Cluster Analysis: Unsupervised Learning via Supervised Learning with a Non-convex Penalty.

Area of Science:

• Data Science
• Machine Learning
• Statistical Modeling

Background:

• Clustering is traditionally unsupervised learning, lacking class labels or response variables.
• Determining the optimal number of clusters is a significant challenge in cluster analysis.

Purpose of the Study:

• To reformulate clustering as a penalized regression problem using grouping pursuit.
• To leverage supervised learning techniques, including model selection criteria, for clustering.
• To introduce a novel non-convex group penalty for enhanced clustering performance.

Main Methods:

• Formulation of clustering as penalized regression with grouping pursuit.
• Application of a non-convex group penalty for novel clustering characteristics.
• Utilizing generalized cross-validation (GCV) based on generalized degrees of freedom (GDF) for cluster number selection.

Main Results:

• The proposed penalized regression method demonstrates promising performance in clustering tasks.
• The approach effectively addresses the challenge of selecting the number of clusters.
• Numerical examples show competitive results against existing clustering methods.

Conclusions:

• The penalized regression framework offers a novel and effective approach to clustering.
• Integrating supervised learning concepts enhances clustering analysis, particularly in determining cluster numbers.
• The proposed method provides a valuable alternative for various clustering applications.