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Celeux, Gilles; Diebolt, Jean

L’algorithme SEM: Un algorithme d’apprentissage probabiliste pour la reconnaissance de mélange de densités. (The SEM algorithm: An algorithm of probabilistic learning for the determination of mixtures of densities). (French) Zbl 0607.62037

Rev. Stat. Appl. 34, No. 2, 35-52 (1986).

Cited in 1 Review
Cited in 9 Documents

MSC:

62F99 Parametric inference
65C99 Probabilistic methods, stochastic differential equations
62H30 Classification and discrimination; cluster analysis (statistical aspects)
65D15 Algorithms for approximation of functions

Keywords:

SEM algorithm; probabilistic learning; mixtures of densities; estimation; maximization; asymptotic behavior; simulations; Gaussian mixture; maximum likelihood; EM algorithm; classification
Cite Review PDF
Full Text: Numdam EuDML

References:

[1] Agrawala . - ” Learning with a probabilistic teacher ” IEEE. Information theory , Vol. 16 , nu. 4. Zbl 0207.49302 · Zbl 0207.49302 · doi:10.1109/TIT.1970.1054472
[2] BRYANT - WYLLIAMSON. - ” Asymptotic behaviour of classification maximum likelihood estimates ”. Biometrika 78 , Vol. 68 . Zbl 0393.62011 · Zbl 0393.62011 · doi:10.1093/biomet/65.2.273
[3] CELEUX, DIEBOLT. - Reconnaissance de mélange de densité et classification, un algorithme d’apprentissage probabiliste : l’algorithme SEM . Rapport de recherche INRIA n^\circ 349 . · Zbl 0607.62037
[4] Cooper . - ” Non supervised adaptative signal detection and pattern recognition ”. Information and Control , Vol. 7 . Zbl 0199.22402 · Zbl 0199.22402 · doi:10.1016/S0019-9958(64)90502-9
[5] DAY. - ” Estimating the components of a mixture of normal distributions ”. Biometrika 69, Vol. 56 . MR 254956 | Zbl 0183.48106 · Zbl 0183.48106 · doi:10.1093/biomet/56.3.463
[6] DIDAY et collaborateurs. - Optimisation en classification automatique . Editeur : INRIA . Zbl 0471.62056 · Zbl 0471.62056
[7] DEMPSTER - LAIRD - RUBIN. - ” Maximum likelihood from incomplete data via the EM algorithm ”. JRSS.B. , Vol. 39 . Zbl 0364.62022 · Zbl 0364.62022
[8] EVERITT - HAND. - Finite mixture distributions . Chapman and Hall . Zbl 0466.62018 · Zbl 0466.62018
[9] Marriott . - ” Separating mixtures of normal distributions ”. Biometrika , 31 . Zbl 0308.62050 · Zbl 0308.62050 · doi:10.2307/2529563
[10] MAKOV - SMITH. - ” Quasi Bayes procedures for unsupervised learning ”. Proc. IEEE. Conf. on Decision and Control. · Zbl 0397.62004
[11] Pearson . - ” Contribution to the mathematic theory of evolution ”. Philos. Trans. Soc. , nu. 185 ( 1894 ). · JFM 25.0347.02
[12] Quandt , Ramsey. - ” Estimating mixtures of normal distributions and switching regression ”. JASA , Vol. 73 . Zbl 0401.62024 · Zbl 0401.62024 · doi:10.2307/2286266
[13] REDNER - WALKER. - ” Mixture densities, maximum likelihood and the EM algorithm ”. SIAM Review , Vol. 26 , No. 2 , April 84. MR 738930 | Zbl 0536.62021 · Zbl 0536.62021 · doi:10.1137/1026034
[14] Schroeder . - ” Analyse d’un mélange de distribution de probabilité de même type ”. RSA , Vol. 24 , nu. 1. Numdam
[15] SCOTT - SYMONS. - ” Clustering methods based on likelihood ratio criteria ”. Biometrics , Vol. 27 .
[16] Shlezinger . - ” An algorithm for solving the selforganization problem ”. Cybernetics , nu. 2.
[17] Silverman . - ” Some asymptotic properties of the probabilistic teacher ” IEEE. Information theory , Vol. 26 , nu. 2. MR 570331 | Zbl 0428.62026 · Zbl 0428.62026 · doi:10.1109/TIT.1980.1056150
[18] SMITH - MAKOV. - ” A quasi Bayes sequential procedure for mixtures ”. JRSS. B. , Vol. 40 , nu. 1. MR 512148 | Zbl 0377.62045 · Zbl 0377.62045
[19] Teicher . - ” Identifiability of finite mixture ”. Ann. Math. Statist. , Vol. 34 . Article | MR 155376 · Zbl 0146.39302
[20] Symons . - ” Clustering criteria and multivariate normal mixtures ”. Biometrics , Vol. 37 . MR 673031 | Zbl 0473.62048 · Zbl 0473.62048 · doi:10.2307/2530520
[21] Wolfe . - ” Pattern clustering by multivariate mixture analysis ”. Multiv. Behav. Res. , Vol. 5 .
[22] YAKOWITZ - SPRAGINS. - ”On the identifiability of finite mixtures” . Ann. Math. Statist. , Vol. 39 . Article | MR 224204 | Zbl 0155.25703 · Zbl 0155.25703 · doi:10.1214/aoms/1177698520
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