{"id":"https://openalex.org/W1991799212","doi":"https://doi.org/10.1109/icip.2012.6467015","title":"Invariance of principal components under low-dimensional random projection of the data","display_name":"Invariance of principal components under low-dimensional random projection of the data","publication_year":2012,"publication_date":"2012-09-01","ids":{"openalex":"https://openalex.org/W1991799212","doi":"https://doi.org/10.1109/icip.2012.6467015","mag":"1991799212"},"language":"en","primary_location":{"id":"doi:10.1109/icip.2012.6467015","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2012.6467015","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 19th IEEE International Conference on Image Processing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079958889","display_name":"Hanchao Qi","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hanchao Qi","raw_affiliation_strings":["Department of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, USA","University of Colorado at Boulder,Department of Electrical, Computer, and Energy Engineering,USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"University of Colorado at Boulder,Department of Electrical, Computer, and Energy Engineering,USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102132389","display_name":"Shannon M. Hughes","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shannon M. Hughes","raw_affiliation_strings":["Department of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, USA","University of Colorado at Boulder,Department of Electrical, Computer, and Energy Engineering,USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"University of Colorado at Boulder,Department of Electrical, Computer, and Energy Engineering,USA","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079958889"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":6.2877,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.96747689,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"937","last_page":"940"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9977999925613403,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/principal-component-analysis","display_name":"Principal component analysis","score":0.9066743850708008},{"id":"https://openalex.org/keywords/random-projection","display_name":"Random projection","score":0.770855188369751},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.6536208391189575},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6400498747825623},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5858802199363708},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5684691667556763},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5599725842475891},{"id":"https://openalex.org/keywords/multidimensional-scaling","display_name":"Multidimensional scaling","score":0.5555397868156433},{"id":"https://openalex.org/keywords/sparse-pca","display_name":"Sparse PCA","score":0.5539002418518066},{"id":"https://openalex.org/keywords/data-set","display_name":"Data set","score":0.5474768280982971},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5187206864356995},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43966278433799744},{"id":"https://openalex.org/keywords/clustering-high-dimensional-data","display_name":"Clustering high-dimensional data","score":0.4368029236793518},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41898196935653687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3866897225379944},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.14009490609169006},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.11812165379524231}],"concepts":[{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.9066743850708008},{"id":"https://openalex.org/C2777036070","wikidata":"https://www.wikidata.org/wiki/Q18393452","display_name":"Random projection","level":2,"score":0.770855188369751},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6536208391189575},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6400498747825623},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5858802199363708},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5684691667556763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5599725842475891},{"id":"https://openalex.org/C91682802","wikidata":"https://www.wikidata.org/wiki/Q620538","display_name":"Multidimensional scaling","level":2,"score":0.5555397868156433},{"id":"https://openalex.org/C24252448","wikidata":"https://www.wikidata.org/wiki/Q7573786","display_name":"Sparse PCA","level":3,"score":0.5539002418518066},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.5474768280982971},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5187206864356995},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43966278433799744},{"id":"https://openalex.org/C184509293","wikidata":"https://www.wikidata.org/wiki/Q5136711","display_name":"Clustering high-dimensional data","level":3,"score":0.4368029236793518},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41898196935653687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3866897225379944},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.14009490609169006},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.11812165379524231},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icip.2012.6467015","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2012.6467015","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 19th IEEE International Conference on Image Processing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1534408902","https://openalex.org/W1582742176","https://openalex.org/W2077661892","https://openalex.org/W2095865158","https://openalex.org/W2104266187","https://openalex.org/W2117377454","https://openalex.org/W2145856765","https://openalex.org/W2149631607","https://openalex.org/W2295549646","https://openalex.org/W2511885285","https://openalex.org/W3099514962"],"related_works":["https://openalex.org/W2515532094","https://openalex.org/W2790862734","https://openalex.org/W345943785","https://openalex.org/W2141406155","https://openalex.org/W1576424959","https://openalex.org/W3015962327","https://openalex.org/W2611813480","https://openalex.org/W2624745934","https://openalex.org/W2807562011","https://openalex.org/W3148922054"],"abstract_inverted_index":{"Algorithms":[0],"that":[1,128,156],"can":[2],"efficiently":[3],"recover":[4],"principal":[5,41,98,104,137],"components":[6,99,105,138],"of":[7,18,25,50,70,76,86,106,116,157],"high-dimensional":[8],"data":[9,51,62,71,80,89,109],"from":[10],"compressive":[11],"sensing":[12],"measurements":[13],"(e.g.":[14],"low-dimensional":[15,47],"random":[16,48,118],"projections)":[17],"it":[19],"have":[20],"been":[21],"an":[22],"important":[23],"topic":[24],"recent":[26],"interest":[27],"in":[28,162],"the":[29,54,60,68,74,77,83,87,97,102,107,114,133,163],"literature.":[30],"In":[31,65],"this":[32,129,166],"paper,":[33],"we":[34],"show":[35],"that,":[36],"under":[37],"certain":[38],"conditions,":[39],"normal":[40],"component":[42],"analysis":[43],"(PCA)":[44],"on":[45,59],"such":[46],"projections":[49],"actually":[52],"returns":[53],"same":[55],"result":[56],"as":[57,67,110],"PCA":[58],"original":[61,88,108,134],"set":[63],"would.":[64],"particular,":[66],"number":[69],"samples":[72],"increases,":[73],"center":[75,85,135],"randomly":[78],"projected":[79],"converges":[81],"to":[82,91,101,155],"true":[84,103],"(up":[90],"a":[92],"known":[93],"scaling":[94],"factor)":[95],"and":[96,136,144],"converge":[100],"well,":[111],"even":[112,153],"if":[113],"dimension":[115],"each":[117],"subspace":[119],"used":[120],"is":[121,152],"very":[122,139],"low.":[123],"Indeed,":[124],"experimental":[125],"results":[126],"verify":[127],"approach":[130],"does":[131],"estimate":[132],"well":[140],"for":[141,165],"both":[142],"synthetic":[143],"real-world":[145],"datasets,":[146],"including":[147],"hyperspectral":[148],"data.":[149],"Its":[150],"performance":[151],"superior":[154],"other":[158],"algorithms":[159],"recently":[160],"developed":[161],"literature":[164],"purpose.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":22},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
