Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Neural Computing and Applications
Erschienen in: Neural Computing and Applications 6/2016

01.08.2016 | Original Article

Extended least squares support vector machines for ordinal regression

verfasst von: Na Zhang

Erschienen in: Neural Computing and Applications | Ausgabe 6/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We extend LS-SVM to ordinal regression, which has wide applications in many domains such as social science and information retrieval where human-generated data play an important role. Most current methods based on SVM for ordinal regression suffer from the problem of ignoring the distribution information reflected by the samples clustered around the centers of each class. This problem would degrade the performance of SVM-based methods since the classifiers only depend on the scattered samples on the border which induce large margin. Our method takes the samples clustered around class centers into account and has a competitive computational complexity. Moreover, our method would easily produce the optimal cut-points according to the prior class probabilities and hence may obtain more reasonable results when the prior class probabilities are not the same. Experiments on simulated datasets and benchmark datasets, especially on the real ordinal datasets, demonstrate the effectiveness of our method.
Vorheriger Artikel Linear combination of densities and its direct estimation framework with applications
Nächster Artikel A hybrid adaptive cuckoo search optimization algorithm for the problem of chaotic systems parameter estimation

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
In the original paper [27], the form of the classifier is \(y(x)=\text{ sign }[\omega ^\top \varphi (x)+b]\). Here, we use the classifier \(y(x)=\text{ sign }[\omega ^\top \varphi (x)-b]\) to keep consistence with Sect. 3.
 
2
The second term should be \(\alpha ^{\top }DKD\alpha\) after this substitution, but we use \(\Vert \alpha \Vert ^2\) instead for regularization and smoothing purpose as in [36, 39].
 
3
Since EBC is a framework of reducing ordinal regression problem to binary classification, the computational complexity varies from \(2N-n_1-n_K\) to KN when the parameters change.
 
4
The cut-points in this section are normalized by \(\frac{b_j}{\Vert w\Vert }\).
 
6
Because the partition for the first four datasets has been given by Chu, we just use these splits in our experiments for comparison purpose.
 
7
The datasets are available at the WEKA website (http://​www.​cs.​waikato.​ac.​nz/​ml/​index.​html).
 
Literatur
1.
Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning, 2nd edn. Springer, HeidelbergCrossRefMATH
2.
Cruz-Ramirez M, Fernandez JC, Valero A, Gutierrez PA, Hervas-Martnez C (2013) Multiobjective Pareto ordinal classification for predictive microbiology. In: Snášel V, Abraham A, Corchado ES (eds) Soft computing models in industrial and environmental applications, Springer, Berlin, Heidelberg, pp 153–162
3.
Kramer S, Widmer G, Pfahringer B, DeGroeve M (2001) Prediction of ordinal classes using regression trees. Fundam Inf 47(1–2):1–13MathSciNetMATH
4.
5.
McCullagh P, Nelder JA (1989) Generalized linear models, 2nd edn. Champman and Hall, LondonCrossRefMATH
6.
Crammer K, Singer Y (2002) Pranking with ranking. In: Dietterich TG, Becher S, Ghahramani Z (eds) Advances in neural information processing systems 14, vol 1. MIT Press, Cambridge, pp 641–647
7.
Herbrich R, Graepel T, Obermayer K (2000) Large margin rank boundaries for ordinal regression. Advances in large margin classifiers. MIT Press, Cambridge
8.
9.
10.
Boser B, Guyon I, Vapnik V (1992) A training algorithm for optimal margin classifier. In: Proceedings of the fifth annual ACM workshop on computational learning research. ACM, pp 144–52
11.
Vapnik V (1998) Statistical learning theory. Wiley, New YorkMATH
12.
Cristianini N, Shawe-Taylor J (1999) An introduction to support vector machines. Cambridge University Press, CambridgeMATH
13.
Gonzalez L, Angulo C, Velasco F, Catala A (2006) Dual unification of bi-class support vector machine formulations. Pattern Recognit 39(7):1325–1332CrossRefMATH
14.
Xue H, Chen S, Yang Q (2011) Structural regularized support vector machine: a framework for structural large margin classifier. IEEE Trans Neural Netw 22(4):573–587CrossRef
15.
Kim S, Park YJ, Toh K, Lee S (2010) SVM-based feature extraction for face recognition. Pattern Recognit 43(8):2871–2881CrossRefMATH
16.
Chen Y, Su C, Yang T (2013) Rule extraction from support vector machines by genetic algorithms. Neural Comput Appl 23(3–4):729–739CrossRef
17.
Rosillo R, Giner J, Fuente D (2014) The effectiveness of the combined use of VIX and support vector machines on the prediction of SP 500. Neural Comput Appl 22(2):321–332
18.
Azar AT, El-Said SA (2014) Performance analysis of support vector machines classifiers in breast cancer mammography recognition. Neural Comput Appl 24(5):1163–1177CrossRef
19.
Angulo C, Ruiz F, Gonzalez L, Ortega JA (2006) Multi-classification by using tri-class SVM. Neural Process Lett 23:90–101CrossRef
20.
Shashua A, Levin A (2003) Ranking with large margin principle: two approaches. In: Becker S, Thrun S, Obermayer K (eds) Advances in neural information processing systems 15, MIT Press, Cambridge, pp 961–968
21.
Zhao B, Wang F, Zhang C (2009) Block-quantized support vector ordinal regression. IEEE Trans Neural Netw 20(5):882–890CrossRef
22.
Pelckmans K, Karsmakers P, Suykens JAK, De Moor B (2006) Ordinal least squares support vector machines—a discriminant analysis approach. In: Proceedings of the machine learning for signal processing (MLSP 2006), pp 1–8
23.
Lin L, Lin HT (2007) Ordinal regression by extended binary classification. In: Advances in neural information processing systems 19. Proceedings of the 2006 Conference (NIPS 2006). MIT Press, pp 865–872
24.
Cardoso JS, Pinto JF (2007) Learning to classify ordinal data: the data replication method. J Mach Learn Res 8:1393–1429MathSciNetMATH
25.
Sun BY, Li J, Wu DD (2010) Kernel discriminant learning for ordinal regression. IEEE Trans Knowl Data Eng 22(6):906–910CrossRef
26.
Kramer KA, Hall LO, Goldgof DB, Remsen A, Luo T (2009) Fast support vector machines for continuous data. IEEE Trans Syst Man Cybern Part B Cybern 39(4):989–1001CrossRef
27.
28.
Suykens JAK, van Gestel T, De Brabanter J (2002) Least squares support vector machines. World Scientific, SingaporeCrossRefMATH
29.
Van Gestel T, Suykens JAK, Lanckriet G (2002) A Bayesian framework for least squares support vector machine classifiers, gaussian processes and Kernel Fisher discriminant analysis. Neural Comput 14(5):1115–1147CrossRefMATH
30.
Adankon MM, Cheriet M (2009) Model selection for the LS-SVM. Application to handwriting recognition. Pattern Recognit 42(12):3264–3270CrossRefMATH
31.
Adankon MM, Cheriet M, Biem A (2011) Semisupervised learning using Bayesian interpretation: application to LS-SVM. IEEE Trans Neural Netw 22(4):513–524CrossRef
32.
33.
Williams CKI (1998) Prediction with Gaussian process: from linear regression to linear prediction and beyond. In: Jordan MI (ed) Learning and inference in graphical models. Kluwer Academic Press, Dordrecht
34.
Saunders C, Gammerman A, Vovk V (1998) Ridge regression learning algorithm in dual variables. In: Proceedings of the 15th International Conference on Machine Learning (ICML98), pp 515–521
35.
Van Gestel T, Suykens JAK (2004) Benchmarking least squares support vector machine classifiers. Mach Learn 54:5–32CrossRefMATH
36.
Fung G, Mangasarian OL (2001) Proximal support vector machine classifiers. ACM Special Internet Group on Management of Data AAAI, ACM, New YorkCrossRefMATH
37.
Cevikalp H, Neamtu M, Barkana A (2007) The kernel common vector method: a novel nonlinear subspace classifier for pattern recognition. IEEE Trans Syst Man Cybern Part B Cybern 37(4):937–951CrossRef
38.
Müller K-R, Mika S, Rätsch G (2001) An introduction to kernel-based learning algorithms. IEEE Trans Neural Netw 12(2):181–201CrossRef
39.
40.
Francis FB, Jordan MI (2005) Predictive low-rank decomposition for kernel methods. In: Proceedings of the 22nd international conference on machine learning (ICML2005), pp 33–40
41.
Gaudette L, Japkowicz N (2009) Evaluation methods for ordinal regression. Canadian AI 2009, LNAI 5549, pp 207–210
42.
Waegeman W, Baetsb BD, Boullarta L (2008) ROC analysis in ordinalregression learning. Pattern Recognit Lett 29(1):1–9CrossRef
43.
Baccianella S, Esuli A, Sebastiani F (2009) Evaluation measures for ordinal regression. In: 2009 Ninth international conference on intelligent systems design and applications
Metadaten
Titel
Extended least squares support vector machines for ordinal regression
verfasst von
Na Zhang
Publikationsdatum
01.08.2016
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 6/2016
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-015-1948-2

Weitere Artikel der Ausgabe 6/2016

Neural Computing and Applications 6/2016 Zur Ausgabe

Original Article

A hybrid adaptive cuckoo search optimization algorithm for the problem of chaotic systems parameter estimation

Original Article

Intelligent exponential sliding-mode control with uncertainty estimator for antilock braking systems

Original Article

Linear combination of densities and its direct estimation framework with applications

Original Article

Knowledge-based extreme learning machines

Original Article

Video-based face recognition and image synthesis from rotating head frames using nonlinear manifold learning by neural networks

Original Article

ADP-based optimal sensor scheduling for target tracking in energy harvesting wireless sensor networks