Class of Monotone Kernelized Classifiers on the basis of the Choquet Integral

The key property of monotone classifiers is that increasing (decreasing) input values lead to increasing (decreasing) the output value. Preserving monotonicity for a classifier typically requires many constraints to be respected by modeling approaches such as artificial intelligence techniques. The type of constraints strongly depends on the modeling assumptions. Of course, for sophisticated models such conditions might be very complex. In this study we present a new family of kernels that we call it Choquet kernels. Henceforth it allows for employing popular kernel-based methods such as support vector machines. Instead of a naive approach with exponential computational complexity we propose an equivalent formulation with quadratic time in the number of attributes. Furthermore, since coefficients derived from kernel solutions are not necessarily monotone in the dual form, different approaches are proposed to monotonize coefficients. Finally experiments illustrate beneficial properties of the Choquet kernels.