Optimization based DC programming and DCA for hierarchical clustering

One of the most promising approaches for clustering is based on methods of mathematical programming. In this paper we propose new optimization methods based on DC (Difference of Convex functions) programming for hierarchical clustering. A bilevel hierarchical clustering model is considered with different optimization formulations. They are all nonconvex, nonsmooth optimization problems for which we investigate attractive DC optimization Algorithms called DCA. Numerical results on some artificial and real-world databases are reported. The results demonstrate that the proposed algorithms are more efficient than related existing methods.

[1]  Le Thi Hoai An,et al.  A DC programming approach for feature selection in support vector machines learning , 2008, Adv. Data Anal. Classif..

[2]  Christoph Schnörr,et al.  Prior Learning and Convex-Concave Regularization of Binary Tomography , 2005, Electron. Notes Discret. Math..

[3]  Douglas H. Fisher,et al.  Iterative Optimization and Simplification of Hierarchical Clusterings , 1996, J. Artif. Intell. Res..

[4]  Le Thi Hoai An,et al.  Large-Scale Molecular Optimization from Distance Matrices by a D.C. Optimization Approach , 2003, SIAM J. Optim..

[5]  T. Schülea,et al.  Discrete tomography by convex – concave regularization and D . C . programming , 2005 .

[6]  A. Gill Waters,et al.  Optimising multicast structures for grid computing , 2004, Comput. Commun..

[7]  T. P. Dinh,et al.  Convex analysis approach to d.c. programming: Theory, Algorithm and Applications , 1997 .

[8]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[9]  Tao Pham Dinh,et al.  Exact penalty in d.c. programming , 1999 .

[10]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

[11]  A. Rubinov,et al.  Optimization based clustering algorithms in Multicast group Hierarchies , 2003 .

[12]  Fionn Murtagh,et al.  A Survey of Recent Advances in Hierarchical Clustering Algorithms , 1983, Comput. J..

[13]  Joachim Weickert,et al.  Geometric Properties for Incomplete Data (Computational Imaging and Vision) , 2005 .

[14]  A. Gill Waters,et al.  Applying clustering algorithms to multicast group hierarchies , 2003 .

[15]  W. Gander,et al.  A D.C. OPTIMIZATION ALGORITHM FOR SOLVING THE TRUST-REGION SUBPROBLEM∗ , 1998 .

[16]  Steven McCanne,et al.  A Preference Clustering Protocol for Large-Scale Multicast Applications , 1999, Networked Group Communication.

[17]  Le Thi Hoai An,et al.  Solving a Class of Linearly Constrained Indefinite Quadratic Problems by D.C. Algorithms , 1997, J. Glob. Optim..

[18]  Gabriele Steidl,et al.  SVM-Based Feature Selection by Direct Objective Minimisation , 2004, DAGM-Symposium.

[19]  J. Hiriart-Urruty,et al.  Convex analysis and minimization algorithms , 1993 .

[20]  Le Thi Hoai An,et al.  A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem , 1998, SIAM J. Optim..

[21]  C. Schnörr,et al.  Binary Tomography by Iterating Linear Programs , 2006 .

[22]  Le Thi Hoai An,et al.  The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems , 2005, Ann. Oper. Res..

[23]  Hoai An Le Thi,et al.  Solving a Class of Linearly Constrained Indefinite Quadratic Problems by D.C. Algorithms , 1997 .