{"paper":{"title":"Practical Algorithms for Learning Near-Isometric Linear Embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Hao-Jun Michael Shi, Jerry Luo, Kan Zhu, Kayla Shapiro, Qi Yang","submitted_at":"2016-01-01T09:06:11Z","abstract_excerpt":"We propose two practical non-convex approaches for learning near-isometric, linear embeddings of finite sets of data points. Given a set of training points $\\mathcal{X}$, we consider the secant set $S(\\mathcal{X})$ that consists of all pairwise difference vectors of $\\mathcal{X}$, normalized to lie on the unit sphere. The problem can be formulated as finding a symmetric and positive semi-definite matrix $\\boldsymbol{\\Psi}$ that preserves the norms of all the vectors in $S(\\mathcal{X})$ up to a distortion parameter $\\delta$. Motivated by non-negative matrix factorization, we reformulate our pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00062","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":""},"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"}