Convex Clustering with Exemplar-Based Models.

Area of Science:

• Machine Learning
• Data Mining
• Computational Statistics

Background:

• Clustering is commonly approached via maximum likelihood estimation of mixture models.
• The Expectation-Maximization (EM) algorithm, used for this, is gradient-descent based and sensitive to initial values, often yielding local optima.
• This initialization sensitivity poses challenges for clustering large datasets into numerous clusters.

Purpose of the Study:

• To develop a novel clustering approach that circumvents the local optima problem inherent in traditional methods.
• To introduce an exemplar-based likelihood function for approximating mixture models.
• To achieve guaranteed convergence to a globally optimal clustering solution.

Main Methods:

• Formulation of an exemplar-based likelihood function approximating the exact likelihood.
• Development of a convex minimization problem based on this formulation.
• Implementation of an efficient algorithm guaranteeing global convergence.

Main Results:

• The proposed method results in a convex minimization problem, unlike the non-convex problems often encountered.
• The algorithm demonstrates guaranteed convergence to the globally optimal solution.
• Clustering is framed as a probabilistic mapping to exemplars, minimizing distance and information-theoretic cost.

Conclusions:

• The exemplar-based approach provides a robust alternative to conventional mixture model clustering.
• This method addresses the critical challenge of initialization sensitivity in clustering algorithms.
• Experimental results validate the algorithm's performance and superiority over conventional techniques.