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

摘要

The aim of this paper is to show the interest in fitting features with an$\alpha$-stable distribution to classify imperfect data. The supervised patternrecognition is thus based on the theory of continuous belief functions, whichis a way to consider imprecision and uncertainty of data. The distributions offeatures are supposed to be unimodal and estimated by a single Gaussian and$\alpha$-stable model. Experimental results are first obtained from syntheticdata by combining two features of one dimension and by considering a vector oftwo features. Mass functions are calculated from plausibility functions byusing the generalized Bayes theorem. The same study is applied to the automaticclassification of three types of sea floor (rock, silt and sand) with featuresacquired by a mono-beam echo-sounder. We evaluate the quality of the$\alpha$-stable model and the Gaussian model by analyzing qualitative results,using a Kolmogorov-Smirnov test (K-S test), and quantitative results withclassification rates. The performances of the belief classifier are comparedwith a Bayesian approach.