Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Cluster analysis and mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
ACM Computing Surveys (CSUR)
An Interior Point Algorithm for Minimum Sum-of-Squares Clustering
SIAM Journal on Scientific Computing
Learning mixtures of arbitrary gaussians
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Clustering Algorithms
A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem
SIAM Journal on Optimization
Mathematical Programming in Data Mining
Data Mining and Knowledge Discovery
Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Journal of Global Optimization
Knowledge Acquisition Via Incremental Conceptual Clustering
Machine Learning
Feature Selection via Concave Minimization and Support Vector Machines
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Leveraging the margin more carefully
ICML '04 Proceedings of the twenty-first international conference on Machine learning
A Global Optimization RLT-based Approach for Solving the Hard Clustering Problem
Journal of Global Optimization
Trading convexity for scalability
ICML '06 Proceedings of the 23rd international conference on Machine learning
A new efficient algorithm based on DC programming and DCA for clustering
Journal of Global Optimization
NP-hardness of Euclidean sum-of-squares clustering
Machine Learning
New and efficient DCA based algorithms for minimum sum-of-squares clustering
Pattern Recognition
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In this paper, we propose a new approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) to perform clustering via minimum sum-of-squares Euclidean distance. The so called Minimum Sum-of-Squares Clustering (MSSC in short) is first formulated in the form of a hard combinatorial optimization problem. It is afterwards recast as a (continuous)| DC program with the help of exact penalty in DC programming. A DCA scheme is then investigated. The related DCA is original and very inexpensive because it amounts to computing, at each iteration, the projection of points onto a simplex and/or onto a ball, that all are given in the explicit form. Numerical results on real word data sets show the efficiency of DCA and its great superiority with respect to K-means, a standard method of clustering.