First, I want to know how to analyze a dataset to discover its pattern. And second, how can I select the best kernel function for classifying a dataset?
I don't know the SVM lingo but it sounds like you want to do kernel discrimnation. D. J. Hand has a good book on it. Basically you use the kernel method to estimate the class conditional densities. Then you apply the Bayes rule as if the estimated densities were the actual ones. What is best with respect to a kernel function is not usually important although there are assumptions that lead to a theoretical best kernel. But what really matters is the bandwidth. However it is sometimes hard to tell what is too small leading to a density that is too rough versus too large which leads to a density that is too smooth. The book that I think provides the clearest explanation of probability density estimation is Bernie Silverman's book. Check it out if you don't follow what I ahve told you.
Please note that there is a difference between the kernel questioned here and the one in the answer above. See here.
The best and first resource on the kernels in question is "Theory of Reproducing Kernels" by Nachman Aronszajn. You can also look at Grace Wahba's book: "Spline Models for Observational Data".
A reproducing kernel uniquely identifies a reproducing kernel Hilbert space.
I am familiar with Wahba's work in splines using RKHS and her dissertation advisor Manny Parzen. I had no clue that you were talking about that. Part of my problem as I said is that I am not familiar with SVM and its jargon. I was making a guess that since you were talking about classification that you were talking about kernel discriminant analysis. Since I was wrong about that you can ignore my comments on that topic.