Support vector machines over a discrete structure: a kernel for qualitative orders of magnitude spaces

This paper is within the domain of the study of learning algorithms based on kernels, precisely of the Support Vector Machines. A kernel is constructed over the discrete structure of absolute orders of magnitudes spaces. This kernel is based on an explicit function, defined from the space of k-tuples of qualitative labels to a feature space, which captures the remoteness between the components of the patterns by using certain weights exponentially. A simple example that allows interpreting the kernel in terms of proximity of the patterns is presented.