Separating hypersurfaces of SVMs in input spaces

It is well-known that the separating hyperplane given by a (standard) support vector machine (SVM) is located in the middle of the margin with equal distance from the support vectors of the partitioned two clusters in the high-dimensional feature space. Whereas we expect that the corresponding separating hypersurface is also located in the middle of the margin with equal distance from the two clusters in the input sample space, in reality, it is not. We illustrate that in theory, the above “middle-located-hypersurface” expectation in input sample spaces is not ideally supported by SVMs. A few illustrative examples and additional experiments on large data sets are correspondingly investigated.