On Perfect Clustering for Gaussian Processes

Published: 26 Sept 2023, Last Modified: 27 Nov 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: In this paper, we propose a data based transformation for infinite-dimensional Gaussian processes and derive its limit theorem. For a clustering problem using mixture models, an appropriate modification of this transformation asymptotically leads to perfect separation of the populations under rather general conditions, except the scenario in which differences between clusters depend only on the locations; in which case our procedure is useless. Theoretical properties related to label consistency are studied for the k-means clustering algorithm when used on this transformed data. Good empirical performance of the proposed methodology is demonstrated using simulated as well as benchmark data sets, when compared with some popular parametric and nonparametric methods for such functional data.
Submission Length: Regular submission (no more than 12 pages of main content)
Supplementary Material: pdf
Changes Since Last Submission: We thank the AE and three reviewers for their constructive comments. We are now submitting the camera-ready version.
Video: https://youtu.be/NkV7sgdMioE
Code: https://www.dropbox.com/sh/ont3ggvz44g5j07/AAC1PRuzIWx9_yFUiR5mk4Zna?dl=0
Assigned Action Editor: ~Brian_Kulis1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 1336