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Unsupervised and Semisupervised Classification Via Absolute Value Inequalities

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Abstract

We consider the problem of classifying completely or partially unlabeled data by using 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. By using such absolute value inequalities in linear and nonlinear support vector machines, unlabeled or partially labeled data can be successfully partitioned into two classes that capture most of the correct labels dropped from the unlabeled data.

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References

  1. Bennett, K.P., Demiriz, A.: Semi-supervised support vector machines. In: Kearns, M .S., Solla, S .A., Cohn, D .A. (eds.) Advances in Neural Information Processing Systems, vol. 10, pp. 368–374. MIT Press, Cambridge, MA (1998)

    Google Scholar 

  2. Fung, G., Mangasarian, O.L.: Semi-supervised support vector machines for unlabeled data classification. Optim. Methods Softw. 15, 29–44 (2001)

    Article  MATH  Google Scholar 

  3. Al-Sultan, K.: A tabu search approach to the clustering problem. Pattern Recognit. 28(9), 1443–1451 (1995)

    Article  Google Scholar 

  4. Anderberg, M.R.: Cluster Analysis for Applications. Academic Press, New York (1973)

    MATH  Google Scholar 

  5. Bradley, P.S., Mangasarian, O.L., Street, W.N.: Clustering via concave minimization. In: Mozer, M.C., Jordan, M.I., Petsche, T. (eds.) Advances in Neural Information Processing Systems, vol. 9, pp. 368–374. MIT Press, Cambridge, MA (1997)

    Google Scholar 

  6. Celeux, G., Govaert, G.: Gaussian parsimonious clustering models. Pattern Recognit. 28, 781–793 (1995)

    Article  Google Scholar 

  7. Mangasarian, O.L., Wild, E.W.: Feature Selection in \(k\)-Median Clustering. Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, Report 04-01, January 2004. SIAM International Conference on Data Mining, Workshop on Clustering High Dimensional Data and Its Applications, April 24, 2004. La Buena Vista, FL, Proceedings pp. 23–28. http://www.siam.org/meetings/sdm04

  8. Mangasarian, O.L.: Absolute value programming. Comput. Optim. Appl. 36(1), 43–53 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rohn, J.: Systems of linear interval equations. Linear Algebra Appl. 126, 39–78 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  10. Rohn, J.: On unique solvability of the absolute value equation. Optim. Lett. 3, 603–606 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mangasarian, O.L., Meyer, R.R.: Absolute value equations. Linear Algebra Appl. 419, 359–367 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mangasarian, O.L.: Absolute value equation solution via concave minimization. Optim. Lett. 1(1), 3–8 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Mangasarian, O.L.: Absolute value equation solution via dual complementarity. Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, Report, (September 2011) ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/11-03.pdf. Optim. Lett. 7(4), 625–630 (2013)

  14. Mangasarian O.L.: Unsupervised classification via convex absolute value inequalities. Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, Report 14-01, (March 2014), ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/14-01.pdf. Optimization 64(1), 81–86 (2015)

  15. Mangasarian, O.L.: Generalized support vector machines. In: Smola, A., Bartlett, P., Schölkopf, B., Schuurmans, D. (eds.) Advances in Large Margin Classifiers, pp. 135–146. MIT Press, Cambridge, MA (2000)

    Google Scholar 

  16. Mangasarian, O.L.: Data mining via support vector machines. In: Sachs, E.W., Tichatschke, R. (eds.) System Modeling and Optimization, pp. 91–112. Kluwer Academic Publishers, Boston, MA (2003)

    Google Scholar 

  17. Mangasarian, O.L., Wild, E.W.: Nonlinear knowledge-based classification. IEEE Trans. Neural Netw. 19, 1826–1832 (2008)

    Article  Google Scholar 

  18. Fung, G., Mangasarian, O.L., Smola, A.: Minimal kernel classifiers. J. Mach. Learn. Res. 303–321 (2002). University of Wisconsin Data Mining Institute Technical Report 00-08, November 200, ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/00-08.ps

  19. Fung, G., Mangasarian, O.L.: Proximal support vector machine classifiers. In: Provost, F., Srikant, R. (eds.) Proceedings KDD-2001: Knowledge Discovery and Data Mining, August 26–29 (2001), pp. 77–86. Association for Computing Machinery, San Francisco, CA, New York (2001)

  20. Murphy, P.M., Aha, D.W.: UCI Machine Learning Repository (1992) http://archive.ics.uci.edu/ml/

  21. Fung, G.: The disputed federalist papers: SVM feature selection via concave minimization. In: Proceedings of the 2003 Conference on Diversity in Computing, pp. 42–46. Association for Computing Machinery, New York (2003)

  22. MATLAB. User’s Guide. The MathWorks, Inc., Natick, MA 01760, 1994–2006. http://www.mathworks.com

  23. Spath, H.: Cluster Dissection and Analysis: Theory, FORTRAN Programs, Examples, Translated by J. Goldschmidt. Halsted Press, New York (1985)

    Google Scholar 

  24. Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20(1), 53–65 (1987)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Business and Customer Operations Unit, American Family Insurance, Madison, WI, 53783, USA

    Glenn M. Fung

  2. Computer Sciences Department, University of Wisconsin, Madison, WI, 53706, USA

    Olvi L. Mangasarian

  3. Department of Mathematics, University of California at San Diego, La Jolla, CA, 92093, USA

    Olvi L. Mangasarian

Authors
  1. Glenn M. Fung
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  2. Olvi L. Mangasarian
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Correspondence to Olvi L. Mangasarian.

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Fung, G.M., Mangasarian, O.L. Unsupervised and Semisupervised Classification Via Absolute Value Inequalities. J Optim Theory Appl 168, 551–558 (2016). https://doi.org/10.1007/s10957-015-0818-5

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  • DOI: https://doi.org/10.1007/s10957-015-0818-5

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