{"doi":"10.1162/089976603321780317","title":"Laplacian Eigenmaps for Dimensionality Reduction and Data Representation","abstract":"<jats:p> One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed. </jats:p>","journal":"Neural Computation","year":2003,"id":1108,"datarank":1.3412710677544748,"base_score":8.941807118363164,"endowment":8.941807118363164,"self_citation_contribution":1.3412710677544748,"citation_network_contribution":0.0,"self_endowment_contribution":1.3412710677544748,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":7644,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.0433,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2003-06-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":14939,"name":"Partha Niyogi","orcid":null,"position":1,"is_corresponding":false},{"id":14938,"name":"Mikhail Belkin","orcid":"0009-0005-8633-3926","position":0,"is_corresponding":true}],"reference_count":9,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-03-01T18:20:47.508186Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}