{"paper":{"title":"Manifold Learning Using Kernel Density Estimation and Local Principal Components Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Hariharan Narayanan, Kitty Mohammed","submitted_at":"2017-09-11T22:45:10Z","abstract_excerpt":"We consider the problem of recovering a $d-$dimensional manifold $\\mathcal{M} \\subset \\mathbb{R}^n$ when provided with noiseless samples from $\\mathcal{M}$. There are many algorithms (e.g., Isomap) that are used in practice to fit manifolds and thus reduce the dimensionality of a given data set. Ideally, the estimate $\\mathcal{M}_\\mathrm{put}$ of $\\mathcal{M}$ should be an actual manifold of a certain smoothness; furthermore, $\\mathcal{M}_\\mathrm{put}$ should be arbitrarily close to $\\mathcal{M}$ in Hausdorff distance given a large enough sample. Generally speaking, existing manifold learning "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03615","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"}