A Contribution to the Schlesinger’s Algorithm Separating Mixtures of Gaussians

  • Vojtěch Franc
  • Václav Hlaváč
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2124)


This paper contributes to the statistical pattern recognition problem in which two classes of objects are considered and either of them is described by a mixture of Gaussian distributions. The components of either mixture are known, and unknown are only their weights. The class (state) of the object k is to be found at the mentioned incomplete a priori knowledge of the statistical model and the known observation x. The task can be expressed as a statistical decision making with non-random interventions. The task was formulated and solved first by Anderson and Bahadur [1] for a simpler case where each of two classes is described by a single Gaussian. The more general formulation with more Gaussians describing each of two classes was suggested by M.I. Schlesinger under the name generalized Anderson’s task (abbreviated GAT in the sequel). The linear solution to GAT was proposed in [5] and described recently in a more general context in a monograph [4].

This contribution provides (i) a formulation of GAT, (ii) a taxonomy of various solutions to GAT including their brief description, (iii) the novel improvement to one of its solutions by proposing better direction vector for next iteration, (iv) points to our implementation of GAT in a more general Statistical Pattern Recognition Toolbox (in MATLAB, public domain) and (v) shows experimentally the performance of the improvement (iii).


pattern recognition Gaussian separation 


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  1. 1.
    Anderson, T.W., Bahadur, R.R.: Classification into two multivariate normal distributions with differrentia covariance matrices. Annals Math. Stat. 33 (Jun 1962) 420–431Google Scholar
  2. 2.
    Burges C.J.: A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2 (1998) 121–167CrossRefGoogle Scholar
  3. 3.
    Franc, V.: Statistical pattern recognition toolbox for Matlab, Master thesis, Czech Technical University in Prague (2000).
  4. 4.
    Schlesinger, M.I., Hlaváč, V.: Deset přednášek z teorie statistického a strukturního rozpoznávání, in Czech (Ten lectures on statistical and structural pattern recognition). Czech Technical University Publishing House, Praha, Czech Republic (1999). (English version is supposed to be published by Kluwer Academic Publishers (2001))Google Scholar
  5. 5.
    Schlesinger, M.I., Kalmykov, V.G., Suchorukov, A.A.: Sravnitelnyj analiz algoritmov sinteza linejnogo reshajushchego pravila dlja proverki slozhnych gipotez, in Russian (Comparative analysis of algorithms synthesising linear decision rule for analysis of complex hypotheses). Automatika, 1 (1981) 3–9Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Vojtěch Franc
    • 1
  • Václav Hlaváč
    • 1
  1. 1.Faculty of Electrical Engineering, Center for Machine PerceptionCzech Technical UniversityPraha 2Czech Republic

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