Artificial Intelligence · 11.08.2026, 17:55 UTC
Machine Learning and Data Analysis Using Posets: A Survey
| Schweregrad | info |
|---|---|
| Kategorie | Artificial Intelligence |
| Quelle | arXiv cs.LG ↗ |
| Veröffentlicht | 11.08.2026 UTC |
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arXiv:2404.03082v3 Announce Type: replace Abstract: Partially ordered sets (posets) are discrete mathematical structures that formalize the notion of comparison without forcing every pair of objects to be comparable. This makes them a natural representation for the many machine learning and data-analysis settings in which objects are related by dominance, containment, priority, or refinement relations rather than by a single scalar score. Over the past two decades, a substantial and fragmented literature has connected posets and lattice theory to ranking, clustering, formal concept analysis, multidimensional and multi-criteria data analysis, structured and safe learning, graph and topological deep learning, and explainable artificial intelligence, spanning a wide range of application domains. Despite this activity, the field has lacked (i) an organizing taxonomy that relates these disparate strands of work, and (ii) an up-to-date account extending through 2025--2026 that incorporates recent developments in poset-structured learning methods, including poset-structured safety layers for reinforcement learning, poset-valued neural pooling operators, functor-calculus approaches to multiparameter persistent homology. This survey addresses both gaps. We propose a four-axis taxonomy of poset-based methods (representation, learning paradigm, data modality, and task), provide a comprehensive and comparative review of representative models and algorithms organized along this taxonomy, curate an extensive collection of datasets, software packages, and algorithmic resources, and …