Duality, Geometry, and Support Vector Regression
We develop an intuitive geometric framework for support vector regression (SVR). By examining when ∊-tubes exist, we show that SVR can be regarded as a classification problem in the dual space. Hard and soft ∊-tubes are constructed by separating the convex or reduced convex hulls respectively of the training data with the response variable shifted up and down by ∊. A novel SVR model is proposed based on choosing the max-margin plane between the two shifted datasets. Maximizing the margin corresponds to shrinking the effective ∊-tube. In the proposed approach the effects of the choices of all parameters become clear geometrically.