Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2001141328', 'doi': 'https://doi.org/10.1126/science.290.5500.2319', 'title': 'A Global Geometric Framework for Nonlinear Dimensionality Reduction', 'display_name': 'A Global Geometric Framework for Nonlinear Dimensionality Reduction', 'publication_year': 2000, 'publication_date': '2000-12-22', 'ids': {'openalex': 'https://openalex.org/W2001141328', 'doi': 'https://doi.org/10.1126/science.290.5500.2319', 'mag': '2001141328', 'pmid': 'https://pubmed.ncbi.nlm.nih.gov/11125149'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1126/science.290.5500.2319', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S3880285', 'display_name': 'Science', 'issn_l': '0036-8075', 'issn': ['0036-8075', '1095-9203'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315823', 'host_organization_name': 'American Association for the Advancement of Science', 'host_organization_lineage': ['https://openalex.org/P4310315823'], 'host_organization_lineage_names': ['American Association for the Advancement of Science'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref', 'pubmed'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5071093940', 'display_name': 'Joshua B. Tenenbaum', 'orcid': 'https://orcid.org/0000-0002-1925-2035'}, 'institutions': [{'id': 'https://openalex.org/I97018004', 'display_name': 'Stanford University', 'ror': 'https://ror.org/00f54p054', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I97018004']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Joshua B. Tenenbaum', 'raw_affiliation_strings': ['Department of Psychology, Stanford University, Stanford, CA 94305, USA. [email protected]'], 'affiliations': [{'raw_affiliation_string': 'Department of Psychology, Stanford University, Stanford, CA 94305, USA. [email protected]', 'institution_ids': ['https://openalex.org/I97018004']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5045901848', 'display_name': 'Vin de Silva', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I97018004', 'display_name': 'Stanford University', 'ror': 'https://ror.org/00f54p054', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I97018004']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Vin de Silva', 'raw_affiliation_strings': ['Department of Mathematics, Stanford University, Stanford, CA 94305, USA.'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Stanford University, Stanford, CA 94305, USA.', 'institution_ids': ['https://openalex.org/I97018004']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5005003250', 'display_name': 'John Langford', 'orcid': 'https://orcid.org/0000-0002-9811-3550'}, 'institutions': [{'id': 'https://openalex.org/I74973139', 'display_name': 'Carnegie Mellon University', 'ror': 'https://ror.org/05x2bcf33', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I74973139']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'John C. Langford', 'raw_affiliation_strings': ['Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15217, USA.'], 'affiliations': [{'raw_affiliation_string': 'Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15217, USA.', 'institution_ids': ['https://openalex.org/I74973139']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 68.783, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 13279, 'citation_normalized_percentile': {'value': 0.999797, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 99, 'max': 100}, 'biblio': {'volume': '290', 'issue': '5500', 'first_page': '2319', 'last_page': '2323'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10688', 'display_name': 'Image and Signal Denoising Methods', 'score': 0.9942, 'subfield': {'id': 'https://openalex.org/subfields/1707', 'display_name': 'Computer Vision and Pattern Recognition'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10688', 'display_name': 'Image and Signal Denoising Methods', 'score': 0.9942, 'subfield': {'id': 'https://openalex.org/subfields/1707', 'display_name': 'Computer Vision and Pattern Recognition'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11447', 'display_name': 'Blind Source Separation Techniques', 'score': 0.9941, 'subfield': {'id': 'https://openalex.org/subfields/1711', 'display_name': 'Signal Processing'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10689', 'display_name': 'Remote-Sensing Image Classification', 'score': 0.994, 'subfield': {'id': 'https://openalex.org/subfields/2214', 'display_name': 'Media Technology'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/isomap', 'display_name': 'Isomap', 'score': 0.62201434}, {'id': 'https://openalex.org/keywords/multidimensional-scaling', 'display_name': 'Multidimensional scaling', 'score': 0.5631354}, {'id': 'https://openalex.org/keywords/diffusion-map', 'display_name': 'Diffusion map', 'score': 0.5420036}, {'id': 'https://openalex.org/keywords/handwriting', 'display_name': 'Handwriting', 'score': 0.44288898}], 'concepts': [{'id': 'https://openalex.org/C70518039', 'wikidata': 'https://www.wikidata.org/wiki/Q16000077', 'display_name': 'Dimensionality reduction', 'level': 2, 'score': 0.8211601}, {'id': 'https://openalex.org/C27438332', 'wikidata': 'https://www.wikidata.org/wiki/Q2873', 'display_name': 'Principal component analysis', 'level': 2, 'score': 0.6501244}, {'id': 'https://openalex.org/C2778626561', 'wikidata': 'https://www.wikidata.org/wiki/Q6086067', 'display_name': 'Isomap', 'level': 4, 'score': 0.62201434}, {'id': 'https://openalex.org/C151876577', 'wikidata': 'https://www.wikidata.org/wiki/Q7049464', 'display_name': 'Nonlinear dimensionality reduction', 'level': 3, 'score': 0.59570044}, {'id': 'https://openalex.org/C91682802', 'wikidata': 'https://www.wikidata.org/wiki/Q620538', 'display_name': 'Multidimensional scaling', 'level': 2, 'score': 0.5631354}, {'id': 'https://openalex.org/C158622935', 'wikidata': 'https://www.wikidata.org/wiki/Q660848', 'display_name': 'Nonlinear system', 'level': 2, 'score': 0.5555341}, {'id': 'https://openalex.org/C111030470', 'wikidata': 'https://www.wikidata.org/wiki/Q1430460', 'display_name': 'Curse of dimensionality', 'level': 2, 'score': 0.5518006}, {'id': 'https://openalex.org/C176217482', 'wikidata': 'https://www.wikidata.org/wiki/Q860554', 'display_name': 'Metric (unit)', 'level': 2, 'score': 0.5497957}, {'id': 'https://openalex.org/C55128770', 'wikidata': 'https://www.wikidata.org/wiki/Q5275440', 'display_name': 'Diffusion map', 'level': 4, 'score': 0.5420036}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.54126155}, {'id': 'https://openalex.org/C111335779', 'wikidata': 'https://www.wikidata.org/wiki/Q3454686', 'display_name': 'Reduction (mathematics)', 'level': 2, 'score': 0.4999833}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.48890868}, {'id': 'https://openalex.org/C177264268', 'wikidata': 'https://www.wikidata.org/wiki/Q1514741', 'display_name': 'Set (abstract data type)', 'level': 2, 'score': 0.44959277}, {'id': 'https://openalex.org/C153180895', 'wikidata': 'https://www.wikidata.org/wiki/Q7148389', 'display_name': 'Pattern recognition (psychology)', 'level': 2, 'score': 0.44622087}, {'id': 'https://openalex.org/C208081375', 'wikidata': 'https://www.wikidata.org/wiki/Q274502', 'display_name': 'Degrees of freedom (physics and chemistry)', 'level': 2, 'score': 0.44396108}, {'id': 'https://openalex.org/C2779386606', 'wikidata': 'https://www.wikidata.org/wiki/Q2393642', 'display_name': 'Handwriting', 'level': 2, 'score': 0.44288898}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.31836534}, {'id': 'https://openalex.org/C119857082', 'wikidata': 'https://www.wikidata.org/wiki/Q2539', 'display_name': 'Machine learning', 'level': 1, 'score': 0.22861987}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.13065657}, {'id': 'https://openalex.org/C21547014', 'wikidata': 'https://www.wikidata.org/wiki/Q1423657', 'display_name': 'Operations management', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}], 'mesh': [{'descriptor_ui': 'D000465', 'descriptor_name': 'Algorithms', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': True}, {'descriptor_ui': 'D010364', 'descriptor_name': 'Pattern Recognition, Visual', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': True}, {'descriptor_ui': 'D014796', 'descriptor_name': 'Visual Perception', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': True}, {'descriptor_ui': 'D001185', 'descriptor_name': 'Artificial Intelligence', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D005145', 'descriptor_name': 'Face', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D006801', 'descriptor_name': 'Humans', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}, {'descriptor_ui': 'D008433', 'descriptor_name': 'Mathematics', 'qualifier_ui': '', 'qualifier_name': None, 'is_major_topic': False}], 'locations_count': 2, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1126/science.290.5500.2319', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S3880285', 'display_name': 'Science', 'issn_l': '0036-8075', 'issn': ['0036-8075', '1095-9203'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315823', 'host_organization_name': 'American Association for the Advancement of Science', 'host_organization_lineage': ['https://openalex.org/P4310315823'], 'host_organization_lineage_names': ['American Association for the Advancement of Science'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://pubmed.ncbi.nlm.nih.gov/11125149', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306525036', 'display_name': 'PubMed', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1299303238', 'host_organization_name': 'National Institutes of Health', 'host_organization_lineage': ['https://openalex.org/I1299303238'], 'host_organization_lineage_names': ['National Institutes of Health'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [{'id': 'https://metadata.un.org/sdg/13', 'display_name': 'Climate action', 'score': 0.83}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 26, 'referenced_works': ['https://openalex.org/W1509342228', 'https://openalex.org/W1967087917', 'https://openalex.org/W1967550037', 'https://openalex.org/W1983520516', 'https://openalex.org/W1989674304', 'https://openalex.org/W2001460034', 'https://openalex.org/W2029428797', 'https://openalex.org/W2032647857', 'https://openalex.org/W2046432185', 'https://openalex.org/W2047870719', 'https://openalex.org/W2051719061', 'https://openalex.org/W2055688528', 'https://openalex.org/W2070320140', 'https://openalex.org/W2072706575', 'https://openalex.org/W2086220442', 'https://openalex.org/W2099741732', 'https://openalex.org/W2101701835', 'https://openalex.org/W2107636931', 'https://openalex.org/W2108384452', 'https://openalex.org/W2122538988', 'https://openalex.org/W2123977795', 'https://openalex.org/W2131477567', 'https://openalex.org/W2138451337', 'https://openalex.org/W3099624472', 'https://openalex.org/W4232015735', 'https://openalex.org/W4251002338'], 'related_works': ['https://openalex.org/W4294294766', 'https://openalex.org/W3193686696', 'https://openalex.org/W3086013422', 'https://openalex.org/W2992760655', 'https://openalex.org/W2394040199', 'https://openalex.org/W2375574759', 'https://openalex.org/W2153105632', 'https://openalex.org/W2119700376', 'https://openalex.org/W2037225398', 'https://openalex.org/W1991207049'], 'abstract_inverted_index': {'Scientists': [0], 'working': [1], 'with': [2], 'large': [3], 'volumes': [4], 'of': [5, 23, 62, 89, 110, 115, 128, 156], 'high-dimensional': [6, 33, 48], 'data,': [7], 'such': [8, 96, 122], 'as': [9, 97, 123], 'global': [10, 87], 'climate': [11], 'patterns,': [12], 'stellar': [13], 'spectra,': [14], 'or': [15, 54, 126], 'human': [16, 36, 124], 'gene': [17], 'distributions,': [18], 'regularly': [19], 'confront': [20], 'the': [21, 39, 85, 112, 165], 'problem': [22, 41], 'dimensionality': [24, 73, 142], 'reduction:': [25], 'finding': [26], 'meaningful': [27], 'low-dimensional': [28], 'structures': [29], 'hidden': [30], 'in': [31, 42], 'their': [32], 'observations.': [34], 'The': [35], 'brain': [37], 'confronts': [38], 'same': [40], 'everyday': [43], 'perception,': [44], 'extracting': [45], 'from': [46], 'its': [47], 'sensory': [49], 'inputs—30,000': [50], 'auditory': [51], 'nerve': [52, 57], 'fibers': [53], '106': [55], 'optic': [56], 'fibers—a': [58], 'manageably': [59], 'small': [60], 'number': [61], 'perceptually': [63], 'relevant': [64], 'features.': [65], 'Here': [66], 'we': [67], 'describe': [68], 'an': [69, 153], 'approach': [70, 107], 'to': [71, 83, 137, 161, 164], 'solving': [72], 'reduction': [74], 'problems': [75], 'that': [76, 117], 'uses': [77], 'easily': [78], 'measured': [79], 'local': [80], 'metric': [81], 'information': [82], 'learn': [84], 'underlying': [86], 'geometry': [88], 'a': [90, 129, 147], 'data': [91, 157], 'set.': [92], 'Unlike': [93], 'classical': [94], 'techniques': [95], 'principal': [98], 'component': [99], 'analysis': [100], '(PCA)': [101], 'and': [102], 'multidimensional': [103], 'scaling': [104], '(MDS),': [105], 'our': [106], 'is': [108, 159], 'capable': [109], 'discovering': [111], 'nonlinear': [113, 141], 'degrees': [114], 'freedom': [116], 'underlie': [118], 'complex': [119], 'natural': [120], 'observations,': [121], 'handwriting': [125], 'images': [127], 'face': [130], 'under': [131], 'different': [132], 'viewing': [133], 'conditions.': [134], 'In': [135], 'contrast': [136], 'previous': [138], 'algorithms': [139], 'for': [140, 152], 'reduction,': [143], 'ours': [144], 'efficiently': [145], 'computes': [146], 'globally': [148], 'optimal': [149], 'solution,': [150], 'and,': [151], 'important': [154], 'class': [155], 'manifolds,': [158], 'guaranteed': [160], 'converge': [162], 'asymptotically': [163], 'true': [166], 'structure.': [167]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2001141328', 'counts_by_year': [{'year': 2024, 'cited_by_count': 353}, {'year': 2023, 'cited_by_count': 535}, {'year': 2022, 'cited_by_count': 589}, {'year': 2021, 'cited_by_count': 802}, {'year': 2020, 'cited_by_count': 821}, {'year': 2019, 'cited_by_count': 845}, {'year': 2018, 'cited_by_count': 743}, {'year': 2017, 'cited_by_count': 673}, {'year': 2016, 'cited_by_count': 684}, {'year': 2015, 'cited_by_count': 751}, {'year': 2014, 'cited_by_count': 771}, {'year': 2013, 'cited_by_count': 732}, {'year': 2012, 'cited_by_count': 730}], 'updated_date': '2024-12-21T11:00:55.659456', 'created_date': '2016-06-24'}