Positive Definite Kernels for Partitions

Abstract

This paper presents a comprehensive exploration of various families of positive definite kernels for comparing partitions. It not only reviews existing examples from the literature but also introduces novel classes of positive definite kernels. These new classes include kernels based on agreement and ones designed using the concept of hidden variables. The study also focuses on assessing the compatibility of these kernels with structural properties that capture the intrinsic notion of proximity between partitions. Notably, agreement-based kernels are demonstrated to align well with this notion. Moreover, the paper provides two generic procedures for designing hidden-feature-based kernels that also adhere to the specified structural properties.