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Erschienen in: Neural Computing and Applications 1/2017

24.05.2016 | Original Article

Ellipsoidal support vector data description

verfasst von: Kasemsit Teeyapan, Nipon Theera-Umpon, Sansanee Auephanwiriyakul

Erschienen in: Neural Computing and Applications | Sonderheft 1/2017

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Abstract

This paper presents a data domain description formed by the minimum volume covering ellipsoid around a dataset, called “ellipsoidal support vector data description (eSVDD).” The method is analogous to support vector data description (SVDD), but instead, with an ellipsoidal domain description allowing tighter space around the data. In eSVDD, a hyperellipsoid extends its ability to describe more complex data patterns by kernel methods. This is explicitly achieved by defining an “empirical feature map” to project the images of given samples to a higher-dimensional space. We compare the performance of the kernelized ellipsoid in one-class classification with SVDD using standard datasets.

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Literatur
1.
Zurück zum Zitat Ahipaşaoğlu S (2015) A first-order algorithm for the a-optimal experimental design problem: a mathematical programming approach. Stat Comput 25(6):1113–1127 MathSciNetCrossRefMATH Ahipaşaoğlu S (2015) A first-order algorithm for the a-optimal experimental design problem: a mathematical programming approach. Stat Comput 25(6):1113–1127 MathSciNetCrossRefMATH
3.
Zurück zum Zitat Ahmadi A, Dmitry Malioutov RL (2014) Robust minimum volume ellipsoids and higher-order polynomial level sets. In: 7th NIPS workshop on optimization for machine learning, Montreal, Quebec, Canada Ahmadi A, Dmitry Malioutov RL (2014) Robust minimum volume ellipsoids and higher-order polynomial level sets. In: 7th NIPS workshop on optimization for machine learning, Montreal, Quebec, Canada
4.
Zurück zum Zitat Barnett V, Lewis T (1994) Outliers in statistical data, 3rd edn. Wiley series in probability and mathematical statistics. Wiley, Chichester Barnett V, Lewis T (1994) Outliers in statistical data, 3rd edn. Wiley series in probability and mathematical statistics. Wiley, Chichester
5.
Zurück zum Zitat Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, CambridgeCrossRefMATH Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, CambridgeCrossRefMATH
6.
Zurück zum Zitat Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297MATH Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297MATH
7.
Zurück zum Zitat Dolia A, Bie T, Harris C, Shawe-Taylor J, Titterington DM (2006) The minimum volume covering ellipsoid estimation in Kernel-defined feature spaces, Lecture Notes in Computer Science, vol 4212. Springer, Berlin, Heidelberg, pp 630–637 Dolia A, Bie T, Harris C, Shawe-Taylor J, Titterington DM (2006) The minimum volume covering ellipsoid estimation in Kernel-defined feature spaces, Lecture Notes in Computer Science, vol 4212. Springer, Berlin, Heidelberg, pp 630–637
8.
9.
Zurück zum Zitat Glineur F (1998) Pattern separation via ellipsoids and conic programming. Master’s thesis, Faculté Polytechnique de Mons, Mons, Belgium Glineur F (1998) Pattern separation via ellipsoids and conic programming. Master’s thesis, Faculté Polytechnique de Mons, Mons, Belgium
10.
Zurück zum Zitat Henk M (2012) Löwner–John Ellipsoids. Doc Math (extra volume: optimization stories) pp 95–106 Henk M (2012) Löwner–John Ellipsoids. Doc Math (extra volume: optimization stories) pp 95–106
11.
Zurück zum Zitat Huang G, Chen H, Zhou Z, Yin F, Guo K (2011) Two-class support vector data description. Pattern Recognit 44(2):320–329CrossRefMATH Huang G, Chen H, Zhou Z, Yin F, Guo K (2011) Two-class support vector data description. Pattern Recognit 44(2):320–329CrossRefMATH
14.
Zurück zum Zitat Lasserre JB (2013) A generalization of the Löwner-John’s ellipsoid theorem. In: 52nd IEEE Conference on Decision and Control (CDC). Florence, Italy, pp 415–420 Lasserre JB (2013) A generalization of the Löwner-John’s ellipsoid theorem. In: 52nd IEEE Conference on Decision and Control (CDC). Florence, Italy, pp 415–420
16.
Zurück zum Zitat Mu T, Nandi AK (2009) Multiclass classification based on extended support vector data description. IEEE Trans Syst Man Cybern B 39(5):1206–1216CrossRef Mu T, Nandi AK (2009) Multiclass classification based on extended support vector data description. IEEE Trans Syst Man Cybern B 39(5):1206–1216CrossRef
17.
Zurück zum Zitat PW R, Juszczak P, Paclik P, Pekalska E, de Ridder D, Tax D, Verzakov S (2015) PRTools 5.0. A Matlab toolbox for pattern recognition, software and documentation downloaded March PW R, Juszczak P, Paclik P, Pekalska E, de Ridder D, Tax D, Verzakov S (2015) PRTools 5.0. A Matlab toolbox for pattern recognition, software and documentation downloaded March
18.
Zurück zum Zitat Rimon E, Boyd SP (1997) Obstacle collision detection using best ellipsoid fit. J Intell Robot Syst 18(2):105–126CrossRefMATH Rimon E, Boyd SP (1997) Obstacle collision detection using best ellipsoid fit. J Intell Robot Syst 18(2):105–126CrossRefMATH
20.
Zurück zum Zitat Schölkopf B, Mika S, Burges CJC, Knirsch P, Müller KR, Rätsch G, Smola AJ (1999) Input space versus feature space in kernel-based methods. IEEE Trans Neural Netw 10:1000–1017CrossRef Schölkopf B, Mika S, Burges CJC, Knirsch P, Müller KR, Rätsch G, Smola AJ (1999) Input space versus feature space in kernel-based methods. IEEE Trans Neural Netw 10:1000–1017CrossRef
23.
Zurück zum Zitat Sylvester JJ (1857) A question in the geometry of situation. Q J Pure Appl Math 1:79 Sylvester JJ (1857) A question in the geometry of situation. Q J Pure Appl Math 1:79
24.
Zurück zum Zitat Tax DM, Duin RP (1999) Support vector domain description. Pattern Recogn Lett 20(11–13):1191–1199CrossRef Tax DM, Duin RP (1999) Support vector domain description. Pattern Recogn Lett 20(11–13):1191–1199CrossRef
25.
27.
Zurück zum Zitat Tax DMJ (2015b) DDtools, the data description toolbox for Matlab. Version 2.1.2 Tax DMJ (2015b) DDtools, the data description toolbox for Matlab. Version 2.1.2
29.
Zurück zum Zitat Todd MJ, Yıldırım EA (2007) On Khachiyan’s algorithm for the computation of minimum-volume enclosing ellipsoids. Discret Appl Math 155(13):1731–1744MathSciNetCrossRefMATH Todd MJ, Yıldırım EA (2007) On Khachiyan’s algorithm for the computation of minimum-volume enclosing ellipsoids. Discret Appl Math 155(13):1731–1744MathSciNetCrossRefMATH
30.
Zurück zum Zitat Toh KC (1999) Primal-dual path-following algorithms for determinant maximization problems with linear matrix inequalities. Comput Optim Appl 14(3):309–330MathSciNetCrossRefMATH Toh KC (1999) Primal-dual path-following algorithms for determinant maximization problems with linear matrix inequalities. Comput Optim Appl 14(3):309–330MathSciNetCrossRefMATH
31.
32.
Zurück zum Zitat Vandenberghe L, Boyd S, Wu SP (1998) Determinant maximization with linear matrix inequality constraints. SIAM J Matrix Anal Appl 19:499–533MathSciNetCrossRefMATH Vandenberghe L, Boyd S, Wu SP (1998) Determinant maximization with linear matrix inequality constraints. SIAM J Matrix Anal Appl 19:499–533MathSciNetCrossRefMATH
33.
Zurück zum Zitat Wei X, Löfberg J, Feng Y, Li Y (2007) Enclosing machine learning for class description. Lect Notes Comput Sci LNCS 4491(Part 1):424–433CrossRef Wei X, Löfberg J, Feng Y, Li Y (2007) Enclosing machine learning for class description. Lect Notes Comput Sci LNCS 4491(Part 1):424–433CrossRef
34.
Zurück zum Zitat Wei XK, Li YH, Li YF, Zhang DF (2007b) Enclosing machine learning: concepts and algorithms. Neural Comput Appl 17(3):237–243MathSciNetCrossRef Wei XK, Li YH, Li YF, Zhang DF (2007b) Enclosing machine learning: concepts and algorithms. Neural Comput Appl 17(3):237–243MathSciNetCrossRef
35.
Zurück zum Zitat Xiong H, Swamy MNS, Ahmad MO (2005) Optimizing the kernel in the empirical feature space. IEEE Trans Neural Netw 16(2):460–474CrossRef Xiong H, Swamy MNS, Ahmad MO (2005) Optimizing the kernel in the empirical feature space. IEEE Trans Neural Netw 16(2):460–474CrossRef
Metadaten
Titel
Ellipsoidal support vector data description
verfasst von
Kasemsit Teeyapan
Nipon Theera-Umpon
Sansanee Auephanwiriyakul
Publikationsdatum
24.05.2016
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe Sonderheft 1/2017
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-016-2343-3

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