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Volumn 79, Issue 1-3, 1997, Pages 191-215

Cluster analysis and mathematical programming

Author keywords

Cluster analysis; Hierarchy; Partition

Indexed keywords


EID: 0000950204     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02614317     Document Type: Article
Times cited : (485)

References (120)
  • 1
    • 0005835320 scopus 로고
    • Finding k points with minimum diameter and related problems
    • A. Aggarwal, H. Imai, N. Katoh and S. Suri, Finding k points with minimum diameter and related problems, J. Algorithms 12 (1991) 38-56.
    • (1991) J. Algorithms , vol.12 , pp. 38-56
    • Aggarwal, A.1    Imai, H.2    Katoh, N.3    Suri, S.4
  • 2
    • 0024488765 scopus 로고
    • Weak hierarchies associated with similarity measures: An additive clustering technique
    • H.J. Bandelt and A.W.M. Dress, Weak hierarchies associated with similarity measures: An additive clustering technique, Bulletin Mathematical Biology 51 (1989) 133-166.
    • (1989) Bulletin Mathematical Biology , vol.51 , pp. 133-166
    • Bandelt, H.J.1    Dress, A.W.M.2
  • 6
    • 0004026685 scopus 로고
    • English translation: Wiley, Chichester, UK
    • J.-P. Barthelemy and A. Guénoche, Le s Arbres et les Représentations des Proximités (Masson, Paris, 1988); English translation: Trees and Proximity Relations (Wiley, Chichester, UK, 1991).
    • (1991) Trees and Proximity Relations
  • 7
    • 0015758935 scopus 로고
    • A note on cluster analysis and dynamic programming
    • R. Bellman, A note on cluster analysis and dynamic programming, Math. Biosci. 18 (1973) 311-312.
    • (1973) Math. Biosci. , vol.18 , pp. 311-312
    • Bellman, R.1
  • 8
    • 0000670412 scopus 로고
    • Construction d'une classification ascendante hiérarchique par la recherche en chaîne des voisins réciproques
    • J.P. Benzecri, Construction d'une classification ascendante hiérarchique par la recherche en chaîne des voisins réciproques, Les Cahiers de l'Analyse des Données VII (2) (1982) 209-218.
    • (1982) Les Cahiers de l'Analyse des Données , vol.7 , Issue.2 , pp. 209-218
    • Benzecri, J.P.1
  • 10
    • 0347500822 scopus 로고
    • Structural properties of pyramidal clustering
    • I. Cox, P. Hansen and B. Julesz, eds., American Mathematical Society, Providence, RI
    • P. Bertrand, Structural Properties of Pyramidal Clustering, in: I. Cox, P. Hansen and B. Julesz, eds., Partitioning Data Sets (American Mathematical Society, Providence, RI, 1995) 35-53.
    • (1995) Partitioning Data Sets , pp. 35-53
    • Bertrand, P.1
  • 12
    • 38249022112 scopus 로고
    • On clustering problems with connected optima in Euclidean spaces
    • E. Boros and P.L. Hammer, On clustering problems with connected optima in Euclidean spaces, Discrete Mathematics 75 (1989) 81-88.
    • (1989) Discrete Mathematics , vol.75 , pp. 81-88
    • Boros, E.1    Hammer, P.L.2
  • 13
    • 0001773546 scopus 로고
    • On the complexity of clustering problems
    • M. Beckmann and H.P. Kunzi, eds., Optimization and Operations Research, Springer, Heidelberg
    • P. Brucker, On the complexity of clustering problems, in: M. Beckmann and H.P. Kunzi, eds., Optimization and Operations Research, Lecture Notes in Economics and Mathematical Systems, Vol. 157 (Springer, Heidelberg, 1978) 45-54.
    • (1978) Lecture Notes in Economics and Mathematical Systems , vol.157 , pp. 45-54
    • Brucker, P.1
  • 14
    • 0002817795 scopus 로고
    • Classification ascendante hiérarchique des grands ensembles de données: Un algorithme rapide fondé sur la construction des voisinages réductibles
    • M. Bruynooghe, Classification ascendante hiérarchique des grands ensembles de données: Un algorithme rapide fondé sur la construction des voisinages réductibles, Les Cahiers de l'Analyse des Données 3 (1978) 7-33.
    • (1978) Les Cahiers de l'Analyse des Données , vol.3 , pp. 7-33
    • Bruynooghe, M.1
  • 15
    • 0002074731 scopus 로고
    • The recovery of trees from measures of dissimilarity
    • F.R. Hodson, D.G. Kendall and P. Tautu, eds., Edinburgh University Press, Edinburgh
    • P. Buneman, The recovery of trees from measures of dissimilarity, in: F.R. Hodson, D.G. Kendall and P. Tautu, eds., Mathematics in Archeological and Historical Sciences (Edinburgh University Press, Edinburgh, 1971) 387-395.
    • (1971) Mathematics in Archeological and Historical Sciences , pp. 387-395
    • Buneman, P.1
  • 18
    • 0002017183 scopus 로고
    • Construction de l'ultramétrique la plus proche d'une dissimilarité au sens des moindres carrés
    • J.L. Chandon, J. Lemaire and J. Pouget, Construction de l'ultramétrique la plus proche d'une dissimilarité au sens des moindres carrés, RAIRO-Recherche Opérationnelle 14 (1980) 157-170.
    • (1980) RAIRO-Recherche Opérationnelle , vol.14 , pp. 157-170
    • Chandon, J.L.1    Lemaire, J.2    Pouget, J.3
  • 20
    • 71049166749 scopus 로고
    • On the multiway cut polyhedron
    • S. Chopra and M.R. Rao, On the multiway cut polyhedron, Networks 21 (1991) 51-89.
    • (1991) Networks , vol.21 , pp. 51-89
    • Chopra, S.1    Rao, M.R.2
  • 21
    • 0009114472 scopus 로고    scopus 로고
    • Extended formulations for the A-cut problem
    • S. Chopra and J.H. Owen, Extended formulations for the A-cut problem, Mathematical Programming 73 (1996) 17-30.
    • (1996) Mathematical Programming , vol.73 , pp. 17-30
    • Chopra, S.1    Owen, J.H.2
  • 25
    • 38249018098 scopus 로고
    • The basic algorithm for pseudo-Boolean programming revisited
    • Y. Crama, P. Hansen and B. Jaumard, The basic algorithm for pseudo-Boolean programming revisited, Discrete Applied Mathematics 29 (1990) 171-185.
    • (1990) Discrete Applied Mathematics , vol.29 , pp. 171-185
    • Crama, Y.1    Hansen, P.2    Jaumard, B.3
  • 26
    • 0001275216 scopus 로고
    • Static and dynamic algorithms for k-point clustering problems
    • A. Datta, H.-P. Lenhof, Ch. Schwarz and M. Smid, Static and dynamic algorithms for k-point clustering problems, J. Algorithms 19 (1995) 474-503.
    • (1995) J. Algorithms , vol.19 , pp. 474-503
    • Datta, A.1    Lenhof, H.-P.2    Schwarz, Ch.3    Smid, M.4
  • 27
    • 0002546287 scopus 로고
    • Efficient algorithms for agglomerative hierarchical clustering methods
    • W.H.E. Day and H. Edelsbrunner, Efficient algorithms for agglomerative hierarchical clustering methods, J. Classification 1 (1984) 7-24.
    • (1984) J. Classification , vol.1 , pp. 7-24
    • Day, W.H.E.1    Edelsbrunner, H.2
  • 28
    • 30244442397 scopus 로고
    • Classification d'homogénéité maximum
    • Actes du Colloque Analyse de Données et Informatique
    • M. Delattre and P. Hansen, Classification d'homogénéité maximum, in: Actes du Colloque Analyse de Données et Informatique, INRIA 1 (1977) 99-104.
    • (1977) INRIA , vol.1 , pp. 99-104
    • Delattre, M.1    Hansen, P.2
  • 30
    • 0001468642 scopus 로고
    • A least squares algorithm for fitting additive trees to proximity data
    • G. De Soete, A least squares algorithm for fitting additive trees to proximity data, Psychometrika 48 (1983) 621-626.
    • (1983) Psychometrika , vol.48 , pp. 621-626
    • De Soete, G.1
  • 31
    • 0008981482 scopus 로고
    • A least squares algorithm for fitting an ultrametric tree to a dissimilarity matrix
    • G. De Soete, A least squares algorithm for fitting an ultrametric tree to a dissimilarity matrix, Pattern Recognition Letters 2 (1984) 133-137.
    • (1984) Pattern Recognition Letters , vol.2 , pp. 133-137
    • De Soete, G.1
  • 32
    • 0000169885 scopus 로고
    • Ultrametric tree representation of incomplete dissimilarity data
    • G. De Soete, Ultrametric tree representation of incomplete dissimilarity data, J. Classification 1 (1984) 235-242.
    • (1984) J. Classification , vol.1 , pp. 235-242
    • De Soete, G.1
  • 33
    • 0000355328 scopus 로고
    • Additive tree representations of incomplete dissimilarity data
    • G. De Soete, Additive tree representations of incomplete dissimilarity data, Quality and Quantity 18 (1984) 387-393.
    • (1984) Quality and Quantity , vol.18 , pp. 387-393
    • De Soete, G.1
  • 34
    • 0021691757 scopus 로고
    • Routing with time windows by column generation
    • J. Desrosiers, F. Soumis and M. Desrochers, Routing with time windows by column generation, Networks 14 (1984) 545-565.
    • (1984) Networks , vol.14 , pp. 545-565
    • Desrosiers, J.1    Soumis, F.2    Desrochers, M.3
  • 35
    • 30244573834 scopus 로고
    • From data to knowledge: Probabilistic objects for a symbolic data analysis
    • I. Cox, P. Hansen and B. Julesz, eds., American Mathematical Society, Providence, RI
    • E. Diday, From data to knowledge: Probabilistic objects for a symbolic data analysis, in: I. Cox, P. Hansen and B. Julesz, eds., Partitioning Data Sets (American Mathematical Society, Providence, RI, 1995) 35-53.
    • (1995) Partitioning Data Sets , pp. 35-53
    • Diday, E.1
  • 37
    • 0013336444 scopus 로고
    • Evaluation of a branch and bound algorithm for clustering
    • G. Diehr, Evaluation of a branch and bound algorithm for clustering, SIAM J. Scientific and Statistical Computing 6 (1985) 268-284.
    • (1985) SIAM J. Scientific and Statistical Computing , vol.6 , pp. 268-284
    • Diehr, G.1
  • 38
    • 30244530895 scopus 로고
    • On nonlinear fractional programming
    • W. Dinkelbach, On nonlinear fractional programming, Management Science 61 (1995) 195-212.
    • (1995) Management Science , vol.61 , pp. 195-212
    • Dinkelbach, W.1
  • 39
    • 0004763950 scopus 로고
    • Complexity relaxation of dynamic programming for cluster analysis
    • E. Diday et al., eds., New Approaches in Classification and Data Analysis
    • A. Dodge and T. Gafner, Complexity relaxation of dynamic programming for cluster analysis, in: E. Diday et al., eds., New Approaches in Classification and Data Analysis, Studies in Classification, Data Analysis, and Knowledge Organization (1994) 220-227.
    • (1994) Studies in Classification, Data Analysis, and Knowledge Organization , pp. 220-227
    • Dodge, A.1    Gafner, T.2
  • 40
    • 0000150424 scopus 로고
    • Fast clustering algorithms
    • U. Dorndorf and E. Pesch, Fast clustering algorithms, ORSA J. Computing 6 (1994) 141-153.
    • (1994) ORSA J. Computing , vol.6 , pp. 141-153
    • Dorndorf, U.1    Pesch, E.2
  • 43
    • 0013384487 scopus 로고
    • A dual-based procedure for uncapacitated facility location
    • D. Erlenkotter, A dual-based procedure for uncapacitated facility location, Operations Research 26 (1978) 1590-1602.
    • (1978) Operations Research , vol.26 , pp. 1590-1602
    • Erlenkotter, D.1
  • 45
    • 0016091058 scopus 로고
    • An algorithm for the M-median plant location problem
    • R. Garfinkel, A.W. Neebe and M.R. Rao, An algorithm for the M-median plant location problem, Transportation Science 8 (1974) 217-236.
    • (1974) Transportation Science , vol.8 , pp. 217-236
    • Garfinkel, R.1    Neebe, A.W.2    Rao, M.R.3
  • 46
    • 0030555957 scopus 로고    scopus 로고
    • A reduction algorithm for approximating a (non-metric) dissimilarity by a tree distance
    • O. Gascuel and D. Levy, A reduction algorithm for approximating a (non-metric) dissimilarity by a tree distance, J. Classification 13 (1996) 129-155.
    • (1996) J. Classification , vol.13 , pp. 129-155
    • Gascuel, O.1    Levy, D.2
  • 47
    • 30244484584 scopus 로고
    • A labelling algorithm for minimum sum of diameters partitioning of graphs
    • I. Cox, P. Hansen and B. Julesz, eds., American Mathematical Society, Providence, RI
    • S. Gelinas, P. Hansen and B. Jaumard, A labelling algorithm for minimum sum of diameters partitioning of graphs, in: I. Cox, P. Hansen and B. Julesz, eds., Partitioning Data Sets (American Mathematical Society, Providence, RI, 1995) 89-96.
    • (1995) Partitioning Data Sets , pp. 89-96
    • Gelinas, S.1    Hansen, P.2    Jaumard, B.3
  • 48
    • 0001510482 scopus 로고
    • A linear programming approach to the cutting stock problem
    • P.C. Gilmore and R.E. Gomory, A linear programming approach to the cutting stock problem, Operations Research 9 (1961) 849-859.
    • (1961) Operations Research , vol.9 , pp. 849-859
    • Gilmore, P.C.1    Gomory, R.E.2
  • 50
    • 0001715023 scopus 로고
    • A review of hierarchical classification
    • A.D. Gordon, A review of hierarchical classification, J. Royal Statistical Society 150 (1987) 119-137.
    • (1987) J. Royal Statistical Society , vol.150 , pp. 119-137
    • Gordon, A.D.1
  • 51
    • 0001120850 scopus 로고
    • Minimum spanning trees and single linkage cluster analysis
    • J.C. Gower and G.J.S. Ross, Minimum spanning trees and single linkage cluster analysis, Applied Statistics 18 (1969) 54-64.
    • (1969) Applied Statistics , vol.18 , pp. 54-64
    • Gower, J.C.1    Ross, G.J.S.2
  • 52
    • 0024717601 scopus 로고
    • A cutting plane algorithm for a clustering problem
    • M. Grötschel and Y. Wakabayashi, A cutting plane algorithm for a clustering problem, Mathematical Programming 45 (1989) 59-96.
    • (1989) Mathematical Programming , vol.45 , pp. 59-96
    • Grötschel, M.1    Wakabayashi, Y.2
  • 55
    • 38249005712 scopus 로고
    • Enumération des partitions de diamètre minimum
    • A. Guénoche, Enumération des partitions de diamètre minimum, Discrete Mathematics 111 (1993) 277-287.
    • (1993) Discrete Mathematics , vol.111 , pp. 277-287
    • Guénoche, A.1
  • 56
    • 0004173623 scopus 로고
    • Efficient algorithms for divisive hierarchical clustering with the diameter criterion
    • A. Guénoche, P. Hansen and B. Jaumard, Efficient algorithms for divisive hierarchical clustering with the diameter criterion, J. Classification 8 (1991) 5-30.
    • (1991) J. Classification , vol.8 , pp. 5-30
    • Guénoche, A.1    Hansen, P.2    Jaumard, B.3
  • 57
    • 0021376406 scopus 로고
    • Roof duality, complementation and persistency in quadratic 0-1 optimization
    • P.L. Hammer, P. Hansen and B. Simeone, Roof duality, complementation and persistency in quadratic 0-1 optimization, Mathematical Programming 28 (1984) 121-155.
    • (1984) Mathematical Programming , vol.28 , pp. 121-155
    • Hammer, P.L.1    Hansen, P.2    Simeone, B.3
  • 58
    • 0021443182 scopus 로고
    • A comparison of two dual-based procedures for solving the p-median problem
    • P. Hanjoul and D. Peeters, A comparison of two dual-based procedures for solving the p-median problem, European Journal of Operations Research 20 (1985) 387-396.
    • (1985) European Journal of Operations Research , vol.20 , pp. 387-396
    • Hanjoul, P.1    Peeters, D.2
  • 60
    • 0003780923 scopus 로고
    • Minimum sum of diameters clustering
    • P. Hansen and B. Jaumard, Minimum sum of diameters clustering, J. Classification 4 (1987) 215-226.
    • (1987) J. Classification , vol.4 , pp. 215-226
    • Hansen, P.1    Jaumard, B.2
  • 61
    • 30244557103 scopus 로고
    • Average-linkage divisive hierarchical clustering
    • G-91-55
    • P. Hansen, B. Jaumard and E. da Silva, Average-linkage divisive hierarchical clustering, Les Cahiers du GERAD, G-91-55 (1991); also in: J. Classification, to appear.
    • (1991) Les Cahiers du GERAD
    • Hansen, P.1    Jaumard, B.2    Da Silva, E.3
  • 62
    • 30244543032 scopus 로고    scopus 로고
    • to appear
    • P. Hansen, B. Jaumard and E. da Silva, Average-linkage divisive hierarchical clustering, Les Cahiers du GERAD, G-91-55 (1991); also in: J. Classification, to appear.
    • J. Classification
  • 66
    • 30244534127 scopus 로고    scopus 로고
    • Exact sequential algorithms for additive clustering
    • to appear
    • P. Hansen, B. Jaumard and C. Meyer, Exact sequential algorithms for additive clustering, Les Cahiers du GERAD (1997), to appear.
    • (1997) Les Cahiers du GERAD
    • Hansen, P.1    Jaumard, B.2    Meyer, C.3
  • 67
    • 0007336159 scopus 로고
    • How to choose k entities among N
    • I. Cox, P. Hansen and B. Julesz, eds., American Mathematical Society, Providence, RI
    • P. Hansen, B. Jaumard and N. Mladenovic, How to choose k entities among N, in: I. Cox, P. Hansen and B. Julesz, eds., Partitioning Data Sets (American Mathematical Society, Providence, RI, 1995) 105-116.
    • (1995) Partitioning Data Sets , pp. 105-116
    • Hansen, P.1    Jaumard, B.2    Mladenovic, N.3
  • 68
    • 0039205787 scopus 로고
    • Mixed-integer column generation algorithms and the probabilistic maximum satisfiability problem
    • E. Balas, G. Cornuejols and R. Kannan, eds., Carnegie-Mellon University
    • P. Hansen, B. Jaumard and M. Poggi De Aragão, Mixed-integer column generation algorithms and the probabilistic maximum satisfiability problem, in: E. Balas, G. Cornuejols and R. Kannan, eds., Proceedings of the Second IPCO Conference (Carnegie-Mellon University, 1992) 165-180.
    • (1992) Proceedings of the Second IPCO Conference , pp. 165-180
    • Hansen, P.1    Jaumard, B.2    Poggi De Aragão, M.3
  • 69
    • 85033890900 scopus 로고
    • Weight constrained minimum sum-of-stars clustering
    • G-93-38
    • P. Hansen, B. Jaumard and E. Sanlaville, Weight constrained minimum sum-of-stars clustering, Les Cahiers du GERAD, G-93-38 (1993); also in: J. Classification, to appear.
    • (1993) Les Cahiers du GERAD
    • Hansen, P.1    Jaumard, B.2    Sanlaville, E.3
  • 70
    • 30244573833 scopus 로고    scopus 로고
    • to appear
    • P. Hansen, B. Jaumard and E. Sanlaville, Weight constrained minimum sum-of-stars clustering, Les Cahiers du GERAD, G-93-38 (1993); also in: J. Classification, to appear.
    • J. Classification
  • 71
    • 0004795618 scopus 로고
    • Partitioning problems of cluster analysis: A review of mathematical programming approaches
    • E. Diday et al., eds., Springer, Berlin
    • P. Hansen, B. Jaumard and E. Sanlaville, Partitioning problems of cluster analysis: A review of mathematical programming approaches, in: E. Diday et al., eds., New Approaches in Classification and Data Analysis (Springer, Berlin, 1994) 228-240.
    • (1994) New Approaches in Classification and Data Analysis , pp. 228-240
    • Hansen, P.1    Jaumard, B.2    Sanlaville, E.3
  • 72
    • 0030532266 scopus 로고    scopus 로고
    • Espaliers, A generalization of dendrograms
    • P Hansen, B. Jaumard and B. Simeone, Espaliers, A generalization of dendrograms, J. Classification 13 (1996) 107-127.
    • (1996) J. Classification , vol.13 , pp. 107-127
    • Hansen, P.1    Jaumard, B.2    Simeone, B.3
  • 73
    • 4444258564 scopus 로고    scopus 로고
    • Polynomial algorithms for nested univariate clustering
    • G-96-28
    • P. Hansen, B. Jaumard and B. Simeone, Polynomial algorithms for nested univariate clustering, Les Cahiers du GERAD, G-96-28 (1996).
    • (1996) Les Cahiers du GERAD
    • Hansen, P.1    Jaumard, B.2    Simeone, B.3
  • 74
    • 0042759368 scopus 로고
    • Extension de la programmation linéaire généralisée au cas des programmes mixtes
    • P. Hansen, M. Minoux and M. Labbe, Extension de la programmation linéaire généralisée au cas des programmes mixtes, Comptes Rendus de l'Académie des Sciences 305 (1987) 569-572.
    • (1987) Comptes Rendus de l'Académie des Sciences , vol.305 , pp. 569-572
    • Hansen, P.1    Minoux, M.2    Labbe, M.3
  • 75
    • 30244439943 scopus 로고    scopus 로고
    • Variable neighborhood search
    • G-96-49
    • P. Hansen and N. Mladenovic, Variable neighborhood search, Les Cahiers du GERAD, G-96-49 (1996); also in: Computers and Operations Research, to appear.
    • (1996) Les Cahiers du GERAD
    • Hansen, P.1    Mladenovic, N.2
  • 76
    • 84888901416 scopus 로고    scopus 로고
    • to appear
    • P. Hansen and N. Mladenovic, Variable neighborhood search, Les Cahiers du GERAD, G-96-49 (1996); also in: Computers and Operations Research, to appear.
    • Computers and Operations Research
  • 79
    • 34250425251 scopus 로고
    • Some applications of graph theory to clustering
    • L.J. Hubert, Some applications of graph theory to clustering, Psychometrika 39 (1974) 283-309.
    • (1974) Psychometrika , vol.39 , pp. 283-309
    • Hubert, L.J.1
  • 80
    • 0012218463 scopus 로고
    • Min and max hierarchical clustering using asymmetric similarity measures
    • L.J. Hubert, Min and max hierarchical clustering using asymmetric similarity measures, Psychometrika 38 (1973) 63-72.
    • (1973) Psychometrika , vol.38 , pp. 63-72
    • Hubert, L.J.1
  • 81
    • 85004878775 scopus 로고
    • Iterative projection strategies for the least-squares fitting of tree structure to proximity data
    • L.J. Hubert and P. Arabie, Iterative projection strategies for the least-squares fitting of tree structure to proximity data, The British Journal of Mathematical and Statistical Psychology 48 (1995) 281-317.
    • (1995) The British Journal of Mathematical and Statistical Psychology , vol.48 , pp. 281-317
    • Hubert, L.J.1    Arabie, P.2
  • 85
    • 0000784896 scopus 로고
    • A dynamic programming algorithm for cluster analysis
    • R.E. Jensen, A dynamic programming algorithm for cluster analysis, Operations Research 17 (1969) 1034-1057.
    • (1969) Operations Research , vol.17 , pp. 1034-1057
    • Jensen, R.E.1
  • 88
    • 84989737730 scopus 로고
    • Optimal clustering: A model and method
    • G. Klein and J.E. Aronson, Optimal clustering: a model and method, Naval Research Logistics 38 (1991) 447-461.
    • (1991) Naval Research Logistics , vol.38 , pp. 447-461
    • Klein, G.1    Aronson, J.E.2
  • 90
    • 0022735230 scopus 로고
    • NP-hard problems in hierarchical-tree clustering
    • M. Krivanek and J. Moravek, NP-hard problems in hierarchical-tree clustering, Acta Informatica 23 (1986) 311-323.
    • (1986) Acta Informatica , vol.23 , pp. 311-323
    • Krivanek, M.1    Moravek, J.2
  • 91
    • 0003126317 scopus 로고
    • A general theory of classificatory sorting strategies. 1. Hierarchical systems
    • G.N. Lance and W.T. Williams, A general theory of classificatory sorting strategies. 1. Hierarchical systems, The Computer Journal 9 (1967) 373-380.
    • (1967) The Computer Journal , vol.9 , pp. 373-380
    • Lance, G.N.1    Williams, W.T.2
  • 92
    • 0039824104 scopus 로고
    • Description combinatoire des ultramétriques
    • B. Leclerc, Description combinatoire des ultramétriques, Mathématiques et Sciences Humaines 73 (1981) 5-37.
    • (1981) Mathématiques et Sciences Humaines , vol.73 , pp. 5-37
    • Leclerc, B.1
  • 93
    • 0007436170 scopus 로고
    • Clustering a data array and the traveling salesman problem
    • J.K. Lenstra, Clustering a data array and the traveling salesman problem, Operations Research 22 (1974) 413-414.
    • (1974) Operations Research , vol.22 , pp. 413-414
    • Lenstra, J.K.1
  • 95
    • 0020781464 scopus 로고
    • Smallest-last ordering and clustering and graph-coloring algorithms
    • D.W. Matula and L.L. Beck, Smallest-last ordering and clustering and graph-coloring algorithms, J. ACM 30 (1983) 417-427.
    • (1983) J. ACM , vol.30 , pp. 417-427
    • Matula, D.W.1    Beck, L.L.2
  • 96
    • 0015397231 scopus 로고
    • Problem decomposition and data reorganization by a clustering technique
    • W.T. McCormick Jr, P.J. Schweitzer and T.W. White, Problem decomposition and data reorganization by a clustering technique, Operations Research 20 (1972) 993-1009.
    • (1972) Operations Research , vol.20 , pp. 993-1009
    • McCormick W.T., Jr.1    Schweitzer, P.J.2    White, T.W.3
  • 97
    • 30244437776 scopus 로고
    • Lower bounds to the graph partitioning problem through generalized linear programming and network flows
    • M. Minoux and E. Pinson, Lower bounds to the graph partitioning problem through generalized linear programming and network flows, RAIRO Recherche Opérationnelle 21 (1987) 349-364.
    • (1987) RAIRO Recherche Opérationnelle , vol.21 , pp. 349-364
    • Minoux, M.1    Pinson, E.2
  • 98
    • 34250115918 scopus 로고
    • An examination of procedures for determining the number of clusters in data set
    • G.W. Milligan and M.C. Cooper, An examination of procedures for determining the number of clusters in data set, Psychometrika 50 (1985) 159-179.
    • (1985) Psychometrika , vol.50 , pp. 159-179
    • Milligan, G.W.1    Cooper, M.C.2
  • 99
    • 0002176940 scopus 로고
    • Additive clustering and qualitative factor analysis methods for similarity matrices
    • Erratum 6, 271-272
    • B. Mirkin, Additive clustering and qualitative factor analysis methods for similarity matrices, J. Classification 4 (1987) 7-31, (Erratum 6, 271-272).
    • (1987) J. Classification , vol.4 , pp. 7-31
    • Mirkin, B.1
  • 102
    • 0020848951 scopus 로고
    • A survey of recent advances in hierarchical clustering algorithms
    • F. Murtagh, A survey of recent advances in hierarchical clustering algorithms, The Computer Journal 26 (1983) 329-340.
    • (1983) The Computer Journal , vol.26 , pp. 329-340
    • Murtagh, F.1
  • 104
    • 0020849839 scopus 로고
    • An algorithm for the fixed-charge assignment of users to sources problem
    • A.W. Neebe and M.R. Rao, An algorithm for the fixed-charge assignment of users to sources problem, J. Operations Research Society 34 (1983) 1107-1113.
    • (1983) J. Operations Research Society , vol.34 , pp. 1107-1113
    • Neebe, A.W.1    Rao, M.R.2
  • 105
    • 0002683074 scopus 로고    scopus 로고
    • A branch-and-bound approach using polyhedral results for a clustering problem
    • G. Palubeckis, A branch-and-bound approach using polyhedral results for a clustering problem, INFORMS J. Computing 9 (1997) 30-42.
    • (1997) INFORMS J. Computing , vol.9 , pp. 30-42
    • Palubeckis, G.1
  • 106
    • 84950648422 scopus 로고
    • Cluster analysis and mathematical programming
    • M.R. Rao, Cluster analysis and mathematical programming, J. American Statistical Association 66 (1971) 622-626.
    • (1971) J. American Statistical Association , vol.66 , pp. 622-626
    • Rao, M.R.1
  • 108
    • 0000006646 scopus 로고
    • Sur quelques aspects mathématiques des problèmes de classification
    • S. Régnier, Sur quelques aspects mathématiques des problèmes de classification, ICC Bulletin 4 (1965) 175-191; reprinted in: Mathématiques et Sciences Humaines 82 (1983) 85-111.
    • (1965) ICC Bulletin , vol.4 , pp. 175-191
    • Régnier, S.1
  • 109
    • 30244496880 scopus 로고
    • S. Régnier, Sur quelques aspects mathématiques des problèmes de classification, ICC Bulletin 4 (1965) 175-191; reprinted in: Mathématiques et Sciences Humaines 82 (1983) 85-111.
    • (1983) Mathématiques et Sciences Humaines , vol.82 , pp. 85-111
  • 110
    • 0742265348 scopus 로고
    • L'arbre minimum d'un graphe
    • P. Rosenstiehl, ed., Dunod, Paris
    • P. Rosenstiehl, L'arbre minimum d'un graphe, in: P. Rosenstiehl, ed., Théorie des Graphes (Dunod, Paris, 1967) 357-368.
    • (1967) Théorie des Graphes , pp. 357-368
    • Rosenstiehl, P.1
  • 111
    • 0347143974 scopus 로고    scopus 로고
    • Knowledge spaces and formal concept analysis
    • H. Boch and W. Polasek, eds., Springer, Berlin
    • A. Rusch and R. Wille, Knowledge spaces and formal concept analysis, in: H. Boch and W. Polasek, eds., Data Analysis and Information Systems (Springer, Berlin, 1996) 427-436.
    • (1996) Data Analysis and Information Systems , pp. 427-436
    • Rusch, A.1    Wille, R.2
  • 113
    • 0001869276 scopus 로고
    • Additive clustering representation of similarities as combinations of discrete overlapping properties
    • R.N. Shepard and P. Arabie, Additive clustering representation of similarities as combinations of discrete overlapping properties, Psychol Rev. 86 (1979) 87-123.
    • (1979) Psychol Rev. , vol.86 , pp. 87-123
    • Shepard, R.N.1    Arabie, P.2
  • 115
    • 0022864607 scopus 로고
    • A recursive Lagrangian method for clustering problems
    • L.E. Stanfel, A recursive Lagrangian method for clustering problems, European Journal of Operations Research 27 (1986) 332-342.
    • (1986) European Journal of Operations Research , vol.27 , pp. 332-342
    • Stanfel, L.E.1
  • 117
    • 0020787001 scopus 로고
    • An improved algorithm for hierarchical clustering using strong components
    • R.E. Tarjan, An improved algorithm for hierarchical clustering using strong components, Information Processing Letters 17 (1983) 37-41.
    • (1983) Information Processing Letters , vol.17 , pp. 37-41
    • Tarjan, R.E.1
  • 118
    • 0003436773 scopus 로고
    • Ph.D. Thesis, Faculté des Sciences Appliquées, Université Catholique de Louvain, Louvain-la-Neuve
    • F. Vanderbeck, Decomposition and column generation for integer programs, Ph.D. Thesis, Faculté des Sciences Appliquées, Université Catholique de Louvain, Louvain-la-Neuve, 1994.
    • (1994) Decomposition and Column Generation for Integer Programs
    • Vanderbeck, F.1
  • 119
    • 0000217783 scopus 로고
    • Integer programming and the theory of grouping
    • H.D. Vinod, Integer programming and the theory of grouping, J. American Statistical Association 64 (1969) 506-519.
    • (1969) J. American Statistical Association , vol.64 , pp. 506-519
    • Vinod, H.D.1
  • 120
    • 30244462467 scopus 로고
    • Algorithmic complexity - Three NP-hard problems in computational statistics
    • W.J. Welch, Algorithmic complexity - Three NP-hard problems in computational statistics, J. Statistical Computing 15 (1982) 68-86.
    • (1982) J. Statistical Computing , vol.15 , pp. 68-86
    • Welch, W.J.1


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