A fast clustering algorithm for data with a few labeled instances.

Area of Science:

• Data Science
• Machine Learning
• Clustering Algorithms

Background:

• Clustering quality is often assessed using metrics like cluster diameter and split.
• Existing metric learning algorithms can be computationally intensive, often relying on semidefinite programming.

Purpose of the Study:

• To develop a fast clustering algorithm that finds optimal solutions under specific conditions.
• To propose computationally efficient metric learning algorithms that maximize the split-to-diameter ratio (RSD).
• To demonstrate the effectiveness of learned metrics and supervision in improving clustering quality.

Main Methods:

• A novel clustering algorithm is presented, guaranteeing optimality for certain RSD values.
• Metric learning is formulated as a linear programming problem, offering computational advantages over semidefinite programming.
• Empirical evaluations are conducted to validate the proposed methods.

Main Results:

• The proposed clustering algorithm achieves optimal solutions when the RSD of the optimal solution exceeds one.
• The linear programming-based metric learning approach is computationally efficient.
• Empirical results show significant improvements in clustering quality due to learned metrics and supervision.

Conclusions:

• The developed clustering and metric learning techniques offer efficient and effective solutions for data analysis.
• The learned metric and use of supervision demonstrably enhance the quality of clustering outcomes.
• This work provides a computationally efficient alternative for metric learning in clustering tasks.