Is there any better approaches to select kernel parameters other than grid search?
It depends on the specific kernel algorithm you are referring to. In the case of Support Vector Machines there are a few alternatives, not necessarily better than grid search, for example:
1) The gradient based approach of [1] (this is an iterative procedure).
2) Heuristic criteria such as the one presented in [2].
3) Tuning by means of evolutionary algorithms, possibly in conjunction with other parameters, e.g. [3].
[1] Chapelle, Olivier, et al. "Choosing multiple parameters for support vector machines." Machine learning 46.1-3 (2002): 131-159.
[2] Wu, Kuo-Ping, and Sheng-De Wang. "Choosing the kernel parameters for support vector machines by the inter-cluster distance in the feature space." Pattern Recognition 42.5 (2009): 710-717.
[3] Friedrichs, Frauke, and Christian Igel. "Evolutionary tuning of multiple SVM parameters." Neurocomputing 64 (2005): 107-117.
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