Fractal Belief Rényi Divergence With its Applications in Pattern Classification

Multisource information fusion is a comprehensive and interdisciplinary subject. Dempster-Shafer (D-S) evidence theory copes with uncertain information effectively. Pattern classification is the core research content of pattern recognition, and multisource information fusion based on D-S evidence theory can be effectively applied to pattern classification problems. However, in D-S evidence theory, highly-conflicting evidence may cause counterintuitive fusion results. Belief divergence theory is one of the theories that are proposed to address problems of highly-conflicting evidence. Although belief divergence can deal with conflict between evidence, none of the existing belief divergence methods has considered how to effectively measure the discrepancy between two pieces of evidence with time evolutionary. In this study, a novel fractal belief Rényi (FBR) divergence is proposed to handle this problem. We assume that it is the first divergence that extends the concept of fractal to Rényi divergence. The advantage is measuring the discrepancy between two pieces of evidence with time evolution, which satisfies several properties and is flexible and practical in various circumstances. Furthermore, a novel algorithm for multisource information fusion based on FBR divergence, namely FBReD-based weighted multisource information fusion, is developed. Ultimately, the proposed multisource information fusion algorithm is applied to a series of experiments for pattern classification based on real datasets, where our proposed algorithm achieved superior performance.

I. Introduction

Multisource information fusion is a process that integrates multiple information sources to obtain more accurate, reliable, consistent and complex information for decision-making support [1], [2]. In multisource information fusion, dealing with uncertainty information is necessary. There are a number of methods that are proposed to deal with uncertainty information, including random permutation set [3], [4], probability theory [5], [6], intuitionistic fuzzy sets [7], quantum evidence theory [8], [9], [10], Euler–Lagrange systems [11], evidential reasoning [12], [13] and evidence theory [14]. And here are numerous application fields of these well-known methods, including interval criteria satisfactions [15], COVID-19 wave superposition [16], decision-making [17], [18], [19], community detection [20], reliability analysis [21], analytic network [22], fault analysis [23], counter-terrorism analysis [24], driving task recordings [25], optimization problem [26], dynamics modeling of multi-agent learning [27], [28], image scene classification [29] and rapid source localization [30].