The HPSVM Procedure

KERNEL Statement

  • KERNEL kernel-type / kernel-parameters;

The KERNEL statement specifies the type of kernel and any associated parameters to be used during training. You can specify one of the following kernel-types; for some kernel-types, you must specify one or two kernel-parameters.

LINEAR

uses a linear kernel during training. No kernel-parameter is needed. The kernel is defined as

k left-parenthesis x 1 comma x 2 right-parenthesis equals less-than x 1 comma x 2 greater-than

where x 1 and x 2 are two vectors and less-than comma greater-than is the inner product.

POLYNOM

uses a polynomial kernel during training. Specify the polynomial degree as the kernel-parameter. For example, specify KERNEL POLYNOM / DEGREE=2. The kernel is defined as

k left-parenthesis x 1 comma x 2 right-parenthesis equals left-parenthesis less-than x 1 comma x 2 greater-than plus 1 right-parenthesis Superscript p

where p is the degree of the polynomial.

RBF

uses a radial basis function (RBF) kernel during training. Specify K_PAR as the kernel-parameter. For example, specify KERNEL RBF / K_PAR=1. The kernel is defined as

k left-parenthesis x 1 comma x 2 right-parenthesis equals e x p left-parenthesis minus StartFraction StartAbsoluteValue EndAbsoluteValue x 1 minus x 2 StartAbsoluteValue EndAbsoluteValue squared Over 2 sigma squared EndFraction right-parenthesis

where sigma is a positive number, which is K_PAR.

SIGMOID

uses a sigmoid kernel during training. Specify two kernel-parameters, K_PAR and K_PAR2. For example, specify KERNEL SIGMOID / K_PAR=1 K_PAR2=–1. The kernel is defined as

k left-parenthesis x 1 comma x 2 right-parenthesis equals t a n h left-parenthesis p 1 less-than x 1 comma x 2 greater-than plus p 2 right-parenthesis

where p 1 is a positive number(as K_PAR) and p 2 is a negative number(as K_PAR2).

The default kernel type is LINEAR.

Last updated: May 25, 2022