On the Local Optimality of the Fuzzy Isodata Clustering Algorithm

Shokri Z. Selim; M. A. Ismail

doi:10.1109/TPAMI.1986.4767783

On the Local Optimality of the Fuzzy Isodata Clustering Algorithm

Shokri Z. Selim, M. A. Ismail

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

Abstract

The convergence of the fuzzy ISODATA clusteringalgorithm was proved by Bezdek [3]. Two sets of conditions were derived and it was conjectured that they are necessary and sufficient for a local minimum point. In this paper, we address this conjecture and explore the properties of the underlying optimization problem. The notions of reduced objective function and improving and feasible directions are used to examine this conjecture. Finally, based on the derived properties of the problem, a new stopping criterion for the fuzzy ISODATA algorithm is proposed.

Original language	English
Pages (from-to)	284-288
Number of pages	5
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	PAMI-8
Issue number	2
DOIs	https://doi.org/10.1109/TPAMI.1986.4767783
State	Published - 1986

Keywords

Fuzzy clustering algorithms
fuzzy ISODATA algorithm
fuzzy c-means algorithm
fuzzy unsupervised classification
local optimality

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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10.1109/TPAMI.1986.4767783

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title = "On the Local Optimality of the Fuzzy Isodata Clustering Algorithm",

abstract = "The convergence of the fuzzy ISODATA clusteringalgorithm was proved by Bezdek [3]. Two sets of conditions were derived and it was conjectured that they are necessary and sufficient for a local minimum point. In this paper, we address this conjecture and explore the properties of the underlying optimization problem. The notions of reduced objective function and improving and feasible directions are used to examine this conjecture. Finally, based on the derived properties of the problem, a new stopping criterion for the fuzzy ISODATA algorithm is proposed.",

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T1 - On the Local Optimality of the Fuzzy Isodata Clustering Algorithm

AU - Selim, Shokri Z.

AU - Ismail, M. A.

PY - 1986

Y1 - 1986

N2 - The convergence of the fuzzy ISODATA clusteringalgorithm was proved by Bezdek [3]. Two sets of conditions were derived and it was conjectured that they are necessary and sufficient for a local minimum point. In this paper, we address this conjecture and explore the properties of the underlying optimization problem. The notions of reduced objective function and improving and feasible directions are used to examine this conjecture. Finally, based on the derived properties of the problem, a new stopping criterion for the fuzzy ISODATA algorithm is proposed.

AB - The convergence of the fuzzy ISODATA clusteringalgorithm was proved by Bezdek [3]. Two sets of conditions were derived and it was conjectured that they are necessary and sufficient for a local minimum point. In this paper, we address this conjecture and explore the properties of the underlying optimization problem. The notions of reduced objective function and improving and feasible directions are used to examine this conjecture. Finally, based on the derived properties of the problem, a new stopping criterion for the fuzzy ISODATA algorithm is proposed.

KW - Fuzzy clustering algorithms

KW - fuzzy ISODATA algorithm

KW - fuzzy c-means algorithm

KW - fuzzy unsupervised classification

KW - local optimality

UR - https://www.scopus.com/pages/publications/0022690032

U2 - 10.1109/TPAMI.1986.4767783

DO - 10.1109/TPAMI.1986.4767783

M3 - Article

AN - SCOPUS:0022690032

SN - 0162-8828

VL - PAMI-8

SP - 284

EP - 288

JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

IS - 2

ER -

On the Local Optimality of the Fuzzy Isodata Clustering Algorithm

Abstract

Keywords

ASJC Scopus subject areas

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