{"paper":{"title":"Multiplication-Avoiding Variant of Power Iteration with Applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"eess.SP","authors_text":"Ahmet Enis Cetin, Diaa Badawi, Erdem Koyuncu, Hongyi Pan, Runxuan Miao","submitted_at":"2021-10-22T20:59:49Z","abstract_excerpt":"Power iteration is a fundamental algorithm in data analysis. It extracts the eigenvector corresponding to the largest eigenvalue of a given matrix. Applications include ranking algorithms, recommendation systems, principal component analysis (PCA), among many others. In this paper, we introduce multiplication-avoiding power iteration (MAPI), which replaces the standard $\\ell_2$-inner products that appear at the regular power iteration (RPI) with multiplication-free vector products which are Mercer-type kernel operations related with the $\\ell_1$ norm. Precisely, for an $n\\times n$ matrix, MAPI"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.12065","kind":"arxiv","version":2},"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/2110.12065/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"}