A high order fractal-based Kullback–Leibler divergence with application in classification

Dempster–Shafer evidence theory (DSET) is extensively employed in multi-source data fusion applications. Nonetheless, when belief probability assignments (BPAs) exhibit considerable conflict, unexpected results can occur. To address this limitation, the high-order fractals are explored and a K-order fractal-based Kullback–Leibler divergence (KO-FKL) is introduced, which defines the K-order as the optimal fractal epoch. This measure is employed to quantify the divergence between BPAs and demonstrates superior performance in assessing the conflict between two BPAs in numerical examples, compared to existing belief divergence methods. To utilize the KO-FKL divergence measure to real-world problems, a novel KO-FKL-based multi-source data fusion (KO-FKL-MSDF) algorithm is designed. Through comparisons with well-known related methods, our proposed KO-FKL-MSDF algorithm demonstrates superiority and enhanced robustness. Lastly, the KO-FKL-MSDF algorithm is applied to real-world classification problems, underlining its high practical applicability. •High-order fractal BPA and KL divergence using continuous Pignistic process.•Optimal fractal high-order K via proposed Difference of Deng entropy convergence.•K-order fractal KL divergence outperforms existing measures in plentiful examples.•KO-FKL multi-source data fusion algorithm via extensive validation and analysis.•KO-FKL-MSDF algorithm excels in pattern classification on multiple datasets.