# Does a linear SVM behave in the same way as correlation except with the imposition of a large margin?

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)?

• Your question is somewhat meaningless. Correlation is a number, while SVM is a classifer (it's also a regression algorithm), i.e. a function. A better question perhaps might be: what is the relationship between an SVM classifier and a, say logistic regression classifier. Or, maybe, SVM-regression and linear regression. Commented Jun 23, 2012 at 19:07
• I think my question is vague and poorly posed. Might try again when I've thought it through better. Commented Jun 23, 2012 at 23:22

In a great simplification, the point of SVM is to make function of predictors $f(X_i)$ so that $f(X_i)<0$ for class A and $>0$ for B; the core of SVM is that this $f$ is done so that the distance between maximum value of $f$ for A and minimal for B is as large as possible, not counting outliers.
So the linear SVM (for which $f=A_iX_i+B$) is a kind of weird linear regression, thus in fact can be just described in means of inter-class correlation minimization (plus minus usual attribute normalisation step) and claimed nothing interesting.
However, this is not really the point -- you can swap linear kernel with other, arbitrarily sophisticated method of comparing observations; this way your $f$ can become arbitrary interesting while the margin should protect you from overfitting.