David Delgado Gomez <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > Hello, > > Can anyone tell me if there is any method to determine the number of > components in a mixture of Gaussians automatically in advance. are there > any papers written on this subject? > Thanks > David
I am not sure what you mean by "automatically in advance". The # of components needed depends on the data, and is usually determined during the calculation. Chapter 6 of the book "Finite Mixture Models", by Mclachlan and Peel, entitled "Assessing the Number of Components in Mixture Models", devotes 46 pages to your question. One can use likelihood ratios and information criteria. The following papers from my list of references look relevant. Whitaker, Stephan and Lee, Thomas C. M. (2003) "An Effective Method for Selecting the Number of Components in Density Mixtures" Multivariate Gaussian mixture modeling with unknown number of components Nikos Vlassis, Aristidis Likas, Ben Kr�se "On Bayesian analysis of mixtures with an unknown number of components", by Sylvia Richardson and Peter Green, February 1996, revised October 1996. An Entropy criterion for assessing the number of clusters in a mixture model Celeux, Gilles - Soromenho, G. Abstract: In this paper, we consider an entropy criterion to estimate the number of clusters arising from a mixture model. This criterion is derived from a relation linking the likelihood and the classification likelihood of a mixture. Its performances are investigated through Monte-Carlo numerical experiments and show favourable results as compared with other classical criteria. Stephens, M. (1998). Bayesian Analysis of Mixtures with an Unknown Number of Components --- an alternative to Reversible Jump methods. Submitted to Annals of Statistics. George W. Rogers, David J. Marchette, Carey E. Priebe A Procedure for Model Complexity Selection in Semiparametric Mixture Model Density Estimation Author: M Salom� Cabral Title: Testing in multivariate normal mixtures Email: [EMAIL PROTECTED] Abstract: We propose a test to identify the existence of a mixture of two or more multivariate (or univariate) normal distributions with common covariance matrix. Based on the test and the estimation algorithm EM a procedure is derived to identify the number of components in the mixture. The asymptotic power function of the test is given and a simulation study is also made. An example with real data is analysed. McLachlan, G. J., Basford, K. E. & Green, M. On Inferring the Number of Components in Normal Mixture Models June 1993. McLachlan, G.J., Peel, D., Adams, P. and Basford, K.E. Assessing by Resampling the P-value of the Likelihood Ratio Test on the Number of Components in Normal Mixture Models April 1995. McLachlan, G.J. and Peel, D. On a Resampling Approach to Choosing the Number of Components in Normal Mixture Models June 1996. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
