Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
A deterministic annealing approach to clustering
Pattern Recognition Letters
A smoothing technique for nondifferentiable optimization problems
Proceedings of the international seminar on Optimization
Elements of information theory
Elements of information theory
Entropic proximal mappings with applications to nonlinear programming
Mathematics of Operations Research
Deterministic annealing EM algorithm
Neural Networks
ACM Computing Surveys (CSUR)
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Alternatives to the k-means algorithm that find better clusterings
Proceedings of the eleventh international conference on Information and knowledge management
Convergence of Proximal-Like Algorithms
SIAM Journal on Optimization
Penalty and Barrier Methods: A Unified Framework
SIAM Journal on Optimization
Feature Weighting in k-Means Clustering
Machine Learning
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Interior Gradient and Proximal Methods for Convex and Conic Optimization
SIAM Journal on Optimization
Grouping Multidimensional Data: Recent Advances in Clustering
Grouping Multidimensional Data: Recent Advances in Clustering
ICML '06 Proceedings of the 23rd international conference on Machine learning
Clustering with Bregman Divergences
The Journal of Machine Learning Research
The spectral method for general mixture models
COLT'05 Proceedings of the 18th annual conference on Learning Theory
IEEE Transactions on Information Theory
An axiomatic approach to soft learning vector quantization and clustering
IEEE Transactions on Neural Networks
Probabilistic distance clustering adjusted for cluster size
Probability in the Engineering and Informational Sciences
Clustering Multivariate Normal Distributions
Emerging Trends in Visual Computing
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Sided and symmetrized Bregman centroids
IEEE Transactions on Information Theory
Local matrix adaptation in topographic neural maps
Neurocomputing
Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach
International Journal of Computer Vision
Model-Based Multiple Rigid Object Detection and Registration in Unstructured Range Data
International Journal of Computer Vision
Clustering and the perturbed spatial median
Mathematical and Computer Modelling: An International Journal
A generalized Weiszfeld method for the multi-facility location problem
Operations Research Letters
Journal of Visual Communication and Image Representation
A fast partitioning algorithm and its application to earthquake investigation
Computers & Geosciences
A modification of the DIRECT method for Lipschitz global optimization for a symmetric function
Journal of Global Optimization
Hi-index | 0.06 |
Center-based partitioning clustering algorithms rely on minimizing an appropriately formulated objective function, and different formulations suggest different possible algorithms. In this paper, we start with the standard nonconvex and nonsmooth formulation of the partitioning clustering problem. We demonstrate that within this elementary formulation, convex analysis tools and optimization theory provide a unifying language and framework to design, analyze and extend hard and soft center-based clustering algorithms, through a generic algorithm which retains the computational simplicity of the popular k-means scheme. We show that several well known and more recent center-based clustering algorithms, which have been derived either heuristically, or/and have emerged from intuitive analogies in physics, statistical techniques and information theoretic perspectives can be recovered as special cases of the proposed analysis and we streamline their relationships.