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About this paper
Alexander J. Gates
Alexander J. Gates developed an analytical framework that unifies pair-counting and information-theoretic clustering similarity measures by demonstrating their shared dependence on an independence baseline and their differing weighting schemes for deviations. This work introduces a hierarchy of higher-order tuple-counting measures, connecting them to Rényi entropies, to offer a more nuanced understanding of structural coherence.
Key insights
- Mutual Information's effective weighting scheme up-weights deviations in rare cells, making it sensitive to fine-grained alignments in smaller clusters.
- Pair-counting measures, lacking marginal weighting, primarily react to large absolute deviations, thus prioritizing agreement within high-mass clusters.
- The k-tuple hierarchy provides a spectrum of similarity measures that capture increasingly complex co-assignment patterns, from simple pairs to higher-order group consistency.
Summary by alphaXiv.
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