A belief Rényi divergence for multi-source information fusion and its application in pattern recognition

Deep Evidential Remote Sensing Landslide Image Classification With a New Divergence, Multiscale Saliency and an Improved Three-Branched Fusion

“…However, some belief divergences have inherent shortcomings [40]. The present study points out the Belief Renyi divergence [43] and Generalized Belief Renyi divergence [44] can lead to explainability and decision-invariance losses on the newly developed evidence-theoretic system (before formally providing a solution, we set two Analyses to illustrate the two mentioned losses at first). To address this issue, this paper provides a multi-evidence remedy, i.e.…”

“…The major motivation to develop the new divergence is to fix the "belief divergence" challenge of Belief Renyi divergence and Generalized Belief Renyi divergence via a multi-BPAs' approach. Namely, the Belief Renyi divergence is defined as follows [43]:…”

“…) where α ∈ (0, 1) ∪ (1, +∞), θ i ∈ Θ, Θ is the FoD (Frame of Discrimination, the set containing all the hypothesis in evidence theory [47]), P Bl m (θ i ) = Bel(θi)+P l(θi) θ i ∈Θ Bel(θi)+P l(θi) . The Bel and P l functions can be found in [43], [44].…”

“…1 Here the multi-BPAs based belief divergences, for instance, the Generalized Evidential Jensen-Shannon divergence GEJSω [55], are excluded. [43] and (c)-(d) the Generalized Renyi divergence [44]. Note that (a) and (c) are symmetric cases, while (b) and (d) are non-symmetric cases.…”

“…Note that (a) and (c) are symmetric cases, while (b) and (d) are non-symmetric cases. The abscissa is on behalf of the number of fusion times with Dempster's combination rule [38] when fusing the weighted evidence in [43] and [44]'s proposal. where i, j ∈ {1, ..., N }.…”