Kernel k-Groups via Hartigan's Method.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Energy statistics, inspired by classical mechanics, offers model-free distribution comparison.
• Generalizations of energy statistics to metric spaces of negative type enable broader applications.
• Clustering and community detection are fundamental problems in data analysis.

Purpose of the Study:

• To formulate a clustering approach using weighted energy statistics in spaces of negative type.
• To connect this formulation to quadratic programming and kernel methods.
• To introduce kernel k-groups as an efficient clustering algorithm.

Main Methods:

• A weighted energy statistics formulation for clustering in metric spaces of negative type.
• Derivation of a quadratically constrained quadratic program in a kernel space.
• Development of kernel k-groups, extending Hartigan's method to kernel spaces.

Main Results:

• The proposed method establishes connections between energy statistics, graph partitioning, and kernel methods.
• Kernel k-groups demonstrates improved performance over spectral clustering, especially in high dimensions.
• The method shows efficiency in community detection for stochastic block models.

Conclusions:

• Kernel k-groups provides a computationally efficient and high-performing clustering solution.
• This work extends the applicability of energy statistics to machine learning tasks.
• The findings have implications for community detection in various scientific domains.