A Penalized Likelihood Method for Classification With Matrix-Valued Predictors

We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean ma...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of computational and graphical statistics Jg. 28; H. 1; S. 11 - 22
Hauptverfasser: Molstad, Aaron J., Rothman, Adam J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Alexandria Taylor & Francis 02.01.2019
American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America
Taylor & Francis Ltd
Schlagworte:
Algorithms
Alternating minimization algorithm
Classification
Discriminant analysis
Estimators
Mathematical models
Matrix methods
Optimization
Optimization with Penalization
Penalized likelihood
ISSN:1061-8600, 1537-2715
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method's applicability. Supplementary materials, including an R package implementing our method, are available online.
AbstractList We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method's applicability. Supplementary materials, including an R package implementing our method, are available online.
Author Molstad, Aaron J.
Rothman, Adam J.
Author_xml – sequence: 1
  givenname: Aaron J.
  surname: Molstad
  fullname: Molstad, Aaron J.
  email: amolstad@fredhutch.org
  organization: Biostatistics Program, Fred Hutchinson Cancer Research Center
– sequence: 2
  givenname: Adam J.
  surname: Rothman
  fullname: Rothman, Adam J.
  organization: School of Statistics, University of Minnesota
BookMark eNqFkMlKQzEUhoMoOD6CcMH1rZmT4kYpTlCHhcMypBlo6vVGkxSHpze16sKFrk445_9OON8mWO1j7wDYRXCAoIT7CHIkOYQDDJEcICo4psMVsIEYES0WiK3Wd820i9A62Mx5BiFEfCg2wOVRc-163YV3Z5txeHBdmMZomwtXprX4mJpRp3MOPhhdQuyb-1CmzYUuKby2d7qbV-46ORtMiSlvgzWvu-x2vuoWuD05vhmdteOr0_PR0bg1hMPSejrB2FFtiOETSbhAEiGIGSZDgjlHRlNp4URIz63EzNaGl1YMpbCeYkbJFthb7n1K8XnuclGzOE_1jqwwRoIyxugidbBMmRRzTs4rE8rnFSXp0CkE1UKg-haoFgLVl8BKs1_0UwqPOr39y-0uuVmuSn4gyhBhUPI6P1zOQ1_1PuqXmDqrin7rYvJJ9yZkRf7-4gMo-ZFV
CitedBy_id crossref_primary_10_1080_10618600_2019_1696208
crossref_primary_10_1109_LSP_2024_3378578
crossref_primary_10_1093_biostatistics_kxab007
crossref_primary_10_1002_sta4_720
crossref_primary_10_1016_j_jeconom_2021_09_014
crossref_primary_10_1016_j_patcog_2023_109803
crossref_primary_10_1007_s13171_021_00255_2
Cites_doi 10.1080/00949659908811970
10.1080/01621459.2014.998760
10.1214/13-AOS1187
10.1198/jcgs.2011.11051a
10.1016/j.jmva.2012.03.013
10.1016/j.jmva.2005.07.005
10.1137/120896219
10.3150/bj/1106314847
10.5705/ss.202016.0117
10.1137/0329006
10.1214/009053605000000200
10.1093/bioinformatics/btq046
10.1007/978-0-387-21706-2
10.1080/10618600.2015.1114491
10.32614/CRAN.package.eegkit
10.1561/2200000016
10.1109/SSP.2012.6319849
10.1111/biom.12633
10.1016/S0895-7177(97)00265-3
10.1371/journal.pbio.0030002
10.1109/TPAMI.2008.167
10.1111/j.1467-9868.2011.00783.x
10.1093/biostatistics/kxq023
10.1214/11-AOAS494
10.1214/11-BA606
10.1093/biostatistics/kxm045
10.1016/j.jmva.2015.05.019
10.1080/00401706.2014.965347
10.1093/biostatistics/kxs023
10.1561/2400000003
10.1093/biomet/asu049
10.1198/TECH.2011.08118
10.1080/01621459.2012.706133
10.1198/jcgs.2010.09188
10.1080/01621459.2016.1193022
10.1016/j.patrec.2004.09.007
10.1111/rssb.12031
10.1080/10618600.2014.948181
10.1214/09-AOS737
10.1016/j.cam.2012.09.017
10.1214/09-AOAS314
ContentType Journal Article
Copyright 2019 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America 2019
2019 American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America
2019 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
Copyright_xml – notice: 2019 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America 2019
– notice: 2019 American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America
– notice: 2019 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
DBID AAYXX
CITATION
JQ2
DOI 10.1080/10618600.2018.1476249
DatabaseName CrossRef
ProQuest Computer Science Collection
DatabaseTitle CrossRef
ProQuest Computer Science Collection
DatabaseTitleList ProQuest Computer Science Collection
DeliveryMethod fulltext_linktorsrc
Discipline Statistics
Mathematics
EISSN 1537-2715
EndPage 22
ExternalDocumentID 10_1080_10618600_2018_1476249
45135086
1476249
Genre Article
GroupedDBID -~X
.4S
.7F
.DC
.QJ
0BK
0R~
2AX
30N
4.4
5GY
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABBHK
ABCCY
ABFAN
ABFIM
ABJNI
ABLIJ
ABLJU
ABPAQ
ABPEM
ABQDR
ABTAI
ABXUL
ABXYU
ABYWD
ACGFO
ACGFS
ACIWK
ACMTB
ACTIO
ACTMH
ADCVX
ADGTB
ADODI
ADXHL
AEGXH
AELLO
AENEX
AEOZL
AEPSL
AEUPB
AEYOC
AFRVT
AFVYC
AGDLA
AGMYJ
AHDZW
AIAGR
AIJEM
AKBRZ
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
ALRMG
AMVHM
AQRUH
AQTUD
ARCSS
AVBZW
AWYRJ
BLEHA
CCCUG
CS3
D0L
DGEBU
DKSSO
DQDLB
DSRWC
DU5
EBS
ECEWR
EJD
E~A
E~B
F5P
GTTXZ
H13
HF~
HQ6
HZ~
H~P
IPNFZ
IPSME
J.P
JAA
JAAYA
JBMMH
JBZCM
JENOY
JHFFW
JKQEH
JLEZI
JLXEF
JMS
JPL
JST
KYCEM
LJTGL
M4Z
MS~
NA5
NY~
O9-
P2P
PQQKQ
RIG
RNANH
ROSJB
RTWRZ
RWL
RXW
S-T
SA0
SNACF
TAE
TASJS
TBQAZ
TDBHL
TEJ
TFL
TFT
TFW
TN5
TTHFI
TUROJ
TUS
UT5
UU3
WZA
XWC
ZGOLN
~S~
AAYXX
CITATION
JQ2
ID FETCH-LOGICAL-c360t-f4b22e4ac3c6b8367181102523932661ca48d0b78f6d825d1caf8d7987df42543
IEDL.DBID TFW
ISICitedReferencesCount 12
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000465333200002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1061-8600
IngestDate Wed Aug 13 09:38:42 EDT 2025
Sat Nov 29 07:48:48 EST 2025
Tue Nov 18 22:02:54 EST 2025
Tue Nov 11 03:03:29 EST 2025
Mon Oct 20 23:49:38 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c360t-f4b22e4ac3c6b8367181102523932661ca48d0b78f6d825d1caf8d7987df42543
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 2217455544
PQPubID 29738
PageCount 12
ParticipantIDs proquest_journals_2217455544
informaworld_taylorfrancis_310_1080_10618600_2018_1476249
jstor_primary_45135086
crossref_citationtrail_10_1080_10618600_2018_1476249
crossref_primary_10_1080_10618600_2018_1476249
PublicationCentury 2000
PublicationDate 2019-01-02
PublicationDateYYYYMMDD 2019-01-02
PublicationDate_xml – month: 01
  year: 2019
  text: 2019-01-02
  day: 02
PublicationDecade 2010
PublicationPlace Alexandria
PublicationPlace_xml – name: Alexandria
PublicationTitle Journal of computational and graphical statistics
PublicationYear 2019
Publisher Taylor & Francis
American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America
Taylor & Francis Ltd
Publisher_xml – name: Taylor & Francis
– name: American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America
– name: Taylor & Francis Ltd
References cit0011
cit0033
cit0034
cit0031
cit0010
Zhang Y. (cit0043) 2010
cit0030
Gupta A. K. (cit0012) 2000
cit0019
cit0017
cit0039
cit0018
Buuren S. van (cit0005) 2010; 45
cit0037
cit0016
cit0038
cit0013
cit0035
cit0014
cit0036
cit0022
cit0044
cit0001
cit0023
cit0045
cit0020
cit0042
cit0021
cit0040
cit0041
R Core Team (cit0032) 2017
Lyu T. (cit0025) 2017; 18
cit0008
cit0009
cit0006
cit0028
cit0007
cit0029
cit0004
cit0026
cit0027
cit0002
cit0024
cit0046
cit0003
cit0047
References_xml – ident: cit0008
  doi: 10.1080/00949659908811970
– ident: cit0029
  doi: 10.1080/01621459.2014.998760
– volume: 45
  start-page: 1
  year: 2010
  ident: cit0005
  publication-title: Journal of Statistical Software
– ident: cit0046
  doi: 10.1214/13-AOS1187
– ident: cit0038
  doi: 10.1198/jcgs.2011.11051a
– ident: cit0020
  doi: 10.1016/j.jmva.2012.03.013
– ident: cit0028
  doi: 10.1016/j.jmva.2005.07.005
– ident: cit0010
  doi: 10.1137/120896219
– ident: cit0003
  doi: 10.3150/bj/1106314847
– ident: cit0026
  doi: 10.5705/ss.202016.0117
– ident: cit0035
  doi: 10.1137/0329006
– ident: cit0017
  doi: 10.1214/009053605000000200
– ident: cit0031
  doi: 10.1093/bioinformatics/btq046
– ident: cit0037
  doi: 10.1007/978-0-387-21706-2
– ident: cit0047
  doi: 10.1080/10618600.2015.1114491
– ident: cit0013
  doi: 10.32614/CRAN.package.eegkit
– ident: cit0004
  doi: 10.1561/2200000016
– ident: cit0036
  doi: 10.1109/SSP.2012.6319849
– ident: cit0040
  doi: 10.1111/biom.12633
– volume-title: R: A Language and Environment for Statistical Computing
  year: 2017
  ident: cit0032
– ident: cit0018
  doi: 10.1016/S0895-7177(97)00265-3
– ident: cit0002
  doi: 10.1371/journal.pbio.0030002
– ident: cit0019
  doi: 10.1109/TPAMI.2008.167
– ident: cit0039
  doi: 10.1111/j.1467-9868.2011.00783.x
– ident: cit0011
  doi: 10.1093/biostatistics/kxq023
– ident: cit0042
  doi: 10.1214/11-AOAS494
– ident: cit0014
  doi: 10.1214/11-BA606
– ident: cit0009
  doi: 10.1093/biostatistics/kxm045
– ident: cit0033
  doi: 10.1016/j.jmva.2015.05.019
– ident: cit0044
  doi: 10.1080/00401706.2014.965347
– ident: cit0016
  doi: 10.1093/biostatistics/kxs023
– ident: cit0030
  doi: 10.1561/2400000003
– ident: cit0041
  doi: 10.1093/biomet/asu049
– ident: cit0007
  doi: 10.1198/TECH.2011.08118
– ident: cit0021
  doi: 10.1080/01621459.2012.706133
– ident: cit0034
  doi: 10.1198/jcgs.2010.09188
– ident: cit0023
  doi: 10.1080/01621459.2016.1193022
– ident: cit0024
  doi: 10.1016/j.patrec.2004.09.007
– ident: cit0045
  doi: 10.1111/rssb.12031
– ident: cit0006
  doi: 10.1080/10618600.2014.948181
– volume: 18
  start-page: 434
  year: 2017
  ident: cit0025
  publication-title: Biostatistics
– volume-title: Matrix Variate Distributions
  year: 2000
  ident: cit0012
– ident: cit0022
  doi: 10.1214/09-AOS737
– ident: cit0027
  doi: 10.1016/j.cam.2012.09.017
– ident: cit0001
  doi: 10.1214/09-AOAS314
– start-page: 2550
  year: 2010
  ident: cit0043
  publication-title: Advances in Neural Information Processing Systems
SSID ssj0001697
Score 2.3038845
Snippet We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the...
SourceID proquest
crossref
jstor
informaworld
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 11
SubjectTerms Algorithms
Alternating minimization algorithm
Classification
Discriminant analysis
Estimators
Mathematical models
Matrix methods
Optimization
Optimization with Penalization
Penalized likelihood
Title A Penalized Likelihood Method for Classification With Matrix-Valued Predictors
URI https://www.tandfonline.com/doi/abs/10.1080/10618600.2018.1476249
https://www.jstor.org/stable/45135086
https://www.proquest.com/docview/2217455544
Volume 28
WOSCitedRecordID wos000465333200002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor & Francis Journals Complete
  customDbUrl:
  eissn: 1537-2715
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0001697
  issn: 1061-8600
  databaseCode: TFW
  dateStart: 19920301
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NT8IwFG8M8YAHP1AiiqYHr1PpurU7EiPxAIQDordlXdtIJGhgGONf73tdRyTGeNDjlrx1a99n9-vvEXIhYpUngqnAcM0DnicyUCYGu4rAM4bCKumwOZO-GA7l42My8mjCpYdVYg1tS6II56vRuDO1rBBxV1jFSAjUCMySYOpgzxyP8EFmj6C-ce9h7Ys7vr0KSAQoUp3h-ekpG9Fpg7u0wit-89kuEPX2_uET9smuz0Jpt1SbA7Jl5g2yM1hTuC4bpI5paMnifEiGXToymLJ_GE3702czmyIdMh24_tMU3p-67pqIO3JLTR-mxRMdIP__ezDJZiuQGy3wpxB29zki973b8c1d4DsxBHkYXxeB5Yoxw7M8zGMlwxgCGqQNLEL-NIzwSI2ur5WQNtZQcmq4YaUWiRTacjxu3yS1-cvcHBPaYTpSUFMyKzSPMpFJDRWYMllmQUkUaxFerUCae5py7JYxSzuezbSauxTnLvVz1yKXa7HXkqfjN4Hk6_KmhdsgsWU3kzT8RbbpdGE9Eo86IWS6cYu0K-VIvS9YpgyrvgjSNn7yhzFPSR0uE7f7w9qkVixW5oxs52-gCotzp_WfUM35_g
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NS8MwFH_oFJwHv8X5mYPXqmvTJj2KOBS34WF-3ELTJDgcU-Ym4l_ve2k7FBEPem15DUneZ_ry-wEcikTnqQh1YLnhAc9TGWiboF3F6Bkj4bT0vTm3bdHtyvv79PNdGGqrpBraFUAR3leTcdNhdNUSd0xljMRITZ1ZEm0dDZqnszBH7HRUgPVad1Nv3CwJVlAkIJnqFs9Pn_kSn76gl1Ydi9-8tg9FreX_mMQKLJWJKDstNGcVZuxwDRY7UxTXlzWoUyZaADmvQ_eUXVvK2t-tYe3-ox30CRGZdTwFNcMJME-wSa1HfrfZXX_8wDpEAfAW3GaDCcpdj-i_EBH8bMBN67x3dhGUZAxBHiUn48BxHYaWZ3mUJ1riOmNqgMlJTBBqFOQJHd2caCFdYrDqNPjASSNSKYzjdON-E2rDp6HdAtYMTayxrAydMDzORCYNFmHaZplDPdFhA3i1BSovkcqJMGOgmiWgabV2itZOlWvXgKOp2HMB1fGbQPp5f9XYn5G4gtBERb_IbnplmI7E42aEyW7SgN1KO1TpDl5USIVfjJkb3_7DmAewcNHrtFX7snu1A3V8lfrDoHAXauPRxO7BfP6KajHa9ybwASHf_iE
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NT9swFH8aMCF2AMZAK-PDB67ZqOPEzhExKtDaqge-blYc21q1qlRtmRB__d5znAo0IQ5wTfTixH6fzvPvB3Akc1MVkpvECSsSURUqMS5Hu8rQM6bSGxV6c667st9Xt7fFIHYTzmJbJdXQvgaKCL6ajHtifdMR94OqGIWBmhqzFJo62rMolmAFU-eMFPuyc7Nwxu3Ir4IiCck0h3heesyz8PQMvLRpWPzPaYdI1Nl4h2_YhPWYhrKTWm8-wwc33oJPvQWG62wL1igPrWGcv0D_hA0c5eyPzrLu8I8bDQkPmfUCATXD92eBXpMaj8Jas5vh_DfrEQHAQ3Jdju5RbjClv0JE77MNV52zy9PzJFIxJFWaH88TLwznTpRVWuVGpTlGNMwbeEYAahTiCRvdHhupfG6x5rR4wSsrCyWtF3TefgeWx3dj9xVYm9vMYFHJvbQiK2WpLJZgxpWlRy0xvAWiWQFdRZxyossY6XaEM23mTtPc6Th3Lfi-EJvUQB2vCRRPl1fPww6Jr-lMdPqK7E7QhcVIImunmOrmLdhrlENHZzDTnMq-DPM2sfuGMQ9hdfCzo7sX_V_fYA3vFGEniO_B8nx67_bhY_UXtWJ6EAzgHxZP_NM
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Penalized+Likelihood+Method+for+Classification+With+Matrix-Valued+Predictors&rft.jtitle=Journal+of+computational+and+graphical+statistics&rft.au=Molstad%2C+Aaron+J&rft.au=Rothman%2C+Adam+J&rft.date=2019-01-02&rft.pub=Taylor+%26+Francis+Ltd&rft.issn=1061-8600&rft.eissn=1537-2715&rft.volume=28&rft.issue=1&rft.spage=11&rft_id=info:doi/10.1080%2F10618600.2018.1476249&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1061-8600&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1061-8600&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1061-8600&client=summon