Margin maximization in spherical separation

We face the problem of strictly separating two sets of points by means of a sphere, considering the two cases where the center of the sphere is fixed or free, respectively. In particular, for the former we present a fast and simple solution algorithm, whereas for the latter one we use the DC-Algorithm based on a DC decomposition of the error function. Numerical results for both the cases are presented on several classical binary datasets drawn from the literature.

[1]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[2]  Robert P. W. Duin,et al.  Uniform Object Generation for Optimizing One-class Classifiers , 2002, J. Mach. Learn. Res..

[3]  Annabella Astorino,et al.  DC models for spherical separation , 2010, J. Glob. Optim..

[4]  Chih-Jen Lin,et al.  Working Set Selection Using Second Order Information for Training Support Vector Machines , 2005, J. Mach. Learn. Res..

[5]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[6]  Robert P. W. Duin,et al.  Support vector domain description , 1999, Pattern Recognit. Lett..

[7]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[8]  Hiroshi Konno,et al.  Failure Discrimination by Semi-Definite Programming , 2002 .

[9]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[10]  Le Thi Hoai An,et al.  The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems , 2005, Ann. Oper. Res..

[11]  Le Thi Hoai An,et al.  A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem , 1998, SIAM J. Optim..

[12]  Bernhard Schölkopf,et al.  Support vector learning , 1997 .

[13]  Adil M. Bagirov,et al.  Max–min separability , 2005, Optim. Methods Softw..

[14]  Alexander Zien,et al.  Semi-Supervised Classification by Low Density Separation , 2005, AISTATS.

[15]  Leon N. Cooper,et al.  Pattern Classification via Single Spheres , 2005, Discovery Science.

[16]  S. Odewahn,et al.  Automated star/galaxy discrimination with neural networks , 1992 .

[17]  Annabella Astorino,et al.  A fixed-center spherical separation algorithm with kernel transformations for classification problems , 2009, Comput. Manag. Sci..

[18]  Thorsten Joachims,et al.  Making large scale SVM learning practical , 1998 .

[19]  William W. Hager,et al.  An Affine-Scaling Interior-Point Method for Continuous Knapsack Constraints with Application to Support Vector Machines , 2011, SIAM J. Optim..

[20]  Annabella Astorino,et al.  Ellipsoidal separation for classification problems , 2005, Optim. Methods Softw..

[22]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[23]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[24]  Annabella Astorino,et al.  Nonsmooth Optimization Techniques for Semisupervised Classification , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Antonio Fuduli,et al.  Minimizing Nonconvex Nonsmooth Functions via Cutting Planes and Proximity Control , 2003, SIAM J. Optim..

[26]  Laura Palagi,et al.  On the convergence of a modified version of SVM light algorithm , 2005, Optim. Methods Softw..

[27]  Jung-Hsien Chiang,et al.  A new maximal-margin spherical-structured multi-class support vector machine , 2009, Applied Intelligence.

[28]  Annabella Astorino,et al.  Polyhedral Separability Through Successive LP , 2002 .