{"paper":{"title":"Mercer Large-Scale Kernel Machines from Ridge Function Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"cs.LG","authors_text":"Karol Dziedziul, Pawe{\\l} Wieczy\\'nski, Sergey Kryzhevich","submitted_at":"2023-07-21T22:08:19Z","abstract_excerpt":"To present Mercer large-scale kernel machines from a ridge function perspective, we recall the results by Lin and Pinkus from {\\it Fundamentality of ridge functions}. We consider the main result of the recent paper by Rachimi and Recht, 2008, {\\it Random features for large-scale kernel machines} from the Approximation Theory point of view. We study which kernels could be approximated by a sum of products of cosine functions with arguments depending on $x$ and $y$ and present the obstacles of such an approach. The results of this article are applied to Image Processing by procedure \"one-vs-rest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.11925","kind":"arxiv","version":3},"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/2307.11925/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"}