# Intuition on interchangeability of regression and classification

I've been trying to gather intuition on the relationship between methods that seems to be escaping me.

Can someone explain how regression and classification can be performed by the same method, such as SVM (Support Vector Machine) and what this implies about the interchangeability of these two tasks?

Background: I understand how an SVM performs discrimination but I cannot really understand how it could regress an arbitrary non-linear function, though I am told this can be done.

• Please spell out SVM - acronyms can be mysterious, especially to people whose native language is not English. – Peter Flom Nov 19 '14 at 11:48
• Support Vector Machines, my mistake, I'll edit it. – mrdevlar Nov 19 '14 at 11:54

• Thank you for completing this thread! I get how classification can be seen as a very special form of regression--in effect, a generalized (possibly non-) linear model for discrete (categorical) responses. I don't see how it goes the other way, though. How is regression the same as classification? The prototypical regression example of fitting a linear function to ordered pairs $(x_i,y_i)$ using OLS would not seem to "approximate" any "probabilities of membership" of anything at all. In what way do you understand OLS to solve a classification problem? – whuber Jan 21 '15 at 17:33