A branch & bound algorithm to determine optimal cross-splits for decision tree induction
State-of-the-art decision tree algorithms are top-down induction heuristics which greedily partition the attribute space by iteratively choosing the best split on an individual attribute. Despite their attractive performance in terms of runtime, simple examples, such as the XOR-Problem, point out th...
Uložené v:
| Vydané v: | Annals of mathematics and artificial intelligence Ročník 88; číslo 4; s. 291 - 311 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Cham
Springer International Publishing
01.04.2020
Springer Springer Nature B.V |
| Predmet: | |
| ISSN: | 1012-2443, 1573-7470 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | State-of-the-art decision tree algorithms are top-down induction heuristics which greedily partition the attribute space by iteratively choosing the best split on an individual attribute. Despite their attractive performance in terms of runtime, simple examples, such as the XOR-Problem, point out that these heuristics often fail to find the best classification rules if there are strong interactions between two or more attributes from the given datasets. In this context, we present a branch and bound based decision tree algorithm to identify optimal bivariate axis-aligned splits according to a given impurity measure. In contrast to a univariate split that can be found in linear time, such an optimal cross-split has to consider every combination of values for every possible selection of pairs of attributes which leads to a combinatorial optimization problem that is quadratic in the number of values and attributes. To overcome this complexity, we use a branch and bound procedure, a well known technique from combinatorial optimization, to divide the solution space into several sets and to detect the optimal cross-splits in a short amount of time. These cross splits can either be used directly to construct quaternary decision trees or they can be used to select only the better one of the individual splits. In the latter case, the outcome is a binary decision tree with a certain sense of foresight for correlated attributes. We test both of these variants on various datasets of the UCI Machine Learning Repository and show that cross-splits can consistently produce smaller decision trees than state-of-the-art methods with comparable accuracy. In some cases, our algorithm produces considerably more accurate trees due to the ability of drawing more elaborate decisions than univariate induction algorithms. |
|---|---|
| AbstractList | State-of-the-art decision tree algorithms are top-down induction heuristics which greedily partition the attribute space by iteratively choosing the best split on an individual attribute. Despite their attractive performance in terms of runtime, simple examples, such as the XOR-Problem, point out that these heuristics often fail to find the best classification rules if there are strong interactions between two or more attributes from the given datasets. In this context, we present a branch and bound based decision tree algorithm to identify optimal bivariate axis-aligned splits according to a given impurity measure. In contrast to a univariate split that can be found in linear time, such an optimal cross-split has to consider every combination of values for every possible selection of pairs of attributes which leads to a combinatorial optimization problem that is quadratic in the number of values and attributes. To overcome this complexity, we use a branch and bound procedure, a well known technique from combinatorial optimization, to divide the solution space into several sets and to detect the optimal cross-splits in a short amount of time. These cross splits can either be used directly to construct quaternary decision trees or they can be used to select only the better one of the individual splits. In the latter case, the outcome is a binary decision tree with a certain sense of foresight for correlated attributes. We test both of these variants on various datasets of the UCI Machine Learning Repository and show that cross-splits can consistently produce smaller decision trees than state-of-the-art methods with comparable accuracy. In some cases, our algorithm produces considerably more accurate trees due to the ability of drawing more elaborate decisions than univariate induction algorithms. State-of-the-art decision tree algorithms are top-down induction heuristics which greedily partition the attribute space by iteratively choosing the best split on an individual attribute. Despite their attractive performance in terms of runtime, simple examples, such as the XOR-Problem, point out that these heuristics often fail to find the best classification rules if there are strong interactions between two or more attributes from the given datasets. In this context, we present a branch and bound based decision tree algorithm to identify optimal bivariate axis-aligned splits according to a given impurity measure. In contrast to a univariate split that can be found in linear time, such an optimal cross-split has to consider every combination of values for every possible selection of pairs of attributes which leads to a combinatorial optimization problem that is quadratic in the number of values and attributes. To overcome this complexity, we use a branch and bound procedure, a well known technique from combinatorial optimization, to divide the solution space into several sets and to detect the optimal cross-splits in a short amount of time. These cross splits can either be used directly to construct quaternary decision trees or they can be used to select only the better one of the individual splits. In the latter case, the outcome is a binary decision tree with a certain sense of foresight for correlated attributes. We test both of these variants on various datasets of the UCI Machine Learning Repository and show that cross-splits can consistently produce smaller decision trees than state-of-the-art methods with comparable accuracy. In some cases, our algorithm produces considerably more accurate trees due to the ability of drawing more elaborate decisions than univariate induction algorithms. Keywords Branch & bound * Decision trees * Classification * Cross-splits Mathematics Subject Classification (2010) 68T05 * 90C27 |
| Audience | Academic |
| Author | Dahmen, Martin Bollwein, Ferdinand Westphal, Stephan |
| Author_xml | – sequence: 1 givenname: Ferdinand orcidid: 0000-0002-4894-5615 surname: Bollwein fullname: Bollwein, Ferdinand email: ferdinand.bollwein@tu-clausthal.de organization: Institute of Mathematics, Clausthal University of Technology – sequence: 2 givenname: Martin surname: Dahmen fullname: Dahmen, Martin organization: Institute of Mathematics, Clausthal University of Technology – sequence: 3 givenname: Stephan surname: Westphal fullname: Westphal, Stephan organization: Institute of Mathematics, Clausthal University of Technology |
| BookMark | eNp9kE9rHCEYh6Wk0CTtF-hJCPRm8jo6o3tcQtoEFnJJIDdxndeNYVY36h7y7etkCoUcggf_8Dy-_H5n5CSmiIT85HDJAdRV4SBVx4CvGKwGLRl8Iae8V4IpqeCknYF3rJNSfCNnpbwAzNhwSp7WdJttdM_0F92mYxypnXYph_q8pzXRESvmfYhI06GGvZ2oy6kUVg5TqIX6lBviQgkp0poRaYjj0dV2_U6-ejsV_PFvPyePv28erm_Z5v7P3fV6w5zodWW9W3kJyvoRPNc4DJ0QA8CoFerBbbEfOXI3yBGl5agQXA8cQfCt5oDOi3Nysfx7yOn1iKWal3TMsY003YrrrqEaGnW5UDs7oQnRp5qta2vEfXCtSx_a-1pxJWZBNkEvwnvejN64UO0crIlhMhzMXLxZijetePNevJlndR_UQ27V5bfPJbFIpcFxh_l_jE-svxGil58 |
| CitedBy_id | crossref_primary_10_3390_agriculture14101763 |
| Cites_doi | 10.1016/0020-0190(76)90095-8 10.1007/978-3-642-13105-9_2 10.1016/j.dss.2009.05.016 10.1016/j.eswa.2007.12.020 10.1016/j.eswa.2008.07.018 10.1023/A:1009744630224 10.1007/978-1-4419-9226-0_5 10.1287/opre.43.4.570 10.1016/j.enbuild.2012.03.003 10.1186/1475-925X-6-23 10.1023/A:1022604100933 10.1023/A:1009869804967 10.1613/jair.63 10.1109/ICCKE.2015.7365834 10.1016/j.eswa.2012.05.028 |
| ContentType | Journal Article |
| Copyright | Springer Nature Switzerland AG 2020 COPYRIGHT 2020 Springer Springer Nature Switzerland AG 2020. |
| Copyright_xml | – notice: Springer Nature Switzerland AG 2020 – notice: COPYRIGHT 2020 Springer – notice: Springer Nature Switzerland AG 2020. |
| DBID | AAYXX CITATION 8FE 8FG ABJCF AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.1007/s10472-019-09684-0 |
| DatabaseName | CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One Community College ProQuest Central Korea ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection |
| DatabaseTitle | CrossRef 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 SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Computer Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Computer Science |
| EISSN | 1573-7470 |
| EndPage | 311 |
| ExternalDocumentID | A717303184 10_1007_s10472_019_09684_0 |
| GroupedDBID | -4Z -59 -5G -BR -EM -Y2 -~C .86 .DC .VR 06D 0R~ 0VY 1N0 1SB 2.D 203 23M 28- 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTD ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU 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 BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IAO IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K7- KDC KOV KOW LAK LLZTM M4Y M7S MA- N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9O PF0 PT4 PT5 PTHSS QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7R Z7X Z81 Z83 Z88 Z92 ZMTXR ~A9 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG ADKFA AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 8FE 8FG AZQEC DWQXO GNUQQ JQ2 L6V P62 PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c358t-5c9f407afd0f18e66233600d87e86cbe5d1e1c64de4a1e7e0c501e031b810ecf3 |
| IEDL.DBID | K7- |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000534791700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1012-2443 |
| IngestDate | Wed Nov 05 14:47:52 EST 2025 Sat Nov 29 09:49:16 EST 2025 Sat Nov 29 05:14:37 EST 2025 Tue Nov 18 22:36:42 EST 2025 Fri Feb 21 02:26:56 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | Branch & bound Cross-splits 90C27 68T05 Decision trees Classification |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c358t-5c9f407afd0f18e66233600d87e86cbe5d1e1c64de4a1e7e0c501e031b810ecf3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-4894-5615 |
| PQID | 2918203180 |
| PQPubID | 2043872 |
| PageCount | 21 |
| ParticipantIDs | proquest_journals_2918203180 gale_infotracacademiconefile_A717303184 crossref_citationtrail_10_1007_s10472_019_09684_0 crossref_primary_10_1007_s10472_019_09684_0 springer_journals_10_1007_s10472_019_09684_0 |
| PublicationCentury | 2000 |
| PublicationDate | 20200400 2020-04-00 20200401 |
| PublicationDateYYYYMMDD | 2020-04-01 |
| PublicationDate_xml | – month: 4 year: 2020 text: 20200400 |
| PublicationDecade | 2020 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: Dordrecht |
| PublicationTitle | Annals of mathematics and artificial intelligence |
| PublicationTitleAbbrev | Ann Math Artif Intell |
| PublicationYear | 2020 |
| Publisher | Springer International Publishing Springer Springer Nature B.V |
| Publisher_xml | – name: Springer International Publishing – name: Springer – name: Springer Nature B.V |
| References | MurthySKKasifSSalzbergSA system for induction of oblique decision treesJ. Artif. Intell. Res.199421320900.68335 MurthySKAutomatic construction of decision trees from data: A multi-disciplinary surveyData Mining Knowl. Discov.199824345389 CzerniakJacekZarzyckiHubertApplication of rough sets in the presumptive diagnosis of urinary system diseasesArtificial Intelligence and Security in Computing Systems2003Boston, MASpringer US4151 Murthy, S.K., Kasif, S., Salzberg, S., Beigel, R.: Oc1: A randomized algorithm for building oblique decision trees. In: Proceedings of AAAI, vol. 93, pp 322–327. Citeseer (1993) Bhatt, R., Dhall, A.: Skin segmentation dataset. UCI Machine Learning Repository Cicalese, F., Laber, E.: Approximation algorithms for clustering via weighted impurity measures (2018) Detrano, R., Janosi, A., Steinbrunn, W., Pfisterer, M.: Heart disease databases (1988) MingersJAn empirical comparison of pruning methods for decision tree inductionMach. Learn.198942227243 Anguita, D., Ghio, A., Oneto, L., Parra, X., Reyes-Ortiz, J.L.: A public domain dataset for human activity recognition using smartphones. In: ESANN (2013) LaurentHRivestRLConstructing optimal binary decision trees is np-completeInform. Process. Lett.19765115174135980333.68029 Breiman, L., Friedman, J., Stone, C., Olshen, R.: Classification and Regression Trees. The Wadsworth and Brooks-Cole statistics-probability series. Taylor & Francis. https://books.google.de/books?id=JwQx-WOmSyQC (1984) CortezPCerdeiraAAlmeidaFMatosTReisJModeling wine preferences by data mining from physicochemical propertiesDecis. Support. Syst.2009474547553 BreimanLSome properties of splitting criteriaMach. Learn.199624141470849.68095 BrodleyCEUtgoffPEMultivariate decision treesMach Learn199519145770831.68091 Charytanowicz, M., Niewczas, J., Kulczycki, P., Kowalski, P.A., Łukasik, S., Żak, S.: Complete gradient clustering algorithm for features analysis of x-ray images. In: Information Technologies in Biomedicine, pp 15–24. Springer (2010) MangasarianOLStreetWNWolbergWHBreast cancer diagnosis and prognosis via linear programmingOper. Res.199543457057713564100857.90073 YehICYangKJTingTMKnowledge discovery on rfm model using bernoulli sequenceExpert Syst. Appl.2009363, Part 258665871http://www.sciencedirect.com/science/article/pii/S0957417408004508 FriedmanJHastieTTibshiraniRThe elements of statistical learning, vol. 12001New YorkSpringer Series in Statistics0973.62007 YehICLienChThe comparisons of data mining techniques for the predictive accuracy of probability of default of credit card clientsExpert Syst. Appl.200936224732480 CoppersmithDHongSJHoskingJRPartitioning nominal attributes in decision treesData Min. Knowl. Disc.199932197217 QuinlanJRInduction of decision treesMach. Learn.19861181106 Thrun, S.B., Bala, J., Bloedorn, E., Bratko, I., Cestnik, B., Cheng, J., Jong, K.D., Dzeroski, S., Fahlman, S.E., Fisher, D., Hamann, R., Kaufman, K., Keller, S., Kononenko, I., Kreuziger, J., Michalski, R., Mitchell, T., Pachowicz, P., Reich, Y., Vafaie, H., Welde, W.V.D., Wenzel, W., Wnek, J., Zhang, J.: The monk’s problems a performance comparison of different learning algorithms. Tech rep (1991) TsanasAXifaraAAccurate quantitative estimation of energy performance of residential buildings using statistical machine learning toolsEnergy Build.201249560567 Dheeru, D., Karra Taniskidou, E.: UCI machine learning repository (2017). http://archive.ics.uci.edu/ml LittleMAMcSharryPERobertsSJCostelloDAMorozIMExploiting nonlinear recurrence and fractal scaling properties for voice disorder detectionBiomed. Eng. Online20076123 GilDGirelaJLDe JuanJGomez-TorresMJJohnssonMPredicting seminal quality with artificial intelligence methodsExpert Syst. Appl.201239161256412573 Mirzamomen, Z., Fekri, M.N., Kangavari, M.: Cross split decision trees for pattern classification. In: 2015 5th International Conference on Computer and Knowledge Engineering (ICCKE), pp 240–245. IEEE (2015) Quinlan, J.R.: C4. 5: Programs for Machine Learning. Elsevier (2014) Abreu, N.G.C.F.M., et al.: Analise do perfil do cliente recheio e desenvolvimento de um sistema promocional. Ph.D thesis (2011) IC Yeh (9684_CR28) 2009; 36 L Breiman (9684_CR4) 1996; 24 Jacek Czerniak (9684_CR11) 2003 9684_CR8 SK Murthy (9684_CR21) 1998; 2 9684_CR7 9684_CR5 D Gil (9684_CR15) 2012; 39 9684_CR13 9684_CR12 A Tsanas (9684_CR27) 2012; 49 CE Brodley (9684_CR6) 1995; 19 J Friedman (9684_CR14) 2001 MA Little (9684_CR17) 2007; 6 J Mingers (9684_CR19) 1989; 4 IC Yeh (9684_CR29) 2009; 36 D Coppersmith (9684_CR9) 1999; 3 9684_CR3 9684_CR2 H Laurent (9684_CR16) 1976; 5 9684_CR26 9684_CR1 9684_CR25 9684_CR23 JR Quinlan (9684_CR24) 1986; 1 P Cortez (9684_CR10) 2009; 47 OL Mangasarian (9684_CR18) 1995; 43 9684_CR20 SK Murthy (9684_CR22) 1994; 2 |
| References_xml | – reference: CoppersmithDHongSJHoskingJRPartitioning nominal attributes in decision treesData Min. Knowl. Disc.199932197217 – reference: Mirzamomen, Z., Fekri, M.N., Kangavari, M.: Cross split decision trees for pattern classification. In: 2015 5th International Conference on Computer and Knowledge Engineering (ICCKE), pp 240–245. IEEE (2015) – reference: Breiman, L., Friedman, J., Stone, C., Olshen, R.: Classification and Regression Trees. The Wadsworth and Brooks-Cole statistics-probability series. Taylor & Francis. https://books.google.de/books?id=JwQx-WOmSyQC (1984) – reference: Charytanowicz, M., Niewczas, J., Kulczycki, P., Kowalski, P.A., Łukasik, S., Żak, S.: Complete gradient clustering algorithm for features analysis of x-ray images. In: Information Technologies in Biomedicine, pp 15–24. Springer (2010) – reference: QuinlanJRInduction of decision treesMach. Learn.19861181106 – reference: TsanasAXifaraAAccurate quantitative estimation of energy performance of residential buildings using statistical machine learning toolsEnergy Build.201249560567 – reference: YehICYangKJTingTMKnowledge discovery on rfm model using bernoulli sequenceExpert Syst. Appl.2009363, Part 258665871http://www.sciencedirect.com/science/article/pii/S0957417408004508 – reference: Thrun, S.B., Bala, J., Bloedorn, E., Bratko, I., Cestnik, B., Cheng, J., Jong, K.D., Dzeroski, S., Fahlman, S.E., Fisher, D., Hamann, R., Kaufman, K., Keller, S., Kononenko, I., Kreuziger, J., Michalski, R., Mitchell, T., Pachowicz, P., Reich, Y., Vafaie, H., Welde, W.V.D., Wenzel, W., Wnek, J., Zhang, J.: The monk’s problems a performance comparison of different learning algorithms. Tech rep (1991) – reference: Abreu, N.G.C.F.M., et al.: Analise do perfil do cliente recheio e desenvolvimento de um sistema promocional. Ph.D thesis (2011) – reference: Murthy, S.K., Kasif, S., Salzberg, S., Beigel, R.: Oc1: A randomized algorithm for building oblique decision trees. In: Proceedings of AAAI, vol. 93, pp 322–327. Citeseer (1993) – reference: CzerniakJacekZarzyckiHubertApplication of rough sets in the presumptive diagnosis of urinary system diseasesArtificial Intelligence and Security in Computing Systems2003Boston, MASpringer US4151 – reference: MurthySKAutomatic construction of decision trees from data: A multi-disciplinary surveyData Mining Knowl. Discov.199824345389 – reference: MurthySKKasifSSalzbergSA system for induction of oblique decision treesJ. Artif. Intell. Res.199421320900.68335 – reference: BrodleyCEUtgoffPEMultivariate decision treesMach Learn199519145770831.68091 – reference: Anguita, D., Ghio, A., Oneto, L., Parra, X., Reyes-Ortiz, J.L.: A public domain dataset for human activity recognition using smartphones. In: ESANN (2013) – reference: YehICLienChThe comparisons of data mining techniques for the predictive accuracy of probability of default of credit card clientsExpert Syst. Appl.200936224732480 – reference: GilDGirelaJLDe JuanJGomez-TorresMJJohnssonMPredicting seminal quality with artificial intelligence methodsExpert Syst. Appl.201239161256412573 – reference: BreimanLSome properties of splitting criteriaMach. Learn.199624141470849.68095 – reference: LaurentHRivestRLConstructing optimal binary decision trees is np-completeInform. Process. Lett.19765115174135980333.68029 – reference: Dheeru, D., Karra Taniskidou, E.: UCI machine learning repository (2017). http://archive.ics.uci.edu/ml – reference: LittleMAMcSharryPERobertsSJCostelloDAMorozIMExploiting nonlinear recurrence and fractal scaling properties for voice disorder detectionBiomed. Eng. Online20076123 – reference: Bhatt, R., Dhall, A.: Skin segmentation dataset. UCI Machine Learning Repository – reference: Cicalese, F., Laber, E.: Approximation algorithms for clustering via weighted impurity measures (2018) – reference: FriedmanJHastieTTibshiraniRThe elements of statistical learning, vol. 12001New YorkSpringer Series in Statistics0973.62007 – reference: CortezPCerdeiraAAlmeidaFMatosTReisJModeling wine preferences by data mining from physicochemical propertiesDecis. Support. Syst.2009474547553 – reference: MingersJAn empirical comparison of pruning methods for decision tree inductionMach. Learn.198942227243 – reference: MangasarianOLStreetWNWolbergWHBreast cancer diagnosis and prognosis via linear programmingOper. Res.199543457057713564100857.90073 – reference: Quinlan, J.R.: C4. 5: Programs for Machine Learning. Elsevier (2014) – reference: Detrano, R., Janosi, A., Steinbrunn, W., Pfisterer, M.: Heart disease databases (1988) – ident: 9684_CR8 – ident: 9684_CR25 – volume: 5 start-page: 15 issue: 1 year: 1976 ident: 9684_CR16 publication-title: Inform. Process. Lett. doi: 10.1016/0020-0190(76)90095-8 – ident: 9684_CR7 doi: 10.1007/978-3-642-13105-9_2 – volume: 47 start-page: 547 issue: 4 year: 2009 ident: 9684_CR10 publication-title: Decis. Support. Syst. doi: 10.1016/j.dss.2009.05.016 – volume: 36 start-page: 2473 issue: 2 year: 2009 ident: 9684_CR28 publication-title: Expert Syst. Appl. doi: 10.1016/j.eswa.2007.12.020 – ident: 9684_CR13 – volume: 36 start-page: 5866 issue: 3, Part 2 year: 2009 ident: 9684_CR29 publication-title: Expert Syst. Appl. doi: 10.1016/j.eswa.2008.07.018 – volume: 2 start-page: 345 issue: 4 year: 1998 ident: 9684_CR21 publication-title: Data Mining Knowl. Discov. doi: 10.1023/A:1009744630224 – start-page: 41 volume-title: Artificial Intelligence and Security in Computing Systems year: 2003 ident: 9684_CR11 doi: 10.1007/978-1-4419-9226-0_5 – ident: 9684_CR2 – volume: 1 start-page: 81 issue: 1 year: 1986 ident: 9684_CR24 publication-title: Mach. Learn. – ident: 9684_CR26 – volume: 43 start-page: 570 issue: 4 year: 1995 ident: 9684_CR18 publication-title: Oper. Res. doi: 10.1287/opre.43.4.570 – volume: 49 start-page: 560 year: 2012 ident: 9684_CR27 publication-title: Energy Build. doi: 10.1016/j.enbuild.2012.03.003 – volume: 6 start-page: 23 issue: 1 year: 2007 ident: 9684_CR17 publication-title: Biomed. Eng. Online doi: 10.1186/1475-925X-6-23 – ident: 9684_CR3 – ident: 9684_CR5 – volume: 4 start-page: 227 issue: 2 year: 1989 ident: 9684_CR19 publication-title: Mach. Learn. doi: 10.1023/A:1022604100933 – volume: 24 start-page: 41 issue: 1 year: 1996 ident: 9684_CR4 publication-title: Mach. Learn. – volume: 3 start-page: 197 issue: 2 year: 1999 ident: 9684_CR9 publication-title: Data Min. Knowl. Disc. doi: 10.1023/A:1009869804967 – volume: 19 start-page: 45 issue: 1 year: 1995 ident: 9684_CR6 publication-title: Mach Learn – ident: 9684_CR12 – ident: 9684_CR23 doi: 10.1613/jair.63 – ident: 9684_CR1 – volume: 2 start-page: 1 year: 1994 ident: 9684_CR22 publication-title: J. Artif. Intell. Res. doi: 10.1613/jair.63 – volume-title: The elements of statistical learning, vol. 1 year: 2001 ident: 9684_CR14 – ident: 9684_CR20 doi: 10.1109/ICCKE.2015.7365834 – volume: 39 start-page: 12564 issue: 16 year: 2012 ident: 9684_CR15 publication-title: Expert Syst. Appl. doi: 10.1016/j.eswa.2012.05.028 |
| SSID | ssj0009686 |
| Score | 2.210664 |
| Snippet | State-of-the-art decision tree algorithms are top-down induction heuristics which greedily partition the attribute space by iteratively choosing the best split... |
| SourceID | proquest gale crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 291 |
| SubjectTerms | Algorithms Artificial Intelligence Bivariate analysis Branch and bound methods Combinatorial analysis Complex Systems Computer Science Datasets Decision trees Machine learning Mathematics Optimization Solution space |
| SummonAdditionalLinks | – databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwELVQ4QAHCgVEoSAfEBzAUhYncY4VouJChdjUm5U4NkXqgprA9zOTOC27BOdMHMf2bPLMe4QcRV4iMg_ZywI_Y5BvxCwxqWFRYDhP4VT5TlaSTUT9vhgM4mvbFJbX1e71lWRpqd81u_EIywiwxCcUnEGivgzuTqA63tw-LKB2w5LfEYGrGDgv37bKfD_GB3f02Sh_uR0tnU6v-b_pbpB1G2TSbnUqNsmSnrRIsyZwoFafW2Ttag7amm-RQZemSLMxpMc0RbYlmowep7OnYjimxZRmtnBG0ymYmTGMX_4SyyGMLXIKwS-IVIQ9FK-6KWT7FTTtNrnvXdydXzJLvMCUH4iCBSo2kOglJnOMK3QIIZIPgVEmIi1Cleogc7WrQp5pnrg60o4KHFeDeUiF62hl_B3SmEwnepfQFCISCAodbVJEpuGJbxIQCR2tY9_lXpu49fpLZVHJkRxjJBd4yriQEhZSlgspnTY5nb_zXGFy_Cp9gtsqUWFhZJXYvgOYH0JfyS7WIaBp423SqXdeWk3OpRcjxD08hoHO6p1ePP75u3t_E98nqx6m8mVRUIc0itmLPiAr6rV4ymeH5Ql_A02D8tk priority: 102 providerName: Springer Nature |
| Title | A branch & bound algorithm to determine optimal cross-splits for decision tree induction |
| URI | https://link.springer.com/article/10.1007/s10472-019-09684-0 https://www.proquest.com/docview/2918203180 |
| Volume | 88 |
| WOSCitedRecordID | wos000534791700001&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: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1573-7470 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: P5Z dateStart: 19970301 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1573-7470 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: K7- dateStart: 19970301 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1573-7470 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: M7S dateStart: 19970301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-7470 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: BENPR dateStart: 19970301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1573-7470 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009686 issn: 1012-2443 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NT9wwEB1R4NAegNIitsDKhwoOrVU7cb5OaEEgpKqrFdBq1YuV-AOQYJeSlN_PTNZh1SK4cMklzsTWG9tje_wewOcsKnMbkXpZEluO642Cl77yPEu8UhV6VSxsKzaRDYf5eFyMwoZbHdIquzGxHajt1NAe-beoIKpx9ECxf_uHk2oUna4GCY03sCSjSJKff8_4nHQ3bZUeicKK4zQWh0sz4eqcyigpgRKG0lxx8c_E9P_w_OSctJ1-jldfW_E1WAmBJxvMPOU9LLjJOqx2og4s9PF1ePfjkci1_gDjAatIeuOS7bKKFJhYeX2B1pvLG9ZMmQ3JNI5Ncei5Qftt43iNoW1TMwyIschMxIfR8Te7mtgZXe1H-Hl8dH54woMYAzdxkjc8MYXHxV_prfAydymGTTEGSzbPXJ6ayiVWOmlSZZ0qpcucMImQDttd5VI44-MNWJxMJ24TWIVRCgaKwvmK2GpUGfsSi6TCuSKWKuqB7JDQJjCVk2DGtZ5zLBN6GtHTLXpa9ODL4ze3M56OF0vvEcCaOjFaNmW4i4D1IzosPaDcBMJM9WC7Q1WH3l3rOaQ9-Nr5xfz18__99LK1LXgb0XK-TQzahsXm7q_bgWVz31zVd31YOjgajk77rY_3KUn1DJ-j5Dc-T89-PQBdUAEh |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VgkQ5UChULBTwgY8DWDixkzgHhFZA1WrbFYci7c0k_qCV2t3SBBB_it_ITOJ0BYjeeuAcx07s55mxPX4P4EmRVtqlpF6WScdxvVHyKtSBF1lQqkZUSeE6sYliOtWzWflhBX4Od2EorXKwiZ2hdgtLe-Sv0pKoxhGB4s3pF06qUXS6Okho9LCY-B_fccnWvN59h-P7NE233x-83eFRVYBbmemWZ7YMuIqpghMh0T5H_y_R6ztdeJ3b2mcu8YnNlfOqSnzhhc1E4rHlWifC2yCx3itwVUldEFf_pOBLkt-8U5YkyiyOblPGSzrxqp4qKAmCEpRyrbj4zRH-6Q7-Opft3N32-v_WUbfgZgys2bifCbdhxc83YH0QrWDRhm3Ajf1zotrmDszGrCZpkUP2jNWkMMWq48_4N-3hCWsXzMVkIc8WaFpPsP6uM3mDoXvbMAz4sUgvUsToeJ8dzV1Px3sXPl7K327C6nwx9_eA1RiFYSAsfKiJjUdVMlRYJBfelzJR6QiSYeSNjUzsJAhybJYc0oQWg2gxHVqMGMGL83dOex6SC0s_J0AZMlJYs63iXQv8PqL7MmPKvSCMqBFsDSgy0Xo1ZgmhEbwccLh8_O92719c22O4vnOwv2f2dqeTB7CW0tZFlwS1Bavt2Vf_EK7Zb-1Rc_aom1cMPl02Pn8Bbf9aEw |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9NAEB5VpargQNpA1UBa9lCVA6zqx_p1jNpGRdAoUinKbWXvo4mUOlVs-P3M-JGEApUQZ4_H693Z2RntzPcBnEReGmuP2MsCX3PMNxKe2szyKLBCZGhVvqMrsoloNIonk2S80cVfVbu3V5J1TwOhNOXl2YO2ZxuNbyKikgIq9wljwTFpfyaINIjy9Ztva9jdsOJ6JBArjgeZ37TN_FnHL0fTYwf9201pdQANO_8_9D142QSfbFBbyz5smbwLnZbYgTX7vAsvrldgrsUrmAxYRvQbU3bKMmJhYun8brGcldN7Vi6YbgpqDFug-7lH_dXv8QLD27JgGBSjSE3kw-gKnM1yXUPWvobb4eXX8yveEDJw5QdxyQOVWEwAU6sd68YmxNDJx4BJx5GJQ5WZQLvGVaHQRqSuiYyjAsc16Day2HWMsv4BbOeL3BwCyzBSwWDRMTYjxBqR-jZFkdAxJvFd4fXAbddCqgatnEgz5nKNs0wTKXEiZTWR0unBh9U7DzVWx5PS72mJJW1k1KzSph8Bx0eQWHJA9Qnk8kQP-q0VyGaHF9JLCPoeH6Oij-2qrx___btv_k38HeyOL4byy6fR57fw3KNsv6ob6sN2ufxujmBH_ShnxfK4Mvyfhwj-oQ |
| 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+branch+%26+bound+algorithm+to+determine+optimal+cross-splits+for+decision+tree+induction&rft.jtitle=Annals+of+mathematics+and+artificial+intelligence&rft.au=Bollwein%2C+Ferdinand&rft.au=Dahmen%2C+Martin&rft.au=Westphal%2C+Stephan&rft.date=2020-04-01&rft.issn=1012-2443&rft.eissn=1573-7470&rft.volume=88&rft.issue=4&rft.spage=291&rft.epage=311&rft_id=info:doi/10.1007%2Fs10472-019-09684-0&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10472_019_09684_0 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1012-2443&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1012-2443&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1012-2443&client=summon |