Interface MercerKernel<T>

  • All Superinterfaces:
    java.io.Serializable
    All Known Implementing Classes:
    GaussianKernel

    public interface MercerKernel<T>
    extends java.io.Serializable
    A Mercer Kernel is a kernel that is positive semi-definite. When a kernel is positive semi-definite, one may exploit the kernel trick, the idea of implicitly mapping data to a high-dimensional feature space where some linear algorithm is applied that works exclusively with inner products. Assume we have some mapping Φ from an input space X to a feature space H, then a kernel k(u, v) = <Φ(u), Φ(v)> may be used to define the inner product in feature space H.

    Positive definiteness in the context of kernel functions also implies that a kernel matrix created using a particular kernel is positive semi-definite. A matrix is positive semi-definite if its associated eigenvalues are nonnegative.

    Author:
    Haifeng Li
    • Method Detail

      • k

        double k​(T x,
                 T y)
        Kernel function.