Maximum likelihood clustering via normal mixture models

Abstract We present the approach to clustering whereby a normal mixture model is fitted to the data by maximum likelihood. The general case of normal component densities with unrestricted covariance matrices is considered and so it extends the work of, who imposed the rest, who imposed the restriction of diagonal component covariance matrices. Attention is also focussed on the problem of testing for the number of clusters within this mixture framework, using the likelihood ratio test.

[1]  P. Sen,et al.  On the asymptotic performance of the log likelihood ratio statistic for the mixture model and related results , 1984 .

[2]  H C Thode,et al.  The likelihood ratio test for the two-component normal mixture problem: power and sample size analysis. , 1991, Biometrics.

[3]  Brigitte Mangin,et al.  Testing in Normal Mixture Models with Some Information on the Parameters , 1993 .

[4]  N. Mendell,et al.  Simulated percentage points for the null distribution of the likelihood ratio test for a mixture of two normals. , 1988, Biometrics.

[5]  B. Lindsay,et al.  Testing for the number of components in a mixture of normal distributions using moment estimators , 1994 .

[6]  G. McLachlan.  Discriminant Analysis and Statistical Pattern Recognition , 1992 .

[7]  Donald B. Rubin,et al.  Max-imum Likelihood from Incomplete Data , 1972 .

[8]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[9]  J. Hartigan.  A failure of likelihood asymptotics for normal mixtures , 1985 .

[10]  Adele Cutler,et al.  Information Ratios for Validating Mixture Analysis , 1992 .

[11]  G. McLachlan.  On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture , 1987 .

[12]  Otto Opitz,et al.  Information and Classification , 1993 .

[13]  N. Mendell,et al.  Where is the likelihood ratio test powerful for detecting two component normal mixtures? , 1993, Biometrics.

[14]  A. Raftery,et al.  Model-based Gaussian and non-Gaussian clustering , 1993 .

[15]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[16]  H. Bozdogan.  Choosing the Number of Component Clusters in the Mixture-Model Using a New Informational Complexity Criterion of the Inverse-Fisher Information Matrix , 1993 .

[17]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[18]  Hazem M. Abbas,et al.  Neural networks for maximum likelihood clustering , 1994, Signal Process..

[19]  J. Wolfe.  A Monte Carlo Study of the Sampling Distribution of the Likelihood Ratio for Mixtures of Multinormal Distributions , 1971 .

[20]  Patrice Loisel,et al.  Testing in normal mixture models when the proportions are known , 1992 .

[21]  Geoffrey J. McLachlan,et al.  Mixture models : inference and applications to clustering , 1989 .

[22]  B. Efron,et al.  The Jackknife: The Bootstrap and Other Resampling Plans. , 1983 .