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Evolutionary Adaptive Metric Learning: A Multi-Objective Framework for Learning Local Distance Functions in Nearest Neighbor Classification — arXiv:2611.08549

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.08549
License (as archived): CC0-1.0
Archived: 2026-11-09T22:41:11.907Z
SHA-256 of the archived text: cd655e3c6754662f0c740a60b4e7e06929c6eba457c6a0b58f72a09bfdc38d92
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How to cite

Evolutionary Adaptive Metric Learning: A Multi-Objective Framework for Learning Local Distance Functions in Nearest Neighbor Classification — arXiv:2611.08549 — arXiv (en), https://arxiv.org/abs/2611.08549 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_635cd4a9ea2d (Metraipolis archive dc_635cd4a9ea2d, sha256 cd655e3c6754662f0c740a60b4e7e06929c6eba457c6a0b58f72a09bfdc38d92)

BibTeX

@misc{dc635cd4a9ea2d,
  title = {Evolutionary Adaptive Metric Learning: A Multi-Objective Framework for Learning Local Distance Functions in Nearest Neighbor Classification — arXiv:2611.08549},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.08549},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_635cd4a9ea2d; sha256 cd655e3c6754662f0c740a60b4e7e06929c6eba457c6a0b58f72a09bfdc38d92},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.08549. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Nearest neighbour classifiers inherit the geometry of their distance function. Fixed distances and globally learned metrics apply the same geometry throughout the input space, although relevant feature directions may vary across regions. We propose EAML (Evolutionary Adaptive Metric Learning), a framework that learns instance-dependent positive-definite metrics through a low-dimensional parameterization. Each local metric combines an input-dependent diagonal scaling, generated by softmax interpolation between anchor points, with a global low-rank correlation component. A real-coded elitist genetic algorithm optimizes the parameters using a scalar objective combining leave-one-out prediction error, robustness, metric smoothness, and regularization. We establish positive definiteness, metric equivalence, existence of an optimal solution, and Lipschitz continuity of the metric field. We further investigate prediction stability, generalization bounds, and evolutionary convergence under explicit assumptions. Experiments on synthetic data with region-dependent feature relevance show that EAML can recover local metric variations and outperform global metrics. Evaluation on thirteen public datasets using nested 5-fold cross-validation reveals a more nuanced picture: EAML improves performance on selected datasets but does not significantly outperform global metric baselines overall. Additional experiments show that global diagonal metrics can be preferable under nuisance features and test-time noise. These findings identify the conditions under which evolutionary local metric learning is beneficial and highlight its practical limitations.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2611.08549 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-09T22:33:47.135Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).