{"id":"W2963201904","doi":"","title":"Dimensionality Reduction has Quantifiable Imperfections: Two Geometric Bounds","year":2018,"lang":"en","type":"article","venue":"Neural Information Processing Systems","topic":"Topological and Geometric Data Analysis","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto; University of Alberta","funders":"","keywords":"Measure (data warehouse); Dimensionality reduction; Mathematical proof; Computer science; Reduction (mathematics); Lipschitz continuity; Key (lock); Curse of dimensionality; Algorithm; Mathematics; Mathematical optimization; Point (geometry); Set (abstract data type); Topology (electrical circuits); Data mining; Artificial intelligence; Combinatorics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.01893924,0.00245472,0.003054005,0.00397098,0.002107368,0.00763047,0.003561981,0.004299086,0.004028408],"category_scores_gemma":[0.1264084,0.001712889,0.002463178,0.003566789,0.01448887,0.02583669,0.01329394,0.009580063,0.0006602131],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.005162223,"about_ca_system_score_gemma":0.00151048,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001194583,"about_ca_topic_score_gemma":0.0005688166,"domain_scores_codex":[0.9787105,0.006004469,0.001428184,0.004397871,0.008043058,0.001415934],"domain_scores_gemma":[0.8616626,0.09741894,0.01044965,0.02165238,0.006627856,0.002188578],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001072749,0.00005833693,0.00123038,0.0002935451,0.00009104824,0.0001641737,0.0004381769,0.05696853,0.001514826,0.9002838,0.001934058,0.03691583],"study_design_scores_gemma":[0.00002041463,0.0001411194,0.000982905,0.000120547,0.00004555239,0.0002850488,0.00009046672,0.1513578,0.003218948,0.840311,0.003340336,0.0000857725],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02651263,0.004228335,0.9506854,0.005321116,0.0001505176,0.00007835135,0.0002465544,0.0004103423,0.01236669],"genre_scores_gemma":[0.7234767,0.003371211,0.2637277,0.001487827,0.001119436,0.0005218307,0.0004991341,0.0005693287,0.005226836],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01893924,"threshold_uncertainty_score":0.1001615,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04108341971202272,"score_gpt":0.2859869168908117,"score_spread":0.244903497178789,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}