{"paper":{"title":"On The Radon-Nikodym Spectral Approach With Optimal Clustering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CV","cs.NA","math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Vladislav Gennadievich Malyshkin","submitted_at":"2019-06-02T17:57:08Z","abstract_excerpt":"Problems of interpolation, classification, and clustering are considered. In the tenets of Radon--Nikodym approach $\\langle f(\\mathbf{x})\\psi^2 \\rangle / \\langle\\psi^2\\rangle$, where the $\\psi(\\mathbf{x})$ is a linear function on input attributes, all the answers are obtained from a generalized eigenproblem $|f|\\psi^{[i]}\\rangle = \\lambda^{[i]} |\\psi^{[i]}\\rangle$. The solution to the interpolation problem is a regular Radon-Nikodym derivative. The solution to the classification problem requires prior and posterior probabilities that are obtained using the Lebesgue quadrature[1] technique. Whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00460","kind":"arxiv","version":17},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1906.00460/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}