IEICE TRANSACTIONS on Fundamentals
Fuzzy c-Means Algorithms for Data with Tolerance Using Kernel Functions
Summary :
In this paper, two new clustering algorithms based on fuzzy c-means for data with tolerance using kernel functions are proposed. Kernel functions which map the data from the original space into higher dimensional feature space are introduced into the proposed algorithms. Nonlinear boundary of clusters can be easily found by using the kernel functions. First, two clustering algorithms for data with tolerance are introduced. One is based on standard method and the other is on entropy-based one. Second, the tolerance in feature space is discussed taking account into soft margin algorithm in Support Vector Machine. Third, two objective functions in feature space are shown corresponding to two methods, respectively. Fourth, Karush-Kuhn-Tucker conditions of two objective functions are considered, respectively, and these conditions are re-expressed with kernel functions as the representation of an inner product for mapping from the original pattern space into a higher dimensional feature space. Fifth, two iterative algorithms are proposed for the objective functions, respectively. Through some numerical experiments, the proposed algorithms are discussed.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.9 pp.2520-2534
- Publication Date
- 2008/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e91-a.9.2520
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
- Category
- Soft Computing
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Keyword
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Yuchi KANZAWA, Yasunori ENDO, Sadaaki MIYAMOTO, "Fuzzy c-Means Algorithms for Data with Tolerance Using Kernel Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 9, pp. 2520-2534, September 2008, doi: 10.1093/ietfec/e91-a.9.2520.
Abstract: In this paper, two new clustering algorithms based on fuzzy c-means for data with tolerance using kernel functions are proposed. Kernel functions which map the data from the original space into higher dimensional feature space are introduced into the proposed algorithms. Nonlinear boundary of clusters can be easily found by using the kernel functions. First, two clustering algorithms for data with tolerance are introduced. One is based on standard method and the other is on entropy-based one. Second, the tolerance in feature space is discussed taking account into soft margin algorithm in Support Vector Machine. Third, two objective functions in feature space are shown corresponding to two methods, respectively. Fourth, Karush-Kuhn-Tucker conditions of two objective functions are considered, respectively, and these conditions are re-expressed with kernel functions as the representation of an inner product for mapping from the original pattern space into a higher dimensional feature space. Fifth, two iterative algorithms are proposed for the objective functions, respectively. Through some numerical experiments, the proposed algorithms are discussed.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.9.2520/_p
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@ARTICLE{e91-a_9_2520,
author={Yuchi KANZAWA, Yasunori ENDO, Sadaaki MIYAMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Fuzzy c-Means Algorithms for Data with Tolerance Using Kernel Functions},
year={2008},
volume={E91-A},
number={9},
pages={2520-2534},
abstract={In this paper, two new clustering algorithms based on fuzzy c-means for data with tolerance using kernel functions are proposed. Kernel functions which map the data from the original space into higher dimensional feature space are introduced into the proposed algorithms. Nonlinear boundary of clusters can be easily found by using the kernel functions. First, two clustering algorithms for data with tolerance are introduced. One is based on standard method and the other is on entropy-based one. Second, the tolerance in feature space is discussed taking account into soft margin algorithm in Support Vector Machine. Third, two objective functions in feature space are shown corresponding to two methods, respectively. Fourth, Karush-Kuhn-Tucker conditions of two objective functions are considered, respectively, and these conditions are re-expressed with kernel functions as the representation of an inner product for mapping from the original pattern space into a higher dimensional feature space. Fifth, two iterative algorithms are proposed for the objective functions, respectively. Through some numerical experiments, the proposed algorithms are discussed.},
keywords={},
doi={10.1093/ietfec/e91-a.9.2520},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - Fuzzy c-Means Algorithms for Data with Tolerance Using Kernel Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2520
EP - 2534
AU - Yuchi KANZAWA
AU - Yasunori ENDO
AU - Sadaaki MIYAMOTO
PY - 2008
DO - 10.1093/ietfec/e91-a.9.2520
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2008
AB - In this paper, two new clustering algorithms based on fuzzy c-means for data with tolerance using kernel functions are proposed. Kernel functions which map the data from the original space into higher dimensional feature space are introduced into the proposed algorithms. Nonlinear boundary of clusters can be easily found by using the kernel functions. First, two clustering algorithms for data with tolerance are introduced. One is based on standard method and the other is on entropy-based one. Second, the tolerance in feature space is discussed taking account into soft margin algorithm in Support Vector Machine. Third, two objective functions in feature space are shown corresponding to two methods, respectively. Fourth, Karush-Kuhn-Tucker conditions of two objective functions are considered, respectively, and these conditions are re-expressed with kernel functions as the representation of an inner product for mapping from the original pattern space into a higher dimensional feature space. Fifth, two iterative algorithms are proposed for the objective functions, respectively. Through some numerical experiments, the proposed algorithms are discussed.
ER -
English
