{"paper":{"title":"Spectral Approaches to Nearest Neighbor Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexandr Andoni, Amirali Abdullah, Ravindran Kannan, Robert Krauthgamer","submitted_at":"2014-08-04T17:51:17Z","abstract_excerpt":"We study spectral algorithms for the high-dimensional Nearest Neighbor Search problem (NNS). In particular, we consider a semi-random setting where a dataset $P$ in $\\mathbb{R}^d$ is chosen arbitrarily from an unknown subspace of low dimension $k\\ll d$, and then perturbed by fully $d$-dimensional Gaussian noise. We design spectral NNS algorithms whose query time depends polynomially on $d$ and $\\log n$ (where $n=|P|$) for large ranges of $k$, $d$ and $n$. Our algorithms use a repeated computation of the top PCA vector/subspace, and are effective even when the random-noise magnitude is {\\em muc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0751","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}