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

TL;DR

This paper explores fitting features with an $oldsymbol{ extalpha}$-stable distribution for classifying imperfect data using continuous belief functions, demonstrating improved classification performance over Gaussian models in synthetic and real sea floor data.

Contribution

It introduces a novel approach combining $oldsymbol{ extalpha}$-stable distributions with continuous belief functions for pattern recognition of uncertain data.

Findings

$oldsymbol{ extalpha}$-stable models outperform Gaussian models in classification tasks.

Kolmogorov-Smirnov test confirms better fit of $oldsymbol{ extalpha}$-stable distribution.

Belief classifier shows higher accuracy compared to Bayesian approach.

Abstract

The aim of this paper is to show the interest in fitting features with an $\alpha$-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 $\alpha$-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 $\alpha$-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.