{"paper":{"title":"Landmark Diffusion Maps (L-dMaps): Accelerated manifold learning out-of-sample extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"stat.ML","authors_text":"2) ((1) Department of Materials Science, (2) Department of Chemical, Andrew L. Ferguson (1, Andrew W. Long (1), Biomolecular Engineering, Engineering, University of Illinois at Urbana-Champaign, University of Illinois at Urbana-Champaign)","submitted_at":"2017-06-28T17:59:48Z","abstract_excerpt":"Diffusion maps are a nonlinear manifold learning technique based on harmonic analysis of a diffusion process over the data. Out-of-sample extensions with computational complexity $\\mathcal{O}(N)$, where $N$ is the number of points comprising the manifold, frustrate applications to online learning applications requiring rapid embedding of high-dimensional data streams. We propose landmark diffusion maps (L-dMaps) to reduce the complexity to $\\mathcal{O}(M)$, where $M \\ll N$ is the number of landmark points selected using pruned spanning trees or k-medoids. Offering $(N/M)$ speedups in out-of-sa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09396","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"}