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Volumn 32, Issue 2, 2005, Pages 281-306

A global optimization RLT-based approach for solving the hard clustering problem

Author keywords

Clustering problem; Global optimization; Hard clustering; k Means algorithm; Reformulation Linearization Technique

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; DATA REDUCTION; HEURISTIC METHODS; LINEAR PROGRAMMING; LINEARIZATION; NONLINEAR PROGRAMMING; PROBLEM SOLVING;

EID: 25444530947     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10898-004-2706-7     Document Type: Article
Times cited : (48)

References (35)
  • 1
    • 0030571816 scopus 로고    scopus 로고
    • Computational experience on four algorithms for the hard clustering problem
    • Al-Sultan, K.S. and Khan, M.M. (1996), Computational experience on four algorithms for the hard clustering problem, Pattern Recognition Letters 17, 295-308.
    • (1996) Pattern Recognition Letters , vol.17 , pp. 295-308
    • Al-Sultan, K.S.1    Khan, M.M.2
  • 2
    • 0024140271 scopus 로고
    • On the convex hull of the union of certain polyhedra
    • Balas, E. (1988), On the convex hull of the union of certain polyhedra, Operations Research Letters 7(6), 279-283.
    • (1988) Operations Research Letters , vol.7 , Issue.6 , pp. 279-283
    • Balas, E.1
  • 5
    • 0023523514 scopus 로고
    • How many clusters are best? - An experiment
    • Dubes, R.C. (1987), How many clusters are best? - an experiment, Pattern Recognition 20, 645-663.
    • (1987) Pattern Recognition , vol.20 , pp. 645-663
    • Dubes, R.C.1
  • 6
    • 0000014486 scopus 로고
    • Cluster analysis of multivariate data: Efficiency versus interpretability of classification
    • Biometric Society Meetings, Riverside, CA
    • Forgy, E.W. (1966), Cluster analysis of multivariate data: efficiency versus interpretability of classification, Biometric Society Meetings, Riverside, CA, Abstract in Biometrics 21, 768.
    • (1966) Abstract in Biometrics , vol.21 , pp. 768
    • Forgy, E.W.1
  • 9
    • 0000784896 scopus 로고
    • A dynamic programming algorithm for cluster analysis
    • Jensen, R.E. (1969), A dynamic programming algorithm for cluster analysis, Operations Research 17, 1034-1057.
    • (1969) Operations Research , vol.17 , pp. 1034-1057
    • Jensen, R.E.1
  • 10
    • 84867984200 scopus 로고    scopus 로고
    • A decision criterion for the optimal number of clusters in hierarchical clustering
    • Jung, Y., Park, H., Du, Z. and Drake, B.L. (2003), A decision criterion for the optimal number of clusters in hierarchical clustering, Journal of Global Optimization 25, 91-111.
    • (2003) Journal of Global Optimization , vol.25 , pp. 91-111
    • Jung, Y.1    Park, H.2    Du, Z.3    Drake, B.L.4
  • 11
    • 0023344968 scopus 로고
    • Lower bound on the complexity of the convex hull problem for simply polyhedra
    • Klaapper, A. (1987), Lower bound on the complexity of the convex hull problem for simply polyhedra, Information Processing Letters 25(3), 159-161.
    • (1987) Information Processing Letters , vol.25 , Issue.3 , pp. 159-161
    • Klaapper, A.1
  • 12
    • 0024475960 scopus 로고
    • Experiments in projection and clustering by simulated annealing
    • Klein, R.W. and Dubes, R.C. (1989), Experiments in projection and clustering by simulated annealing, Pattern Recognition 22, 213-220.
    • (1989) Pattern Recognition , vol.22 , pp. 213-220
    • Klein, R.W.1    Dubes, R.C.2
  • 16
    • 0035014159 scopus 로고    scopus 로고
    • Analysis of temporal gene expression profiles: Clustering by simulated annealing and determining the optimal number of clusters
    • Lukashin, A.V. and Fuchs, R. (2000), Analysis of temporal gene expression profiles: clustering by simulated annealing and determining the optimal number of clusters, Bioinformatics 17(5), 405-414.
    • (2000) Bioinformatics , vol.17 , Issue.5 , pp. 405-414
    • Lukashin, A.V.1    Fuchs, R.2
  • 18
    • 0030572617 scopus 로고    scopus 로고
    • A comparison of SOM neural network and hierarchical clustering methods
    • Mangiameli, P., Chen, K.S. and West, D. (1996), A comparison of SOM neural network and hierarchical clustering methods, European Journal of Operations Research 93, 402-417.
    • (1996) European Journal of Operations Research , vol.93 , pp. 402-417
    • Mangiameli, P.1    Chen, K.S.2    West, D.3
  • 19
  • 20
    • 0000062485 scopus 로고
    • Cluster analysis: An application of lagrangian relaxation
    • Mulvey, J.M. and Crowder, H.P. (1979), Cluster analysis: An application of lagrangian relaxation, Management Science 25(4), 329-340.
    • (1979) Management Science , vol.25 , Issue.4 , pp. 329-340
    • Mulvey, J.M.1    Crowder, H.P.2
  • 22
    • 0000318768 scopus 로고    scopus 로고
    • BARON: A general purpose global optimization software package
    • Sahinidis, N.V. (1996), BARON: A general purpose global optimization software package, Journal of Global Optimization 8, 201-205.
    • (1996) Journal of Global Optimization , vol.8 , pp. 201-205
    • Sahinidis, N.V.1
  • 24
    • 25444439541 scopus 로고
    • A global algorithm for the clustering problem
    • San Diego, CA
    • Selim, S.Z. (1982), A global algorithm for the clustering problem, Presentation at the ORSA/TIMS Joint Meeting, San Diego, CA.
    • (1982) ORSA/TIMS Joint Meeting
    • Selim, S.Z.1
  • 25
    • 0026359031 scopus 로고
    • A simulated annealing algorithm for the hard clustering problem
    • Selim, S.Z. and Al-Sultan, K.S. (1991), A simulated annealing algorithm for the hard clustering problem, Pattern Recognition 24, 1003-1008.
    • (1991) Pattern Recognition , vol.24 , pp. 1003-1008
    • Selim, S.Z.1    Al-Sultan, K.S.2
  • 26
    • 0001321687 scopus 로고
    • A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems
    • Sherali, H.D. and Adams, W.P. (1990), A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems, SIAM Journal on Discrete Mathematics 3(3), 411-430.
    • (1990) SIAM Journal on Discrete Mathematics , vol.3 , Issue.3 , pp. 411-430
    • Sherali, H.D.1    Adams, W.P.2
  • 27
    • 0002500749 scopus 로고
    • A hierarchy of relaxations and convex hull characterizations for mixed-integer zero-one programming problems
    • Sherali, H.D. and Adams, W.P. (1994), A hierarchy of relaxations and convex hull characterizations for mixed-integer zero-one programming problems, Discrete Applied Mathematics 52, 83-106.
    • (1994) Discrete Applied Mathematics , vol.52 , pp. 83-106
    • Sherali, H.D.1    Adams, W.P.2
  • 28
    • 25444505042 scopus 로고    scopus 로고
    • Reformulation-linearization techniques for discrete optimization problems
    • Du, D.Z. and Pardalos, P.M. (eds.), Kluwer Academic Publishers
    • Sherali, H.D. and Adams, W.P. (1999), Reformulation-linearization techniques for discrete optimization problems, In: Du, D.Z. and Pardalos, P.M. (eds.), Handbook of Combinatorial Optimization 1, Kluwer Academic Publishers, pp. 479-532.
    • (1999) Handbook of Combinatorial Optimization , vol.1 , pp. 479-532
    • Sherali, H.D.1    Adams, W.P.2
  • 29
    • 0035494147 scopus 로고    scopus 로고
    • Improving discrete model representations via symmetry considerations
    • Sherali, H.D. and Smith, J.C. (2001), Improving discrete model representations via symmetry considerations, Management Science 41(10), 1396-1407.
    • (2001) Management Science , vol.41 , Issue.10 , pp. 1396-1407
    • Sherali, H.D.1    Smith, J.C.2
  • 30
    • 0001642333 scopus 로고
    • A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique
    • Sherali, H.D. and Tuncbilek, C. (1992), A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique, Journal of Global Optimization 2, 101-112.
    • (1992) Journal of Global Optimization , vol.2 , pp. 101-112
    • Sherali, H.D.1    Tuncbilek, C.2
  • 31
    • 0003374522 scopus 로고
    • A reformulation-convexification approach for solving nonconvex quadratic programming problems
    • Sherali, H.D. and Tuncbilek, C. (1995), A reformulation-convexification approach for solving nonconvex quadratic programming problems, Journal of Global Optimization 7, 1-31.
    • (1995) Journal of Global Optimization , vol.7 , pp. 1-31
    • Sherali, H.D.1    Tuncbilek, C.2
  • 33
    • 0012321068 scopus 로고    scopus 로고
    • Binary tree-structured vector quantization approach to clustering and visualizing microarray data
    • Sultan, M., Wigle, D.A., Cumbaa, C.A., Maziarz, M., Glasgow, J., Tsao, M.S. and Jurisica, I. (2002), Binary tree-structured vector quantization approach to clustering and visualizing microarray data, Bioinformatics 18(1), 111-119.
    • (2002) Bioinformatics , vol.18 , Issue.1 , pp. 111-119
    • Sultan, M.1    Wigle, D.A.2    Cumbaa, C.A.3    Maziarz, M.4    Glasgow, J.5    Tsao, M.S.6    Jurisica, I.7
  • 34
    • 0000217783 scopus 로고
    • Integer programming and the theory of grouping
    • Vinod, H.D. (1969), Integer programming and the theory of grouping, Journal of American Statistical Society 64, 506-519.
    • (1969) Journal of American Statistical Society , vol.64 , pp. 506-519
    • Vinod, H.D.1
  • 35
    • 84944178665 scopus 로고
    • Hierarchical grouping to optimize an objective function
    • Ward, J.H. Jr. (1963), Hierarchical grouping to optimize an objective function, Journal of American Statistical Society 58, 236-244.
    • (1963) Journal of American Statistical Society , vol.58 , pp. 236-244
    • Ward Jr., J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.