An algorithm for minimizing clustering functions

References

• Hansen , P and Jaumard , B . 1997 . Cluster analysis and mathematical programming . Mathematical Programming , 79 ( 1–3 ) : 191 – 215 .
   Web of Science ®Google Scholar
• Jain , AK , Murty , MN and Flynn , PJ . 1999 . Data clustering: a review . ACM Computing Surveys , 31 ( 3 ) : 263 – 323 .
   Google Scholar
• Bock HH 1974 Automatische Klassifikation Gottingen Vandenhoeck & Ruprecht
   Google Scholar
• Bock HH 1998 Clustering and neural networks In: A. Rizzi, M. Vichi and H.H. Bock (Eds) Advances in Data Science and Classification Berlin Springer-Verlag pp. 265–277
   Google Scholar
• Spath H 1980 Cluster Analysis Algorithms Chichester Ellis Horwood Limited
   Google Scholar
• Dubes , R and Jain , AK . 1976 . Clustering techniques: the user's dilemma . Pattern Recognition , 8 : 247 – 260 .
   Web of Science ®Google Scholar
• Hansen , P and Mladenovic , N . 2001 . J-means: a new heuristic for minimum sum-of-squares clustering . Pattern Recognition , 4 : 405 – 413 .
   Google Scholar
• Houkins DM Muller MW Ten Krooden JA 1982 Cluster analysis. In: Topics in Applied Multivariate Analysis Cambridge Cambridge University press
   Google Scholar
• Jensen , RE . 1969 . A dynamic programming algorithm for cluster analysis . Operations Research , 17 : 1034 – 1057 .
   Web of Science ®Google Scholar
• Diehr , G . 1985 . Evaluation of a branch and bound algorithm for clustering . SIAM Journal on Scientific and Statistical Computing , 6 : 268 – 284 .
   Web of Science ®Google Scholar
• Hanjoul , P and Peeters , D . 1985 . A comparison of two dual-based procedures for solving the p-median problem . European Journal of Operational Research , 20 : 387 – 396 .
   Google Scholar
• Koontz , WLG , Narendra , PM and Fukunaga , K . 1975 . A branch and bound clustering algorithm . IEEE Transactions on Computers , 24 : 908 – 915 .
   Google Scholar
• Reeves CR (Ed.) 1993 Modern Heuristic Techniques for Combinatorial Problems London Blackwell
   Google Scholar
• Brown , DE and Entail , CL . 1992 . A practical application of simulated annealing to the clustering problem . Pattern Recognition , 25 : 401 – 412 .
   Google Scholar
• Selim , SZ and Al-Sultan , KS . 1991 . A simulated annealing algorithm for the clustering . Pattern Recognition , 24 ( 10 ) : 1003 – 1008 .
   Web of Science ®Google Scholar
• Sun , LX , Xie , YL , Song , XH , Wang , JH and Yu , RQ . 1994 . Cluster analysis by simulated annealing . Computers and Chemistry , 18 : 103 – 108 .
   Google Scholar
• Al-Sultan , KS . 1995 . A tabu search approach to the clustering problem . Pattern Recognition , 28 ( 9 ) : 1443 – 1451 .
   Web of Science ®Google Scholar
• Al-Sultan , KS and Khan , MM . 1996 . Computational experience on four algorithms for the hard clustering problem . Pattern Recognition Letters , 17 : 295 – 308 .
   Google Scholar
• du Merle , O , Hansen , P , Jaumard , B and Maldenovic , N . 2001 . An interior point method for minimum sum-of-squares clustering . SIAM Journal on Scientific Computing , 21 : 1485 – 1505 .
   Google Scholar
• Hansen , P and Mladenovic , N . 2001 . Variable neighborhood decomposition search . Journal of Heuristic , 7 : 335 – 350 .
   Web of Science ®Google Scholar
• Likas , A , Vlassis , M and Verbeek , J . 2003 . The global k-means clustering algorithm . Pattern Recognition , 36 : 451 – 461 .
   Web of Science ®Google Scholar
• Hansen P Ngai E Cheung K Mladenovic N Analysis of global k-means, an incremental heuristic for minimum sum-of-squares clustering Journal of Classification to appear
   Google Scholar
• Bagirov , AM , Rubinov , AM and Yearwood , J . 2002 . A global optimisation approach to classification . Optimization and Engineering , 3 ( 2 ) : 129 – 155 .
   Web of Science ®Google Scholar
• Bagirov AM Yearwood J A new nonsmooth optimisation algorithm for minimum sum-of-squares clustering algorithms European Journal of Operational Research (To appear)
   Google Scholar
• Bagirov , AM , Rubinov , AM , Soukhoroukova , NV and Yearwood , J . 2003 . Supervised and unsupervised data classification via nonsmooth and global optimisation . TOP: Spanish Operations Research Journal , 11 ( 1 ) : 1 – 93 .
   Google Scholar
• Clarke FH 1983 Optimization and Nonsmooth Analysis New York Wiley
   Google Scholar
• Demyanov VF Rubinov AM 1995 Constructive Nonsmooth Analysis Frankfurt am Main Peter Lang
   Google Scholar
• Mifflin , R . 1977 . Semismooth and semiconvex functions in constrained optimization . SIAM Journal on Control and Optimization , 15 ( 6 ) : 959 – 972 .
   Web of Science ®Google Scholar
• Hiriart-Urruty J-P Lemarechal C 1993 Convex Analysis and Minimization Algorithms Vol. 1 and 2 Berlin, New York Springer-Verlag
   Google Scholar
• Kiwiel KC 1985 Methods of Descent for Nondifferentiable Optimization Lecture Notes in Mathematics 1133 Berlin Springer-Verlag
   Google Scholar
• Makela MM Neittaanmaki P 1992 Nonsmooth Optimization Singapore World Scientific
   Google Scholar
• Powell , MJD . 2002 . UOBYQA: unconstrained optimization by quadratic approximation . Mathematical Programming, Series B , 92 ( 3 ) : 555 – 582 .
   Web of Science ®Google Scholar
• Nelder , JA and Mead , R . 1965 . A simplex method for function minimization . Computer Journal , 7 : 308 – 313 .
   Web of Science ®Google Scholar
• Bagirov AM 1999 Minimization methods for one class of nonsmooth functions and calculation of semi-equilibrium prices In: A. Eberhard et al.(Eds) Progress in Optimization: Contribution from Australasia Dordrecht Kluwer Academic Publishers pp. 147–175
   Google Scholar
• Bagirov , AM . 2002 . A method for minimization of quasidifferentiable functions . Optimization Methods and Software , 17 ( 1 ) : 31 – 60 .
   Web of Science ®Google Scholar
• Bagirov , AM . 2003 . Continuous subdifferential approximations and their applications . Journal of Mathematical Sciences , 115 ( 5 ) : 2567 – 2609 .
   Google Scholar
• Bagirov , AM and Gasanov , AA . 1995 . A method of approximating a quasidifferential . Russian Journal of Computational Mathematics and Mathematical Physics , 35 ( 4 ) : 403 – 409 .
   Google Scholar
• Wolfe , PH . 1976 . Finding the nearest point in a polytope . Mathematical Programming , 11 ( 2 ) : 128 – 149 .
   Google Scholar
• Fisher RA 1936 The use of multiple measurements in taxonomic problems Ann Eugenics VII part II 179 188 Reprinted in R.A. Fisher Contributions to Mathematical Statistics, Wiley 1950
   Google Scholar
• Murphy PM Aha DW 1992 UCI repository of machine learning databases Technical report, Department of Information and Computer Science University of California Irvine www.ics.uci.edu/mlearn/MLRepository.html
   Google Scholar
• Reinelt , G . 1991 . TSP-LIB-A Traveling Salesman Library . ORSA J. Comput. , 3 : 319 – 350 .
   Google Scholar