Figure 1.

Schematic of a 2‐dimensional hard‐ (left) and soft‐ (right) margin Support Vector Machine with two classes to separate. Each observation of the learning set is plotted according to its value on the two features included in the analysis. Class 1 is plotted with open circles, Class 2 with closed circles. The dashed lines represent the margins. Thick circles highlight the support vectors (observations that define the margins). The separating hyper‐plane is situated halfway between the two margins. Left: Hard‐margin classifier. In this example, all points of the first class have a positive decision value, and all points of Class 2 have a negative decision value. Right: Soft‐margin classifier. Note the location of the observation and their corresponding slack value (ξ): 0 if outside the margin, < 1 and > 1 if located on the right and wrong side of the hyperplane, respectively.