Learning from Imbalanced Data Sets with Weighted Cross-Entropy Function

This paper presents a novel approach to deal with the imbalanced data set problem in neural networks by incorporating prior probabilities into a cost-sensitive cross-entropy error function. Several classical benchmarks were tested for performance evaluation using different metrics, namely G-Mean, ar...

Full description

Saved in:
Bibliographic Details
Published inNeural processing letters Vol. 50; no. 2; pp. 1937 - 1949
Main Authors Aurelio, Yuri Sousa, de Almeida, Gustavo Matheus, de Castro, Cristiano Leite, Braga, Antonio Padua
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2019
Springer Nature B.V
Subjects
Online AccessGet full text
ISSN1370-4621
1573-773X
DOI10.1007/s11063-018-09977-1

Cover

Loading…
Abstract This paper presents a novel approach to deal with the imbalanced data set problem in neural networks by incorporating prior probabilities into a cost-sensitive cross-entropy error function. Several classical benchmarks were tested for performance evaluation using different metrics, namely G-Mean, area under the ROC curve (AUC), adjusted G-Mean, Accuracy, True Positive Rate, True Negative Rate and F1-score. The obtained results were compared to well-known algorithms and showed the effectiveness and robustness of the proposed approach, which results in well-balanced classifiers given different imbalance scenarios.
AbstractList This paper presents a novel approach to deal with the imbalanced data set problem in neural networks by incorporating prior probabilities into a cost-sensitive cross-entropy error function. Several classical benchmarks were tested for performance evaluation using different metrics, namely G-Mean, area under the ROC curve (AUC), adjusted G-Mean, Accuracy, True Positive Rate, True Negative Rate and F1-score. The obtained results were compared to well-known algorithms and showed the effectiveness and robustness of the proposed approach, which results in well-balanced classifiers given different imbalance scenarios.
Author Braga, Antonio Padua
Aurelio, Yuri Sousa
de Castro, Cristiano Leite
de Almeida, Gustavo Matheus
Author_xml – sequence: 1
  givenname: Yuri Sousa
  orcidid: 0000-0003-2777-1246
  surname: Aurelio
  fullname: Aurelio, Yuri Sousa
  email: yurisousa@ufmg.br
  organization: Federal University of Minas Gerais
– sequence: 2
  givenname: Gustavo Matheus
  surname: de Almeida
  fullname: de Almeida, Gustavo Matheus
  organization: Federal University of Minas Gerais
– sequence: 3
  givenname: Cristiano Leite
  surname: de Castro
  fullname: de Castro, Cristiano Leite
  organization: Federal University of Minas Gerais
– sequence: 4
  givenname: Antonio Padua
  surname: Braga
  fullname: Braga, Antonio Padua
  organization: Federal University of Minas Gerais
BookMark eNp9kEFPAjEQhRujiYD-AU-beK5OW9i2R4OAJCQe1OitGUoXlkAX2xLDv7e4JiYeOM1k8r6ZN69Lzn3jHSE3DO4YgLyPjEEpKDBFQWspKTsjHTaQgkopPs5zLyTQfsnZJenGuAbIGIcOmcwcBl_7ZVGFZltMt3PcoLduUTxiwuLFpVh81WlVvLt6uUp5PgxNjHTkU2h2h2K89zbVjb8iFxVuorv-rT3yNh69Dp_o7HkyHT7MqBVMJ6oGc1UCR63RMaXA9QWiqyqQGsBqpReLilnuGEpELRBKPReCK8YHVpelED1y2-7dheZz72Iy62YffD5puGZK9EX-P6tUq7JHs8FVxtYJjz5TwHpjGJhjbKaNzeTYzE9shmWU_0N3od5iOJyGRAvFLPZLF_5cnaC-AXItgKY
CitedBy_id crossref_primary_10_3390_fractalfract8050267
crossref_primary_10_1109_ACCESS_2021_3051808
crossref_primary_10_1109_TNNLS_2021_3094304
crossref_primary_10_3934_math_2024998
crossref_primary_10_1016_j_compbiomed_2022_105703
crossref_primary_10_1016_j_aap_2024_107544
crossref_primary_10_1016_j_cmpb_2024_108405
crossref_primary_10_1007_s11280_022_01040_3
crossref_primary_10_1049_smt2_12205
crossref_primary_10_1109_LSP_2024_3449852
crossref_primary_10_1016_j_bspc_2025_107772
crossref_primary_10_1038_s41598_022_13550_1
crossref_primary_10_1109_TCBB_2023_3256709
crossref_primary_10_1007_s10479_024_05921_w
crossref_primary_10_1016_j_bspc_2021_103296
crossref_primary_10_1287_ijoo_2022_0086
crossref_primary_10_1109_ACCESS_2023_3298304
crossref_primary_10_1088_1742_6596_2863_1_012017
crossref_primary_10_1155_2020_7307252
crossref_primary_10_1038_s41598_021_95208_y
crossref_primary_10_3390_electronics11203275
crossref_primary_10_1016_j_iswa_2023_200316
crossref_primary_10_3390_s20133765
crossref_primary_10_1007_s11590_024_02112_1
crossref_primary_10_1038_s41598_025_91720_7
crossref_primary_10_2139_ssrn_4001910
crossref_primary_10_1016_j_asoc_2021_108138
crossref_primary_10_1038_s41598_024_82981_9
crossref_primary_10_1016_j_mex_2022_101622
crossref_primary_10_1109_TASE_2021_3127995
crossref_primary_10_1007_s00530_021_00827_0
crossref_primary_10_1093_bib_bbab277
crossref_primary_10_1117_1_JRS_18_044519
crossref_primary_10_1109_JBHI_2024_3363080
crossref_primary_10_1016_j_apenergy_2024_124789
crossref_primary_10_1111_jmp_12722
crossref_primary_10_1109_JBHI_2024_3360002
crossref_primary_10_3390_biomedicines10071717
crossref_primary_10_1371_journal_pdig_0000414
crossref_primary_10_1007_s11063_020_10358_w
crossref_primary_10_1007_s11063_022_10756_2
crossref_primary_10_3390_jimaging9020035
crossref_primary_10_1109_TGRS_2022_3201248
crossref_primary_10_1109_TII_2021_3094186
crossref_primary_10_2197_ipsjjip_32_748
crossref_primary_10_1016_j_ijrmms_2021_104981
crossref_primary_10_3390_s23104688
crossref_primary_10_1016_j_jag_2022_102785
crossref_primary_10_1007_s10334_022_01056_w
crossref_primary_10_1016_j_compbiomed_2020_103735
crossref_primary_10_1016_j_compind_2022_103753
crossref_primary_10_1016_j_compbiomed_2023_106669
crossref_primary_10_1016_j_jenvman_2021_114405
crossref_primary_10_3390_rs13173547
crossref_primary_10_3390_diagnostics13162624
crossref_primary_10_1093_jigpal_jzae027
crossref_primary_10_1371_journal_pgen_1010657
crossref_primary_10_1109_TNS_2022_3169281
crossref_primary_10_1093_jcde_qwad011
crossref_primary_10_1109_JSTSP_2024_3434498
crossref_primary_10_1007_s11063_020_10366_w
crossref_primary_10_1177_1748006X20976817
crossref_primary_10_1007_s00530_021_00782_w
crossref_primary_10_1109_TGRS_2022_3192974
crossref_primary_10_3390_math9243227
crossref_primary_10_3390_signals3020022
crossref_primary_10_1002_mp_15386
crossref_primary_10_1016_j_jbi_2023_104310
crossref_primary_10_1109_TNNLS_2020_3028022
crossref_primary_10_1109_TGRS_2021_3061088
crossref_primary_10_1016_j_conbuildmat_2020_120291
crossref_primary_10_5334_dsj_2021_020
crossref_primary_10_1109_TGRS_2019_2951445
crossref_primary_10_1038_s41523_022_00491_1
crossref_primary_10_7717_peerj_cs_1634
crossref_primary_10_3390_s20174946
crossref_primary_10_1587_transinf_2022EDP7200
crossref_primary_10_3233_JIFS_220937
crossref_primary_10_3390_math10050829
crossref_primary_10_1109_JBHI_2022_3226475
crossref_primary_10_3390_e22060597
crossref_primary_10_1007_s10334_023_01133_8
crossref_primary_10_1016_j_iswcr_2023_11_002
crossref_primary_10_32604_cmc_2023_033765
crossref_primary_10_1007_s10922_024_09874_0
crossref_primary_10_1016_j_eswa_2021_115974
crossref_primary_10_1007_s11042_023_16987_2
crossref_primary_10_1109_ACCESS_2023_3336289
crossref_primary_10_1109_TNNLS_2020_3047335
crossref_primary_10_3390_s21196678
crossref_primary_10_4103_jmss_jmss_52_22
crossref_primary_10_3390_s21062077
crossref_primary_10_1109_JSTARS_2023_3278862
crossref_primary_10_1016_j_future_2022_02_021
crossref_primary_10_1109_JSTARS_2024_3435372
crossref_primary_10_1051_e3sconf_202346419001
crossref_primary_10_3389_fnbot_2020_567571
crossref_primary_10_1016_j_solener_2024_113189
crossref_primary_10_1049_sfw2_12040
crossref_primary_10_1016_j_bspc_2025_107523
crossref_primary_10_1109_JBHI_2021_3102612
crossref_primary_10_1002_mp_16812
crossref_primary_10_1049_iet_gtd_2019_1562
crossref_primary_10_1007_s11548_023_03020_y
crossref_primary_10_1016_j_compbiomed_2022_106215
crossref_primary_10_1016_j_gsf_2023_101769
crossref_primary_10_1016_j_neunet_2023_04_022
crossref_primary_10_1111_mice_12808
crossref_primary_10_1109_LGRS_2024_3453710
crossref_primary_10_1007_s11665_020_05345_0
crossref_primary_10_1093_bib_bbaa018
crossref_primary_10_3390_ijms232213838
crossref_primary_10_1053_j_gastro_2020_02_036
crossref_primary_10_58254_viti_4_2023_04_44
crossref_primary_10_1016_j_jhydrol_2022_127933
crossref_primary_10_3389_feart_2023_1073211
crossref_primary_10_1021_acs_est_4c11085
crossref_primary_10_1016_j_ijepes_2021_107156
crossref_primary_10_3390_app9194062
crossref_primary_10_1080_0144929X_2024_2313142
crossref_primary_10_3390_rs14040984
crossref_primary_10_1080_01431161_2023_2224101
crossref_primary_10_1016_j_bspc_2023_104962
crossref_primary_10_1016_j_compbiomed_2024_108936
crossref_primary_10_1007_s11517_023_02928_6
crossref_primary_10_1109_ACCESS_2020_3026658
crossref_primary_10_1016_j_srs_2024_100168
crossref_primary_10_1155_2021_6683942
crossref_primary_10_1016_j_anucene_2025_111337
crossref_primary_10_1109_TITS_2022_3207665
crossref_primary_10_1016_j_knosys_2023_110399
crossref_primary_10_3389_fgene_2022_1062576
crossref_primary_10_1002_aisy_202400204
crossref_primary_10_1109_ACCESS_2021_3106692
Cites_doi 10.1145/1007730.1007733
10.1109/TEVC.2012.2199119
10.1109/TNNLS.2013.2246188
10.5392/IJoC.2011.7.3.001
10.1016/j.patrec.2005.10.010
10.1109/TNNLS.2016.2580570
10.1007/s00521-005-0467-y
10.1016/j.ins.2013.07.007
10.1016/j.patrec.2017.01.014
10.1016/j.neunet.2013.01.021
10.1080/01621459.1961.10482090
10.1109/TNN.2010.2066988
10.1142/S0219720012500035
10.1109/TKDE.2008.239
10.1023/A:1007614523901
10.1016/j.patcog.2007.04.009
10.1109/TNN.2010.2042730
10.1080/01621459.1937.10503522
10.1023/A:1007601015854
10.1613/jair.953
10.1007/978-3-540-73007-1_20
10.1109/ICNN.1993.298623
ContentType Journal Article
Copyright Springer Science+Business Media, LLC, part of Springer Nature 2019
Copyright Springer Nature B.V. Oct 2019
Copyright_xml – notice: Springer Science+Business Media, LLC, part of Springer Nature 2019
– notice: Copyright Springer Nature B.V. Oct 2019
DBID AAYXX
CITATION
8FE
8FG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
GNUQQ
HCIFZ
JQ2
K7-
P5Z
P62
PHGZM
PHGZT
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PSYQQ
DOI 10.1007/s11063-018-09977-1
DatabaseName CrossRef
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central UK/Ireland
Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Central (subscription)
Technology Collection
ProQuest One Community College
ProQuest Central
ProQuest Central Student
SciTech Premium Collection
ProQuest Computer Science Collection
Computer Science Database
Advanced Technologies & Aerospace Database
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Premium
ProQuest One Academic
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
ProQuest One Psychology
DatabaseTitle CrossRef
Advanced Technologies & Aerospace Collection
ProQuest One Psychology
Computer Science Database
ProQuest Central Student
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
ProQuest One Academic Eastern Edition
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
Advanced Technologies & Aerospace Database
ProQuest One Applied & Life Sciences
ProQuest One Academic UKI Edition
ProQuest Central Korea
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
DatabaseTitleList
Advanced Technologies & Aerospace Collection
Database_xml – sequence: 1
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 1573-773X
EndPage 1949
ExternalDocumentID 10_1007_s11063_018_09977_1
GroupedDBID -4Z
-5F
-5G
-BR
-EM
-Y2
-~C
.86
.DC
.VR
06D
0R~
0VY
123
1N0
1SB
2.D
203
28-
29N
2J2
2JN
2JY
2KG
2LR
2P1
2VQ
2~H
30V
4.4
406
408
409
40D
40E
53G
5QI
5VS
67Z
6NX
8TC
8UJ
95-
95.
95~
96X
AAAVM
AABHQ
AAHNG
AAIAL
AAJKR
AAJSJ
AAKKN
AANZL
AAOBN
AARHV
AARTL
AATVU
AAUYE
AAWCG
AAYIU
AAYOK
AAYQN
AAYTO
AAYZH
ABAKF
ABBBX
ABBXA
ABDZT
ABECU
ABEEZ
ABFTD
ABFTV
ABHLI
ABHQN
ABJNI
ABJOX
ABKCH
ABKTR
ABMNI
ABMOR
ABMQK
ABNWP
ABQBU
ABQSL
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABULA
ABWNU
ABXPI
ACACY
ACBXY
ACGFS
ACHSB
ACHXU
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACSNA
ACULB
ACZOJ
ADHHG
ADHIR
ADIMF
ADINQ
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADYFF
ADZKW
AEBTG
AEFIE
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEKMD
AENEX
AEOHA
AEPYU
AESKC
AETLH
AEVLU
AEXYK
AFBBN
AFEXP
AFGCZ
AFGXO
AFKRA
AFLOW
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGGDS
AGJBK
AGMZJ
AGQEE
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHSBF
AHYZX
AIAKS
AIIXL
AILAN
AITGF
AJBLW
AJRNO
AJZVZ
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMXSW
AMYLF
AMYQR
AOCGG
ARAPS
ARMRJ
ASPBG
AVWKF
AXYYD
AYJHY
AZFZN
B-.
BA0
BBWZM
BDATZ
BENPR
BGLVJ
BGNMA
C24
C6C
CAG
CCPQU
COF
CS3
CSCUP
DDRTE
DL5
DNIVK
DPUIP
DU5
EBLON
EBS
EIOEI
EJD
ESBYG
FEDTE
FERAY
FFXSO
FIGPU
FINBP
FNLPD
FRRFC
FSGXE
FWDCC
GGCAI
GGRSB
GJIRD
GNWQR
GQ6
GQ7
GQ8
GXS
H13
HCIFZ
HF~
HG5
HG6
HMJXF
HQYDN
HRMNR
HVGLF
HZ~
I09
IHE
IJ-
IKXTQ
ITM
IWAJR
IXC
IXE
IZIGR
IZQ
I~X
I~Z
J-C
J0Z
JBSCW
JCJTX
JZLTJ
K7-
KDC
KOV
KOW
LAK
LLZTM
M4Y
MA-
N2Q
NB0
NDZJH
NPVJJ
NQJWS
NU0
O9-
O93
O9G
O9I
O9J
OAM
OVD
P19
P2P
P9O
PF0
PSYQQ
PT5
QOK
QOS
R4E
R89
R9I
RHV
RNI
RNS
ROL
RPX
RSV
RZC
RZE
RZK
S16
S1Z
S26
S27
S28
S3B
SAP
SCJ
SCLPG
SDH
SDM
SHX
SISQX
SNE
SNPRN
SNX
SOHCF
SOJ
SPH
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
T16
TEORI
TSG
TSK
TSV
TUC
U2A
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
W23
W48
WK8
YLTOR
Z45
Z7R
Z7X
Z81
Z83
Z88
Z8M
Z8R
Z8U
Z8W
Z92
ZMTXR
~EX
AASML
AAYXX
ABDBE
ABFSG
ACSTC
ADHKG
AEZWR
AFHIU
AGQPQ
AHPBZ
AHWEU
AIXLP
AYFIA
CITATION
PHGZM
PHGZT
8FE
8FG
AZQEC
DWQXO
GNUQQ
JQ2
P62
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
ID FETCH-LOGICAL-c319t-85b8602a99ae1880e43aaeff07900c989ddf1c2e1a7aa93a069b3328125c96633
IEDL.DBID 8FG
ISSN 1370-4621
IngestDate Wed Aug 13 10:40:16 EDT 2025
Tue Jul 01 01:09:31 EDT 2025
Thu Apr 24 22:54:40 EDT 2025
Fri Feb 21 02:36:40 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Classification problem
Imbalanced data
Multilayer perceptron
Back-propagation
Cost-sensitive function
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c319t-85b8602a99ae1880e43aaeff07900c989ddf1c2e1a7aa93a069b3328125c96633
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0003-2777-1246
PQID 2918343099
PQPubID 2043838
PageCount 13
ParticipantIDs proquest_journals_2918343099
crossref_citationtrail_10_1007_s11063_018_09977_1
crossref_primary_10_1007_s11063_018_09977_1
springer_journals_10_1007_s11063_018_09977_1
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 20191000
2019-10-00
20191001
PublicationDateYYYYMMDD 2019-10-01
PublicationDate_xml – month: 10
  year: 2019
  text: 20191000
PublicationDecade 2010
PublicationPlace New York
PublicationPlace_xml – name: New York
– name: Dordrecht
PublicationTitle Neural processing letters
PublicationTitleAbbrev Neural Process Lett
PublicationYear 2019
Publisher Springer US
Springer Nature B.V
Publisher_xml – name: Springer US
– name: Springer Nature B.V
References Castro, Braga (CR8) 2013; 24
Khoshgoftaar, Van Hulse, Napolitano (CR14) 2010; 21
Chawla, Japkowicz, Kotcz (CR1) 2004; 6
CR19
Kline, Berardi (CR21) 2005; 14
Batuwita, Palade (CR29) 2012; 10
Demšar (CR30) 2006; 7
CR18
Chen, He, Garcia (CR15) 2010; 21
CR13
CR12
Wang, Yang, Chen, Zhang, Orchard (CR7) 2017; 28
CR11
Bhowan, Johnston, Zhang, Yao (CR5) 2013; 17
Friedman (CR31) 1937; 32
Schapire, Singer (CR17) 1999; 37
López, Fernández, García, Palade, Herrera (CR4) 2013; 250
CR2
Oh (CR9) 2011; 7
Provost, Fawcett (CR26) 2001; 42
Dunn (CR32) 1961; 56
Zhu, Wang (CR24) 2017; 88
Tomek (CR25) 1976; 6
CR27
Fawcett (CR28) 2006; 27
Frasca, Bertoni, Re, Valentini (CR6) 2013; 43
CR23
Sun, Kamel, Wong, Wang (CR16) 2007; 40
CR20
He, Garcia (CR3) 2009; 21
Duda, Hart, Stork (CR10) 2001
Berger (CR22) 2010
JO Berger (9977_CR22) 2010
M Frasca (9977_CR6) 2013; 43
RE Schapire (9977_CR17) 1999; 37
9977_CR23
9977_CR20
SH Oh (9977_CR9) 2011; 7
J Demšar (9977_CR30) 2006; 7
C Zhu (9977_CR24) 2017; 88
Y Sun (9977_CR16) 2007; 40
9977_CR2
F Provost (9977_CR26) 2001; 42
9977_CR27
CL Castro (9977_CR8) 2013; 24
OJ Dunn (9977_CR32) 1961; 56
S Chen (9977_CR15) 2010; 21
V López (9977_CR4) 2013; 250
9977_CR12
9977_CR11
H He (9977_CR3) 2009; 21
DM Kline (9977_CR21) 2005; 14
L Wang (9977_CR7) 2017; 28
T Fawcett (9977_CR28) 2006; 27
M Friedman (9977_CR31) 1937; 32
TM Khoshgoftaar (9977_CR14) 2010; 21
RO Duda (9977_CR10) 2001
NV Chawla (9977_CR1) 2004; 6
9977_CR13
I Tomek (9977_CR25) 1976; 6
9977_CR19
U Bhowan (9977_CR5) 2013; 17
9977_CR18
R Batuwita (9977_CR29) 2012; 10
References_xml – volume: 6
  start-page: 1
  issue: 1
  year: 2004
  end-page: 6
  ident: CR1
  article-title: Special issue on learning from imbalanced data sets
  publication-title: SIGKDD Explor
  doi: 10.1145/1007730.1007733
– volume: 17
  start-page: 368
  issue: 3
  year: 2013
  end-page: 386
  ident: CR5
  article-title: Evolving diverse ensembles using genetic programming for classification with unbalanced data
  publication-title: IEEE Trans Evol Comput
  doi: 10.1109/TEVC.2012.2199119
– ident: CR18
– volume: 24
  start-page: 888
  issue: 6
  year: 2013
  end-page: 899
  ident: CR8
  article-title: Novel cost-sensitive approach to improve the multilayer perceptron performance on imbalanced data
  publication-title: IEEE Trans Neural Netw Learn Syst
  doi: 10.1109/TNNLS.2013.2246188
– volume: 7
  start-page: 1
  issue: 3
  year: 2011
  end-page: 5
  ident: CR9
  article-title: A statistical perspective of neural networks for imbalanced data problems
  publication-title: Int J Contents
  doi: 10.5392/IJoC.2011.7.3.001
– volume: 6
  start-page: 769
  year: 1976
  end-page: 772
  ident: CR25
  article-title: Two modifications of cnn
  publication-title: IEEE Trans Syst Man Cybern
– volume: 27
  start-page: 861
  issue: 8
  year: 2006
  end-page: 874
  ident: CR28
  article-title: An introduction to roc analysis
  publication-title: Pattern Recognit Lett
  doi: 10.1016/j.patrec.2005.10.010
– ident: CR2
– volume: 28
  start-page: 2255
  issue: 10
  year: 2017
  end-page: 2267
  ident: CR7
  article-title: Improving neural-network classifiers using nearest neighbor partitioning
  publication-title: IEEE Trans Neural Netw Learn Syst
  doi: 10.1109/TNNLS.2016.2580570
– year: 2001
  ident: CR10
  publication-title: Pattern classification
– ident: CR12
– volume: 14
  start-page: 310
  issue: 4
  year: 2005
  end-page: 318
  ident: CR21
  article-title: Revisiting squared-error and cross-entropy functions for training neural network classifiers
  publication-title: Neural Comput Appl
  doi: 10.1007/s00521-005-0467-y
– volume: 7
  start-page: 1
  issue: Jan
  year: 2006
  end-page: 30
  ident: CR30
  article-title: Statistical comparisons of classifiers over multiple data sets
  publication-title: J Mach Learn Res
– ident: CR27
– volume: 250
  start-page: 113
  year: 2013
  end-page: 141
  ident: CR4
  article-title: An insight into classification with imbalanced data: empirical results and current trends on using data intrinsic characteristics
  publication-title: Inf Sci
  doi: 10.1016/j.ins.2013.07.007
– volume: 88
  start-page: 72
  year: 2017
  end-page: 80
  ident: CR24
  article-title: Entropy-based matrix learning machine for imbalanced data sets
  publication-title: Pattern Recognit Lett
  doi: 10.1016/j.patrec.2017.01.014
– volume: 43
  start-page: 84
  year: 2013
  end-page: 98
  ident: CR6
  article-title: A neural network algorithm for semi-supervised node label learning from unbalanced data
  publication-title: Neural Netw
  doi: 10.1016/j.neunet.2013.01.021
– ident: CR23
– ident: CR19
– volume: 56
  start-page: 52
  issue: 293
  year: 1961
  end-page: 64
  ident: CR32
  article-title: Multiple comparisons among means
  publication-title: J Am Stat Assoc
  doi: 10.1080/01621459.1961.10482090
– volume: 21
  start-page: 1624
  issue: 10
  year: 2010
  end-page: 1642
  ident: CR15
  article-title: Ramoboost: ranked minority oversampling in boosting
  publication-title: IEEE Trans Neural Netw
  doi: 10.1109/TNN.2010.2066988
– volume: 10
  start-page: 1250003
  issue: 04
  year: 2012
  ident: CR29
  article-title: Adjusted geometric-mean: a novel performance measure for imbalanced bioinformatics datasets learning
  publication-title: J Bioinform Comput Biol
  doi: 10.1142/S0219720012500035
– volume: 21
  start-page: 1263
  issue: 9
  year: 2009
  end-page: 1284
  ident: CR3
  article-title: Learning from imbalanced data
  publication-title: IEEE Trans Knowl Data Eng
  doi: 10.1109/TKDE.2008.239
– ident: CR13
– ident: CR11
– volume: 37
  start-page: 297
  issue: 3
  year: 1999
  end-page: 336
  ident: CR17
  article-title: Improved boosting algorithms using confidence-rated predictions
  publication-title: Mach Learn
  doi: 10.1023/A:1007614523901
– volume: 40
  start-page: 3358
  issue: 12
  year: 2007
  end-page: 3378
  ident: CR16
  article-title: Cost-sensitive boosting for classification of imbalanced data
  publication-title: Pattern Recognit
  doi: 10.1016/j.patcog.2007.04.009
– year: 2010
  ident: CR22
  publication-title: Statistical decision theory and Bayesian analysis
– volume: 21
  start-page: 813
  issue: 5
  year: 2010
  end-page: 830
  ident: CR14
  article-title: Supervised neural network modeling: an empirical investigation into learning from imbalanced data with labeling errors
  publication-title: IEEE Trans Neural Netw
  doi: 10.1109/TNN.2010.2042730
– volume: 32
  start-page: 675
  issue: 200
  year: 1937
  end-page: 701
  ident: CR31
  article-title: The use of ranks to avoid the assumption of normality implicit in the analysis of variance
  publication-title: J Am Stat Assoc
  doi: 10.1080/01621459.1937.10503522
– volume: 42
  start-page: 203
  issue: 3
  year: 2001
  end-page: 231
  ident: CR26
  article-title: Robust classification for imprecise environments
  publication-title: Mach Learn
  doi: 10.1023/A:1007601015854
– ident: CR20
– volume: 21
  start-page: 1624
  issue: 10
  year: 2010
  ident: 9977_CR15
  publication-title: IEEE Trans Neural Netw
  doi: 10.1109/TNN.2010.2066988
– ident: 9977_CR11
  doi: 10.1613/jair.953
– ident: 9977_CR13
– ident: 9977_CR2
  doi: 10.1145/1007730.1007733
– volume: 43
  start-page: 84
  year: 2013
  ident: 9977_CR6
  publication-title: Neural Netw
  doi: 10.1016/j.neunet.2013.01.021
– volume: 37
  start-page: 297
  issue: 3
  year: 1999
  ident: 9977_CR17
  publication-title: Mach Learn
  doi: 10.1023/A:1007614523901
– volume-title: Statistical decision theory and Bayesian analysis
  year: 2010
  ident: 9977_CR22
– ident: 9977_CR27
– volume-title: Pattern classification
  year: 2001
  ident: 9977_CR10
– volume: 21
  start-page: 1263
  issue: 9
  year: 2009
  ident: 9977_CR3
  publication-title: IEEE Trans Knowl Data Eng
  doi: 10.1109/TKDE.2008.239
– volume: 14
  start-page: 310
  issue: 4
  year: 2005
  ident: 9977_CR21
  publication-title: Neural Comput Appl
  doi: 10.1007/s00521-005-0467-y
– ident: 9977_CR20
  doi: 10.1007/978-3-540-73007-1_20
– volume: 88
  start-page: 72
  year: 2017
  ident: 9977_CR24
  publication-title: Pattern Recognit Lett
  doi: 10.1016/j.patrec.2017.01.014
– ident: 9977_CR23
  doi: 10.1109/ICNN.1993.298623
– ident: 9977_CR12
– ident: 9977_CR18
– volume: 42
  start-page: 203
  issue: 3
  year: 2001
  ident: 9977_CR26
  publication-title: Mach Learn
  doi: 10.1023/A:1007601015854
– volume: 21
  start-page: 813
  issue: 5
  year: 2010
  ident: 9977_CR14
  publication-title: IEEE Trans Neural Netw
  doi: 10.1109/TNN.2010.2042730
– volume: 6
  start-page: 769
  year: 1976
  ident: 9977_CR25
  publication-title: IEEE Trans Syst Man Cybern
– volume: 27
  start-page: 861
  issue: 8
  year: 2006
  ident: 9977_CR28
  publication-title: Pattern Recognit Lett
  doi: 10.1016/j.patrec.2005.10.010
– volume: 7
  start-page: 1
  issue: 3
  year: 2011
  ident: 9977_CR9
  publication-title: Int J Contents
  doi: 10.5392/IJoC.2011.7.3.001
– volume: 32
  start-page: 675
  issue: 200
  year: 1937
  ident: 9977_CR31
  publication-title: J Am Stat Assoc
  doi: 10.1080/01621459.1937.10503522
– volume: 24
  start-page: 888
  issue: 6
  year: 2013
  ident: 9977_CR8
  publication-title: IEEE Trans Neural Netw Learn Syst
  doi: 10.1109/TNNLS.2013.2246188
– volume: 7
  start-page: 1
  issue: Jan
  year: 2006
  ident: 9977_CR30
  publication-title: J Mach Learn Res
– volume: 17
  start-page: 368
  issue: 3
  year: 2013
  ident: 9977_CR5
  publication-title: IEEE Trans Evol Comput
  doi: 10.1109/TEVC.2012.2199119
– volume: 10
  start-page: 1250003
  issue: 04
  year: 2012
  ident: 9977_CR29
  publication-title: J Bioinform Comput Biol
  doi: 10.1142/S0219720012500035
– volume: 250
  start-page: 113
  year: 2013
  ident: 9977_CR4
  publication-title: Inf Sci
  doi: 10.1016/j.ins.2013.07.007
– volume: 6
  start-page: 1
  issue: 1
  year: 2004
  ident: 9977_CR1
  publication-title: SIGKDD Explor
  doi: 10.1145/1007730.1007733
– ident: 9977_CR19
– volume: 28
  start-page: 2255
  issue: 10
  year: 2017
  ident: 9977_CR7
  publication-title: IEEE Trans Neural Netw Learn Syst
  doi: 10.1109/TNNLS.2016.2580570
– volume: 56
  start-page: 52
  issue: 293
  year: 1961
  ident: 9977_CR32
  publication-title: J Am Stat Assoc
  doi: 10.1080/01621459.1961.10482090
– volume: 40
  start-page: 3358
  issue: 12
  year: 2007
  ident: 9977_CR16
  publication-title: Pattern Recognit
  doi: 10.1016/j.patcog.2007.04.009
SSID ssj0010020
Score 2.606027
Snippet This paper presents a novel approach to deal with the imbalanced data set problem in neural networks by incorporating prior probabilities into a cost-sensitive...
SourceID proquest
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 1937
SubjectTerms Algorithms
Artificial Intelligence
Classification
Complex Systems
Computational Intelligence
Computer Science
Datasets
Decision theory
Entropy
Entropy (Information theory)
Error functions
Neural networks
Performance evaluation
Probability
SummonAdditionalLinks – databaseName: SpringerLink Journals (ICM)
  dbid: U2A
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwELZQWVh4IwoFeWADS34ljceqtBQkWKCiW-Q4DguUioSBf89d6jQCARJrcjlFd7bvO9-LkDNjdGSKSDEruWZaSs-s17CWrStU5HLlHdY7397Fk6m-mUWzUBRWNtnuTUiyPqnbYjfwXjD3B8P1gFoY-DzrEfjuuK6ncrCKHSACqt2sPmc6liKUyvzM46s5ajHmt7BobW3G22QzwEQ6WOp1h6z5-S7ZakYw0LAj98hV6I_6RLFOhF6_ZJiq6HxOL21l6b2vSopXrfSxvgKF50P8DzbCBPXFBx2DWUPV7JPpePQwnLAwG4E52DQVS6IMp0dZY6zHlmpeK2t9UfC-4dyZxOR5IZz0wvatNcry2GRKSTDnkQMPR6kD0pm_zv0hoTzJpQSvA280AL6ZpMhVLhwwk8Lp2HaJaESUutA4HOdXPKdty2MUawpiTWuxpqJLzlffLJZtM_6k7jWST8MWKlNp4LTRCki65KLRRvv6d25H_yM_JhsAgswyQa9HOtXbuz8BoFFlp_W6-gRT7Maz
  priority: 102
  providerName: Springer Nature
Title Learning from Imbalanced Data Sets with Weighted Cross-Entropy Function
URI https://link.springer.com/article/10.1007/s11063-018-09977-1
https://www.proquest.com/docview/2918343099
Volume 50
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV07T8MwELagXVh4Iwql8sAGFvEjbTyhUvoARIWACpgi13FYoC00DPx77lKnFUh0iuQkVnR3zn33JuRYaxXqNJTMiEAxJYRjximQZWNTGdpEOov1zrf9em-grp_DZ-9wm_q0yuKfmP-ok7FFH_mZ0CB8SgKgOZ98MJwahdFVP0JjlZQ5aBqU8KjTnUcREAvlBlcjYKouuC-amZXOgS2EmUQY_AcMxPhvxbRAm38CpLne6WySdQ8YaXPG4S2y4kbbZKMYxkD92dwhXd8p9ZVixQi9eh9i0qJ1Cb00maEPLptSdLrSp9wZCust_A7WxlT1yTftgIJDJu2SQaf92OoxPyWBWTg-GYvCIc6RMlobh83VnJLGuDQNGjoIrI50kqTcCsdNwxgtTVDXQykFKPbQgq0j5R4pjcYjt09oECVCgP2Bvg0AcjpKE5lwC5sJblXdVAgvSBRb30IcJ1m8xYvmx0jWGMga52SNeYWczN-ZzBpoLH26WlA-9odpGi9YXyGnBTcWt__f7WD5bodkDeCPnqXmVUkp-_xyRwAxsmEtl6MaKTe7LzdtuF60-3f3sDoQzR_iMM3b
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3JTsMwEB1VcIALO6KsPsAJLBLbaeMDQqg72wUQ3ILrOFygFBqE-lN8IzNZqECCG9csVjR-mXkzngVgV2sV6CSQ3AhPcSWE48YpxLKxiQxsLJ2leueLy1r3Rp3eBXcV-ChrYSitstSJmaKOny3FyA-FRvApiYTmePjCaWoUna6WIzRyWJy58Tu6bKOjXhP3d0-Iduu60eXFVAFuEW4pD4M-zV0yWhtHzcicksa4JPHq2vOsDnUcJ74Vzjd1Y7Q0Xk33pRRoCAOLvgEFQFHlTyspNaUQhu3O16kFca_Mwat7XNWEXxTp5KV66HtR5hIlGyDn4v53Qzhhtz8OZDM7116AuYKgspMcUYtQcYMlmC-HP7BCFyxDp-jM-sCoQoX1nvqUJGldzJomNezKpSNGQV52mwVf8XqDvoO3KDV-OGZtNKgEihW4-Rf5rcLU4Hng1oB5YSwE-jsUS0HiqMMklrFvcTHhW1UzVfBLEUW2aFlOkzMeo0mzZRJrhGKNMrFGfhX2v94Z5g07_nx6s5R8VPy8o2gCtSoclLsxuf37aut_r7YDM93ri_PovHd5tgGzSL10nha4CVPp65vbQnqT9rczTDG4_28QfwKPYwXL
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwELZQKyEW3ohCAQ9sYDWxnTQeq7ahLVAhlYpulus4LBAqGgb-Pec8GkCAxJrYp-jOl_vO90LoXAjuidhjRFGHE06pIcpwOMtKx8zTETPa1jvfjv3BlI9m3uxTFX-W7V6GJPOaBtulKUlbiyhuVYVv4MnYPCAbugcEQ8D_qQc-wPMaqnc6o8loFUmweChzutoO4T51i8KZn6l8NU4V4vwWJM1sT7iNNgvQiDu5lHfQmkl20VY5kAEX-rmHropuqY_YVo3g4fPcJi5qE-GeShWemHSJ7cUrfsguROF5134H6dt09cU7DsHIWUHto2nYv-8OSDEpgWhQoZQE3tzOklJCKGMbrBnOlDJx7LSF42gRiCiKXU2Nq9pKCaYcX8wZo2DcPQ3-DmMHqJa8JOYQYSeIKAUfxN5vAJgTQRyxyNVAjLqa-6qB3JJFUhdtxO00iydZNUC2bJXAVpmxVboNdLHas8ibaPy5ullyXhYKtZRUwL-HM1jSQJelNKrXv1M7-t_yM7R-1wvlzXB8fYw2AB2JPHOviWrp65s5AQSSzk-LQ_YBcNrPMw
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=Learning+from+Imbalanced+Data+Sets+with+Weighted+Cross-Entropy+Function&rft.jtitle=Neural+processing+letters&rft.au=Aurelio%2C+Yuri+Sousa&rft.au=de+Almeida%2C+Gustavo+Matheus&rft.au=de+Castro%2C+Cristiano+Leite&rft.au=Braga%2C+Antonio+Padua&rft.date=2019-10-01&rft.issn=1370-4621&rft.eissn=1573-773X&rft.volume=50&rft.issue=2&rft.spage=1937&rft.epage=1949&rft_id=info:doi/10.1007%2Fs11063-018-09977-1&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s11063_018_09977_1
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1370-4621&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1370-4621&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1370-4621&client=summon