Title :
On the Local Optimality of the Fuzzy Isodata Clustering Algorithm
Author :
Selim, Shokri Z. ; Ismail, M.A.
Author_Institution :
Department of Systems Engineering, University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
fDate :
3/1/1986 12:00:00 AM
Abstract :
The convergence of the fuzzy ISODATA clustering algorithm 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.
Keywords :
Clustering algorithms; Filtering; Hilbert space; Kalman filters; Minerals; Multidimensional signal processing; Petroleum; Signal processing algorithms; Speech processing; Systems engineering and theory; Fuzzy clustering algorithms; fuzzy ISODATA algorithm; fuzzy c-means algorithm; fuzzy unsupervised classification; local optimality;
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
DOI :
10.1109/TPAMI.1986.4767783
