{"paper":{"title":"Deep nets for local manifold learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Charles K. Chui, H. N. Mhaskar","submitted_at":"2016-07-24T23:23:32Z","abstract_excerpt":"The problem of extending a function $f$ defined on a training data $\\mathcal{C}$ on an unknown manifold $\\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\\mathbb{X}$ embedded in a high dimensional ambient Euclidean space $\\mathbb{R}^D$, a deep learning algorithm is developed for finding a local coordinate system for the manifold {\\bf without eigen--decomposition}, which reduces the problem to the classical problem of function approximation on a low dimensional cube. Deep nets (or multilayered neural networks) are proposed to accom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07110","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"}