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Pattern Separation and Prediction via Linear and Semidefinite Programming

Xing LIU
NewDay Financial LLC 8171
Maple Lawn Blvd, Suite 300 Fulton, MD 20759, USA

Florian A. POTRA
Department of Mathematics and Statistics
University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 22150, USA

Abstract: We present several optimization methods for separating two sets of points in the n-dimensional space that have nondisjoint convex closures. We give five methods based on linear programming techniques, and two methods based on semidefinite programming techniques. For predictive purposes, we construct two parallel hyperplanes, using linear programming, or two similar concentric ellipsoids, using semidefinite programming, so that the intersection of the convex hulls of the two sets is contained between the two hyperplanes, or the two ellipsoids, and the rest of the two sets, are separated completely. We then construct another hyperplane (or ellipsoid) situated between the two constructed hyperplanes (or ellipsoids), in order to achieve a superior pattern separation. We illustrate our methods on two breast cancer databases.

Keywords: Pattern separation, data mining, linear programming, semidefinite programming.

Xing Liu is a senior research scientist at Newday financial LLC located in Fulton, Maryland. He is leading the analytical effort in the marketing department, in charge of developing the core analytical tools, mathematical models, and information driven marketing platforms. Dr. Xing Liu has a Ph.D. degree in numerical optimization from the University of Maryland, Baltimore County, and has published several research papers in professional journals.

Florian A. Potra is a Professor of Mathematics and Statistics at the University of Maryland, Baltimore County, and a faculty appointee at the National Institute of Standards and Technology. He has published over 100 research papers in professional journals, and he serves on the editorial board of four well known mathematical journals. He was invited to give talks and work with research groups in different countries all over the world, including Germany, France, Switzerland, Italy, Belgium, Spain, the Netherlands, Australia, Singapore, Japan and Canada.

>>Full text
Xing LIU, Florian A. POTRA, Pattern Separation and Prediction via Linear and Semidefinite Programming, Studies in Informatics and Control, ISSN 1220-1766, vol. 18 (1), pp. 71-82, 2009.