Optimization approach for clustering datasets with weights

Abstract

We introduce datasets with weights and suggest using the minimization of some highly nonsmooth functions for clustering of such datasets. Datasets with weights often appear as the result of an approximation of large-scale datasets. We examine such approximations and also consider the application of datasets with weights to examine self-organizing maps. Results of some numerical experiments are presented and discussed.

Keywords:

• Datasets with weights
• Nonsmooth optimization
• Cluster function
• Bradley–Mangasarian approximation
• Skeleton
• Self-organizing map

Acknowledgement

The authors are thankful to an anonymous referee for their valuable comments.