Gaussian-like distribution of weights over nodes in the neighbourhood of the winner for a given stimulus. The fact that M > N creates some problem with using learning schemes related to Gaussian MixtureModels.We also show how the objects, Chinese characters in our case, can be topologically ordered on a surface of a 3D sphere. A Chinese character is represented by an angular integral of the Radon Transform (aniRT) which is an RTS-invariant 1-D signature function of an image.

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Paplinski AP. Self-organization on a sphere with application to topological ordering of Chinese characters. In Hirose A, Ozawa S, Doya K, Ikeda K, Lee M, Liu D, editors, Neural Information Processing: 23rd International Conference, ICONIP 2016, Kyoto, Japan, October 16-21, 2016, Proceedings, Part IV. Springer. 2016. p. 452-459. (Lecture Notes in Computer Science). doi: 10.1007/978-3-319-46681-1_54

Self-organization on a sphere with application to topological ordering of Chinese characters

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