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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?

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  • $\begingroup$ What do you mean by "its pattern"? The analyst should have an idea of what to look for. What is the research problem? $\endgroup$ – Emre May 10 '12 at 23:33
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A similar question was asked before.

I would take a look at this simple guide written by the people who created LIBSVM.

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  • $\begingroup$ This doesn't answer your first question on how to analyze a dataset---which is quite a general question. I am currently reading "Statistical Modeling: The Two Cultures" by Leo Breiman. I am sure it can give you some insight on how to approach a dataset. $\endgroup$ – Pardis May 10 '12 at 15:10
  • $\begingroup$ @Pardis- Thank you very much for such quick response. Yes, I have looked at the sample guide of LIBSVM. Now I will look for the book you have mentioned. $\endgroup$ – Raihana May 10 '12 at 15:26
  • $\begingroup$ it's actually a paper published in the journal Statistical Science in 2001 $\endgroup$ – Pardis May 10 '12 at 15:38
  • $\begingroup$ @Pardis-Sorry to bother you again. I will look at the paper. But here I want to clear my situation. I looked at the sample guide of LIBSVM and follow their advice. They say, do your analysis with several different kernels. Choose the kernel that performs the best. I have started with RBF kernel (with diff gamma value) but then finally got good result with Polynomial kernel of degree 3.I need to discuss in my thesis why my dataset achieved good accuracy with polynomial.That's why I need to know how to analyze data which can help me to select suitable kernel.Do you have any suggestions?Thanks. $\endgroup$ – Raihana May 10 '12 at 16:00
  • $\begingroup$ I don't think you will be able to find a clear-cut analysis on this subject, especially if you are dealing with a real-world data set. I'm not sure if there is any analysis at all on the topic. $\endgroup$ – Pardis May 10 '12 at 16:38
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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.

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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.

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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.

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