SVM and kernels Suppose you are given a binary classification problem. How do you know that you have to map the problem into a higher dimensional space? In other words, how would you know that a linear SVM is not suitable for a problem? Would you look at the accuracy?
 A: Mapping to higher dimensions is typically only helpful when working in relatively low-dimensional input spaces. In text mining, for instance, it doesn't help much since the input spaces are typically high dimensional ($\gt 100,000$ dimensions).
Basically, always try the linear kernel first and move on to more complex feature spaces if and only if you get insatisfactory results. Be aware that more complex kernels are no guarantee to a better model.
A: Based on my own experience with SVM, which in fact is limited mainly to financial market applications, I don't generally know what in advance what will be the best SVM kernel to use. Therefore I make a comparison test between linear, polynomial of varying degree, and RBF. For the work that I am doing, I find that linear, polynomial of low & odd degree, and RBF give good results, with 3rd order polynomial and RBF usually being the best, slightly ahead of linear. 
There are a number of different possible metrics for ML quality that you can use based on the confusion matrix. Which metrics are preferred depends to some extent on the specific technical domain in which you are applying your SVM. Accuracy =  (TP+TN)/total is generally NOT the best metric to use. The combination of Sensitivity (Recall) = TPR = TP/(TP+FN) and  FPR = FP/(FP+TN) is what is conventionally plotted on the ROC chart. The combination of these is Informedness = TPR - FPR = distance from random, which you generally seek to maximize. The other unbiased metric is Markedness = Precision + FN/(TN+FN), which is essentially Precision corrected for bias associated with any imbalance between P & N in your input data. The geometric mean of Informedness and markedness is the Matthews correlation coefficient, defined as MCC = (TP*TN-FP*FN)/SQRT[(TP+FP)(TP+FN)(TN+FP)*(TN+FN)]. Other measures such as F1 score = 2*TP/(2*TP+FP+FN) which is commonly used in some applications, suffers from bias associated with input data. The Matthews CC avoids this problem. 
