Clustering and the perturbed spatial median

Authors:
Tuomo Valkonen;Tommi KäRkkäInen
Affiliations:
Department of Mathematical Information Technology, University of Jyväskylä, Finland;Department of Mathematical Information Technology, University of Jyväskylä, Finland
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

Citing 10
Cited 0

The Euclidean multifacility location problem

Operations Research
A projection method for lp norm location-allocation problems

Mathematical Programming: Series A and B
Approximation schemes for Euclidean k-medians and related problems

STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Optimization Problems with Perturbations: A Guided Tour

SIAM Review
DC programming: overview

Journal of Optimization Theory and Applications
Conditions for Global Optimality 2

Journal of Global Optimization
Solution of the Multisource Weber and Conditional Weberproblems by D.-C. Programming

Operations Research
Improvement and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem

Operations Research
A Unified Continuous Optimization Framework for Center-Based Clustering Methods

The Journal of Machine Learning Research
K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality

IEEE Transactions on Pattern Analysis and Machine Intelligence

Quantified Score

Hi-index	0.98

Visualization

Abstract

The application of the Weiszfeld method to diff-convex (DC) problems of so-called perturbed spatial medians are studied with a focus on clustering problems involving incomplete data. Moreover, some level set theorems are provided for general DC problems. These results are then applied to study certain multiobjective formulations of clustering problems, and to yield a new algorithm for solving the multisource Weber problem.