I am using SVM for classification and I am trying to determine the optimal parameters for linear and RBF kernels. For the linear kernel I use cross-validated parameter selection to determine C and for the RBF kernel I use grid search to determine C and gamma.
I have 20 (numeric) features and 70 training examples that should be classified into 7 classes.
Which search range should I use for determining the optimal values for the C and gamma parameters?
Check out A practical guide to SVM Classification for some pointers, particularly page 5.
We recommend a "grid-search" on $C$ and $\gamma$ using cross-validation. Various pairs of $(C,\gamma)$ values are tried and the one with the best cross-validation accuracy is picked. We found that trying exponentially growing sequences of $C$ and $\gamma$ is a practical method to identify good parameters (for example, $C = 2^{-5},2^{-3},\ldots,2^{15};\gamma = 2^{-15},2^{-13},\ldots,2^{3}$).
Remember to normalize your data first and if you can, gather more data because from the looks of it, your problem might be heavily underdetermined.
Check out section 2.3.2 of this paper by Chapelle and Zien. They have a nice heuristic to select a good search range for $\sigma$ of the RBF kernel and $C$ for the SVM. I quote
To determine good values of the remaining free parameters (eg, by CV), it is important to search on the right scale. We therefore fix default values for $C$ and $\sigma$ that have the right order of magnitude. In a $c$-class problem we use the $1/c$ quantile of the pairwise distances $D^\rho_{ij}$ of all data-points as a default for $\sigma$. The default for $C$ is the inverses of the empirical variance $s^2$ in features space, which can be calculated by $s^2 = \frac{1}{n} \sum_i K_{ii} - \frac{1}{n^2}\sum_{i,j} K_{ij}$ from a $n\times n$ kernel matrix $K$.
Afterwards, they use multiples (e.g. $2^k$ for $k\in \{-2,...,2\}$) of the default value as search range in a grid-search using cross-validation. That always worked very well for me.
Of course, we @ciri said, normalizing the data etc. is always a good idea.
