ity -Guided (Re)Clustering with plications to Image Segmentation

When clustering algorithms are applied to image seg- mentation, the goal is to solve a classification problem. However, these algorithms do not directly optimize classification quality. As a result, they are susceptible to two problems: P1) the criterion they optimize may not be a good estimator of "true" classi- fication quality, and P2) they often admit many (suboptha€) solutions. This paper introduces an algorithm that uses cluster validity to mitigate P1 and P2. The validity-guided (re)clustering (VGC) algorithm uses cluster-validity information to guide a fuzzy (re)clustering process toward better solutions. It starts with a partition generated by a soft or fuzzy clustering algorithm. Then it iteratively alters the partition by applying (novel) split- and-merge operations to the clusters. Partition modifications that result in improved partition validity are retained. VGC is tested on both synthetic and real-world data. For magnetic resonance image (MRI) segmentation, evaluations by radiologists show that VGC outperforms the (unsupervised) fuzzy c-means algorithm, and VGC's performance approaches that of the (supervised) k-nearest-neighbors algorithm.

[1]  J. Bezdek Cluster Validity with Fuzzy Sets , 1973 .

[2]  M. P. Windham Cluster validity for fuzzy clustering algorithms , 1981 .

[3]  J. Dunn Well-Separated Clusters and Optimal Fuzzy Partitions , 1974 .

[4]  Michael P. Windham,et al.  Cluster Validity for the Fuzzy c-Means Clustering Algorithrm , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[6]  Raghu Krishnapuram,et al.  Fitting an unknown number of lines and planes to image data through compatible cluster merging , 1992, Pattern Recognit..

[7]  Michio Sugeno,et al.  A fuzzy-logic-based approach to qualitative modeling , 1993, IEEE Trans. Fuzzy Syst..

[8]  L. Hubert,et al.  Quadratic assignment as a general data analysis strategy. , 1976 .

[9]  Gerardo Beni,et al.  A Validity Measure for Fuzzy Clustering , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Enrique H. Ruspini,et al.  A New Approach to Clustering , 1969, Inf. Control..

[11]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[12]  James C. Bezdek,et al.  Fuzzy cluster validity in magnetic resonance images , 1994, Medical Imaging.

[13]  James C. Bezdek,et al.  A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain , 1992, IEEE Trans. Neural Networks.

[14]  Douglas H. Fisher,et al.  Knowledge Acquisition Via Incremental Conceptual Clustering , 1987, Machine Learning.

[15]  G. W. Milligan,et al.  An examination of procedures for determining the number of clusters in a data set , 1985 .

[16]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[17]  E. Backer,et al.  Cluster analysis by optimal decomposition of induced fuzzy sets , 1978 .

[18]  Isak Gath,et al.  Detection and Separation of Ring-Shaped Clusters Using Fuzzy Clustering , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Anil K. Jain,et al.  A Clustering Performance Measure Based on Fuzzy Set Decomposition , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Josef Kittler,et al.  Pattern recognition : a statistical approach , 1982 .

[21]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[22]  Donald W. Bouldin,et al.  A Cluster Separation Measure , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[24]  J. Bezdek Numerical taxonomy with fuzzy sets , 1974 .

[25]  Isak Gath,et al.  Unsupervised Optimal Fuzzy Clustering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..