The Kernel Pitman-Yor Process
This work addresses clustering challenges in domains with spatial or temporal data, but it appears incremental as it builds on existing Pitman-Yor process frameworks.
The authors tackled the problem of nonparametric clustering for data with spatial or temporal dependencies by proposing the kernel Pitman-Yor process, which introduces a kernel function to control discount hyperparameters based on predictor proximity, resulting in a method that adapts to interdependencies without specifying concrete numerical results.
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.