Bsvm

We describe a novel binary classification technique called Banded SVM (B-SVM). In the standard C-SVM formulation of Cortes and Vapnik [1995], the decision rule is encouraged to lie in the interval [1,∞]. The new B-SVM objective function contains a penalty term that encourages the decision rule to lie in a user specified range [ρ1, ρ2]. In addition to the standard set of support vectors (SVs) near the class boundaries, B-SVM results in a second set of SVs in the interior of each class. Notation Scalars and functions will be denoted in a non-bold font (e.g., β0, C, g). Vectors and vector functions will be denoted in a bold font using lower case letters (e.g., x,β,h). Matrices will be denoted in bold font using upper case letters (e.g., B,H). The transpose of a matrix A will be denoted by AT and its inverse will be denoted by A−1. Ip will denote the p × p identity matrix and 0 will denote a vector or matrix of all zeros whose size should be clear from context. |x| will denote the absolute value of x and I(x > a) is an indicator function that returns 1 if x > a and 0 otherwise. The jth component of vector t will be denoted by tj . The element (i, j) of matrixG will be denoted by G(i, j) or Gij . The 2-norm of a p×1 vector x will be denoted by ||x||2 = + √∑p i=1 x 2 i . Probability distribution of a random vector x will be denoted by Px(x). E [f(s,η)] denotes the expectation of f(s,η) with respect to both random variables s and η. 2