2021/10/18 by Leena Chennuru Vankadara, Vankadara, Leena Chennuru, Sebastian Bordt +5 · 1 citation
Computer Science · Mathematics · #Advanced Clustering Algorithms Research #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Bayesian Inference #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2110.09476
arxiv created 2021/10/18 · openalex publication_date 2021/10/18 · arxiv updated 2021/10/19 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28
Despite the ubiquity of kernel-based clustering, surprisingly few statistical guarantees exist beyond settings that consider strong structural assumptions on the data generation process. In this work, we take a step towards bridging this gap by studying the statistical performance of kernel-based clustering algorithms under non-parametric mixture models. We provide necessary and sufficient separability conditions under which these algorithms can consistently recover the underlying true clustering. Our analysis provides guarantees for kernel clustering approaches without structural assumptions on the form of the component distributions. Additionally, we establish a key equivalence between kernel-based data-clustering and kernel density-based clustering. This enables us to provide consistency guarantees for kernel-based estimators of non-parametric mixture models. Along with theoretical implications, this connection could have practical implications, including in the systematic choice of the bandwidth of the Gaussian kernel in the context of clustering.