{"paper":{"title":"Faster Binary Embeddings for Preserving Euclidean Distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","stat.ML"],"primary_cat":"cs.IT","authors_text":"Jinjie Zhang, Rayan Saab","submitted_at":"2020-10-01T22:41:41Z","abstract_excerpt":"We propose a fast, distance-preserving, binary embedding algorithm to transform a high-dimensional dataset $\\mathcal{T}\\subseteq\\mathbb{R}^n$ into binary sequences in the cube $\\{\\pm 1\\}^m$. When $\\mathcal{T}$ consists of well-spread (i.e., non-sparse) vectors, our embedding method applies a stable noise-shaping quantization scheme to $A x$ where $A\\in\\mathbb{R}^{m\\times n}$ is a sparse Gaussian random matrix. This contrasts with most binary embedding methods, which usually use $x\\mapsto \\mathrm{sign}(Ax)$ for the embedding. Moreover, we show that Euclidean distances among the elements of $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00712","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/2010.00712/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"}