I want to understand the relationship between correlation and SVMs. My question is based on initial studies that used correlation as a way to examine distributed processing in the cortex with fMRI. This approach involved showing that within class correlations of evoked activity were greater than between class correlations (apparently this is similar to nearest neighbour methods).
Oddly, many researchers still use simple similarity measures, like correlations, even though there are many more sophisticated techniques available. It seems to me that correlations continue to be used since correlations only assess differences in patterns of response, not changes in magnitude. This is an attractive property since it provides a measure of whether different categories of stimuli evoke distinct patterns of activity within a region without measuring whether the two categories evoke different levels of activation.
I've only recently completed an introduction to kernel methods with SVMs and, to my understanding, the classifier forms the decision boundary based on a 'correlation-like' similarity measure between the examples. So my questions are;
Does a linear SVM behave in the same way as correlation except with the imposition of a large margin?
AND if so, does a linear SVM retain the so called 'independence' to classes that only differ in magnitude?
ELSE if no, can a linear SVM use a correlation matrix instead of the standard similarity measures? (or is this a horrible franken-algorithm)?