Should an SVM grid search show a high-accuracy region with low accuracies around?

I have 12 positive training sets (cancer cells treated with drugs with each of 12 different mechanisms of action). For each of these positive training sets, I would like to train a support-vector machine to distinguish it from a negative set of equal size sampled from the experiment. Each set has between 1000 and 6000 cells, and there are 476 features (image features) of each cell, each scaled linearly to [0, 1].

I use LIBSVM and the Gaussian RGB kernel. Using five-fold crossvalidation, I have done a grid search for log₂ C ∈ [-5, 15] and log₂ ɣ ∈ [-15, 3]. The results are as follows:

I was disappointed that there is not a single set of parameters that give high accuracies for all 12 classification problems. I was also surprised that the grids do not generally show a high-accuracy region surrounded by lower accuracies. Does this just mean that I need to expand the search parameter space, or is the grid search an indication that something else is wrong?

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Re disappointment: You wouldn't expect each problem to have the same parameters, so why would you expect the problems to share good values for the hyperparameters (log gamma and C)? – conjugateprior Jan 4 '11 at 19:19
@Conjugate Prior: The training sets are subsets of the same experiment, and the negative training sets are sampled from the same population, so I had hoped that the same RBF kernel width ɣ would be effective. Because the positive sets are being discriminated from the same background (negative) population, I had hoped that the ideal penalty C would be similar as well. If this is not the case, it makes SVM really hard to apply. Gentle boosting, for instance, seems much easier to tune. – Vebjorn Ljosa Jan 4 '11 at 19:51
Aha. But it seems to me that although it is the same experiment in the physical sense, you are nevertheless attacking separate and different problems in the statistical sense. Particularly if the negative cases are resampled for each treatment. – conjugateprior Jan 4 '11 at 19:59
BTW, grid search is rather inefficient, the Nelder-Mead simplex optimisation algorithm is very effective, as are gradient descent optimzation methods. Grid search is simple, but a bit "brute force". – Dikran Marsupial Jan 5 '11 at 0:59
@Vebjorn Ljosa (a year later), how much do the 5 values scatter, say at the final (C, gamma) ? Are the 12 plots all scaled the same, e.g. 50 % .. 100 % correct prediction ? Thanks – Denis Feb 11 '12 at 14:33