I am trying some new kernel functions.
For some new kernel functions, I have checked the eigen values of corresponding Gram matrix(UCI bench mark data set). The eigen values are positive and for one kernel function it is mixture of positive and negative. Can I conclude that the kernel functions corresponding all positive Eigen values are PD and with mixture is indefinite. I read somewhere that the kernel functions which are not PD may give rise to the Gram matrix with all positive eigen values , Because of this sentence I have confusion.
I have checked the nature of the eigen values taking the parameter values which give good classification accuracy.
I have also confusion between CPD and PD kernels. What is the eigen values of CPD kernels?
I have read "Bernhard Scholkopf, and Alexander J. Smola. Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT press, 2001" . But, still want some easy explanation and proof regrading this.