The Kernel Pitman-Yor Process

TL;DR

This paper introduces the kernel Pitman-Yor process (KPYP), a novel nonparametric clustering method that models data with spatial or temporal dependencies using a kernel-controlled stick-breaking process.

Contribution

The paper develops the KPYP by integrating kernel functions into the Pitman-Yor process, enabling predictor-dependent clustering for data with complex interdependencies.

Findings

Enables clustering of spatially or temporally dependent data.

Incorporates kernel functions into the Pitman-Yor process.

Provides a flexible nonparametric prior for dependent data.

Abstract

In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.