Unsupervised classification via convex absolute value inequalities

We consider the problem of classifying completely unlabelled data using convex inequalities that contain absolute values of the data. This allows each data point to belong to either one of two classes by entering the inequality with a plus or minus value. Using such absolute value inequalities in support vector machine classifiers, unlabelled data can be successfully partitioned into two classes that capture most of the correct labels dropped from the data. Inclusion of partially labelled data leads to a semisupervised classifier. Computational results include unsupervised and semisupervised classification of the Wisconsin Breast Cancer Wisconsin (Diagnostic) Data Set.

[1]  William Nick Street,et al.  Breast Cancer Diagnosis and Prognosis Via Linear Programming , 1995, Oper. Res..

[2]  Robert S. Leiken,et al.  A User’s Guide , 2011 .

[3]  Olvi L. Mangasarian,et al.  Nonlinear Knowledge-Based Classification , 2008, IEEE Transactions on Neural Networks.

[4]  Glenn Fung,et al.  Proximal support vector machine classifiers , 2001, KDD '01.

[5]  Khaled S. Al-Sultan,et al.  A Tabu search approach to the clustering problem , 1995, Pattern Recognit..

[6]  O. Mangasarian,et al.  Semi-Supervised Support Vector Machines for Unlabeled Data Classification , 2001 .

[7]  Paul S. Bradley,et al.  Clustering via Concave Minimization , 1996, NIPS.

[8]  Gérard Govaert,et al.  Gaussian parsimonious clustering models , 1995, Pattern Recognit..

[9]  Stefan Schäffler,et al.  Applied Mathematics and Parallel Computing: Festschrift for Klaus Ritter , 2012 .

[10]  Michael R. Anderberg,et al.  Cluster Analysis for Applications , 1973 .

[11]  Peng Guo,et al.  On the Unique Solvability of the Absolute Value Equation , 2015, Journal of Optimization Theory and Applications.

[12]  Alexander J. Smola,et al.  Minimal Kernel Classifiers , 2002, J. Mach. Learn. Res..

[13]  O. Mangasarian.  Minimum-support solutions of polyhedral concave programs * , 1999 .

[14]  Ayhan Demiriz,et al.  Semi-Supervised Support Vector Machines , 1998, NIPS.

[15]  Jiri Rohn.  On unique solvability of the absolute value equation , 2009, Optim. Lett..

[16]  O. Mangasarian,et al.  Absolute value equations , 2006 .

[17]  J. Rohn.  Systems of linear interval equations , 1989 .

[18]  Olvi L. Mangasarian,et al.  Feature Selection in k-Median Clustering , 2004 .

[19]  Olvi L. Mangasarian,et al.  Machine Learning via Polyhedral Concave Minimization , 1996 .

[20]  Olvi L. Mangasarian,et al.  Absolute value equation solution via concave minimization , 2006, Optim. Lett..

[21]  Olvi L. Mangasarian,et al.  Absolute value programming , 2007, Comput. Optim. Appl..