An algorithm for minimizing clustering functions

Abstract

The problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization. An algorithm for solving the latter optimization problem is developed which allows one to significantly reduce the computational efforts. This algorithm is based on the so-called discrete gradient method. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed algorithm.

Keywords:

• Clustering functions
• Cluster analysis
• Nonsmooth, nonconvex optimization
• Discrete gradient method
• 2000 Mathematics Subject Classifications: 49M25
• 49M37
• 49J52
• 65K05
• 90C26

Acknowledgments

This research was supported by the Australian Research Council.

Notes

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.

Additional information

Notes on contributors

Julien Ugon

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.