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**Bayesian unsupervised classification framework based on stochastic partitions of data and a parallel search strategy.**
*(English)*
Zbl 1231.62031

Summary: Advantages of statistical model-based unsupervised classification over heuristic alternatives have been widely demonstrated in the scientific literature. However, the existing model-based approaches are often both conceptually and numerically instable for large and complex data sets. We consider a Bayesian model-based method for unsupervised classification of discrete valued vectors, that has certain advantages over standard solutions based on latent class models. Our theoretical formulation defines a posterior probability measure on the space of classification solutions corresponding to stochastic partitions of the observed data. To efficiently explore the classification space we use a parallel search strategy based on non-reversible stochastic processes. A decision-theoretic approach is utilized to formalize the inferential process in the context of unsupervised classification. Both real and simulated data sets are used for the illustration of the discussed methods.

### MSC:

62F15 | Bayesian inference |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62M99 | Inference from stochastic processes |

68T99 | Artificial intelligence |

65C40 | Numerical analysis or methods applied to Markov chains |

62C99 | Statistical decision theory |

65C60 | Computational problems in statistics (MSC2010) |

### Keywords:

Bayesian classification; Markov chain Monte Carlo; statistical learning; stochastic optimization### Software:

BAPS 2
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\textit{J. Corander} et al., Adv. Data Anal. Classif., ADAC 3, No. 1, 3--24 (2009; Zbl 1231.62031)

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