Issue No. 09 - September (2000 vol. 22)

ISSN: 0162-8828

pp: 950-955

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.877518

ABSTRACT

<p><b>Abstract</b>—The robust Huber M-estimator, a differentiable cost function that is quadratic for small errors and linear otherwise, is modeled exactly, in the original primal space of the problem, by an easily solvable simple convex quadratic program for both linear and nonlinear support vector estimators. Previous models were significantly more complex or formulated in the dual space and most involved specialized numerical algorithms for solving the robust Huber linear estimator [<ref type="bib" rid="bibI09503">3</ref>], [<ref type="bib" rid="bibI09506">6</ref>], [<ref type="bib" rid="bibI095012">12</ref>], [<ref type="bib" rid="bibI095013">13</ref>], [<ref type="bib" rid="bibI095014">14</ref>], [<ref type="bib" rid="bibI095023">23</ref>], [<ref type="bib" rid="bibI095028">28</ref>]. Numerical test comparisons with these algorithms indicate the computational effectiveness of the new quadratic programming model for both linear and nonlinear support vector problems. Results are shown on problems with as many as 20,000 data points, with considerably faster running times on larger problems.</p>

INDEX TERMS

Support vector machines, regression, Huber M-estimator, kernel methods.

CITATION

Olvi L. Mangasarian, David R. Musicant, "Robust Linear and Support Vector Regression",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol. 22, no. , pp. 950-955, September 2000, doi:10.1109/34.877518