Feature Space Interpretation of SVMs with non Positive Definite Kernels

The widespread habit of “plugging” arbitrary symmetric functions as kernels in support vector machines (SVMs) often yields good empirical classification results. However, in case of non conditionally positive definite (non-cpd) functions they are hard to interpret due to missing geometrical and theoretical understanding. In this paper we provide a step towards comprehension of SVM classifiers in these situations. We give a geometric interpretation of SVMs with non-cpd kernel functions. We show that such SVMs are optimal hyperplane classifiers not by margin maximization but by minimization of distances between convex hulls in pseudo-Euclidean spaces. This interpretation is basis for further analysis, e.g. investigating uniqueness or characterizing situations where SVMs with noncpd kernels are suitable or not.