A comparison of cluster validity criteria for a mixture of normal distributed data

Pattern Recognition Letters

Volumn 21, Issue 6-7, 2000, Pages 511-529

  Geva, Amir B ^a   Steinberg, Yossef ^a   Bruckmair, Shay ^a   Nahum, Gerry ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Cluster validity; Entropy maximization; Generalized Neyman Pearson (GNP) criterion; Hypothesis testing; Mixture of normal distributed data; Unsupervised clustering

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DATA STRUCTURES; FUZZY SETS; MAXIMUM LIKELIHOOD ESTIMATION;

CLUSTER VALIDITY CRITERIA; GENERALIZED NEYMAN-PEARSON (GNP) TEST; UNSUPERVISED OPTIMAL FUZZY CLUSTERING (UOFC) ALGORITHMS;

PATTERN RECOGNITION;

EID: 0033739050     PISSN: 01678655     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8655(00)00016-7     Document Type: Article

References (14)

1. Bezdek, J.C., Castelaz, P.F., 1971. Prototype classification and feature selection with fuzzy sets. IEEE Trans. on SMC-7, pp. 87-92.
2. Bezdek, J.C., Pal, N.R., 1998. Some new validity indexes of cluster validity. IEEE Trans. Syst. Man and Cyber. - Part b: Cyber., Vol. 28 (3).
3. Duda, R.O., Hart, P.E., 1973. Pattern Classification and Scene Analysis, Wiley Interscience, New York.
4. Fukuyama, Y., Sugeno, M., 1989. A new method of choosing the number of clusters for the fuzzy c-means method, In: Proc. Fifth Fuzzy Syst. Symp., pp. 247-250 (in Japanese).
5. Gath, I., Geva, A.B., 1989. Fuzzy clustering for the estimation of the parameters of the components of mixtures of normal distributions, Pattern Recognition Letters, Vol. 9 (3), Elsevier, pp. 77-86.
6. Geva A.B., Pratt H. Unsupervised clustering of evoked potentials by waveform. Medical Biol. Engrg. Comput. 32:1994;543-550.
7. Hathaway R.J. A constrained formulation of maximum likelihood estimation for normal mixture distributions. Ann. Statist. 13:1985;795-800.
8. Hoeffding W. Asymptotically optimal test for multinomial distribution. Ann. Math. Statist. 36:1965;369-400.
9. Pal, N.R., Bezdek, J.C., 1995. On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Sys., Vol. 3 (3).
10. Peters B.C., Walker H. An iterative procedure for obtaining maximum likelihood estimates of the parameters for a mixture of normal distributions. SIAM J. Appl. Math. 35:1978;362-378.
11. Rezaee, M.R., Lelieveldt, B.P.F., Reiber, J.H.C., 1998. A new cluster validity for the fuzzy c-mean. Pattern Recognition Letters, pp. 237-246.
12. Steinberg, Y., Zeitouni, O., 1992. On tests for normality, IEEE Trans. Inform. Theory, Vol. 38 (6).
13. Xie X.L., Beni G.A. Validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Machine Intell. 3(8):1991;841-846.
14. Ziv J. On classification with empirically observed statistics and universal data compression. IEEE Trans. Inform. Theory. 34:1988;278-286.