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Features modeling with an α-stable distribution: Application to pattern recognition based on continuous belief functions

Anthony Fiche 1 Jean-Christophe Cexus 2 Arnaud Martin 3 Ali Khenchaf 1
1 Lab-STICC_ENSTAB_MOM-PIM ; REMS
STIC - Pôle STIC [Brest], Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
2 Lab-STICC_ENSTAB_CID_TOMS ; REMS
STIC - Pôle STIC [Brest], Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : The aim of this paper is to show the interest in fitting features with an α-stable distribution to classify imperfect data. The supervised pattern recognition is thus based on the theory of continuous belief functions, which is a way to consider imprecision and uncertainty of data. The distributions of features are supposed to be unimodal and estimated by a single Gaussian and α-stable model. Experimental results are first obtained from synthetic data by combining two features of one dimension and by considering a vector of two features. Mass functions are calculated from plausibility functions by using the generalized Bayes theorem. The same study is applied to the automatic classification of three types of sea floor (rock, silt and sand) with features acquired by a mono-beam echo-sounder. We evaluate the quality of the α-stable model and the Gaussian model by analyzing qualitative results, using a Kolmogorov-Smirnov test (K-S test), and quantitative results with classification rates. The performances of the belief classifier are compared with a Bayesian approach.
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Anthony Fiche, Jean-Christophe Cexus, Arnaud Martin, Ali Khenchaf. Features modeling with an α-stable distribution: Application to pattern recognition based on continuous belief functions. Information Fusion, Elsevier, 2013, 14, pp.504 - 520. ⟨10.1016/j.inffus.2013.02.004⟩. ⟨hal-01108181⟩

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