Nonparametric Bayes Action Set

Kernel

The LA inference of the gpClass action uses either of two kernel types for the Gaussian process in Gaussian process classification: Gaussian or linear. The kernel type is specified by the kernel parameter.

The Gaussian kernel type represents a covariance matrix that is generated by a squared exponential function with specified input data, as shown in the following equation, where sigma is the Gaussian kernel bandwidth parameter specified by the sigma subparameter. The Gaussian kernel is versatile enough to separate two classes that are not linearly separable.

k left-parenthesis x comma x Superscript prime Baseline right-parenthesis equals normal e normal x normal p left-parenthesis StartFraction StartAbsoluteValue EndAbsoluteValue x minus x prime StartAbsoluteValue EndAbsoluteValue squared Over 2 sigma squared EndFraction right-parenthesis

The linear kernel type represents a covariance matrix that is generated using a linear function, as shown in the following equation, where c is the constant in the linear function that is specified by the constant subparameter. When the classes in the data are linearly separable, the linear type can yield good results and a faster processing time than the Gaussian type.

k left-parenthesis x comma x Superscript prime Baseline right-parenthesis equals less-than x comma x prime greater-than plus c
Last updated: August 04, 2026