Reproduce “A New Framework for Convex Clustering in Kernel Spaces: Finite Sample Bounds, Consistency and Performance Insights” on OpenResearch

About this paper

Shubhayan Pan, Saptarshi Chakraborty, Debolina Paul, Kushal Bose, Swagatam Das

Researchers from the Indian Statistical Institute, University of Michigan, and University of Oxford developed Kernelized Convex Clustering (KCC), a framework extending convex clustering to effectively handle non-linear and non-convex data. KCC consistently outperformed state-of-the-art methods on various datasets, achieving an NMI of 0.999 on a complex synthetic dataset and superior scores across real-world benchmarks, while providing strong theoretical guarantees.

Key insights

• Convex clustering in a kernel space can be precisely reformulated as a standard convex clustering problem on a finite-dimensional embedding of the data.
• The framework provides strong theoretical guarantees, including algorithmic convergence to a unique global minimum, finite sample bounds for centroid estimates, and consistency under appropriate parameter scaling.
• KCC effectively merges the advantages of convex optimization (global optimality, automatic cluster number detection) with the capability of kernel methods to process complex, non-linear data distributions.

Summary by alphaXiv.