Consensus Ranking via Entropy-Based Multi-Objective Optimization: Application of Selection of Biomarker Candidates

Aggregating multiple ordered lists (or score scales) into a single consensus ranking is a recurrent need in decision support, information retrieval, and biomedical feature selection. In EEG biomarker screening, for instance, candidate features may be judged under several clinical and signal-quality criteria, which often leads to partially conflicting rankings. We propose an entropy-based multi-objective aggregation framework that converts heterogeneous inputs (total orders or scales) into a unified optimization problem. The method minimizes a discrepancy objective that can be instantiated with entropy-related divergences (e.g., Kullback–Leibler, Hellinger, or Pearson χ 2 ) and can incorporate rank disagreement through Kendall-type distances, while enforcing feasibility constraints on the aggregated distribution. The resulting continuous solution is then mapped to a discrete consensus permutation through a linear assignment formulation. We demonstrate the approach on an EEG biomarker candidate set evaluated by multiple criteria and show how the proposed aggregation produces a single ordered shortlist that is consistent with the global trade-offs visible in the PCA biplot (Fig. 1). To situate the contribution, we additionally compare against standard rank-aggregation baselines (e.g., Borda and median/Kendall aggregation) using agreement and stability metrics. We finally discuss computational complexity, scalability to larger candidate sets, and practical limitations, with guidance for realtime or large-scale deployments.