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Volumn 2, Issue 3, 2004, Pages 179-219

Combinatorial Optimization and Hierarchical Classifications

Author keywords

Clustering algorithms; Complexity; Hierarchical classification; Quasi hierarchies; Rigid hypergraphs; Subdominant

Indexed keywords


EID: 33745382172     PISSN: 16194500     EISSN: 16142411     Source Type: Journal    
DOI: 10.1007/s10288-004-0051-9     Document Type: Article
Times cited : (23)

References (100)
  • 2
    • 34250218588 scopus 로고
    • Un algorithme pour construire des classes d'après une matrice de distance
    • Asprejan J-D (1966) Un algorithme pour construire des classes d'après une matrice de distance. Mashinnyi perevod i prikladnaja linguisika 9: 3-18.
    • (1966) Mashinnyi perevod i prikladnaja linguisika , vol.9 , pp. 3-18
    • Asprejan, J.-D.1
  • 4
    • 0024488765 scopus 로고
    • Weak hierarchies associated with a similarity measure-an additive clustering technique
    • Bandelt H-J, Dress WM (1989) Weak hierarchies associated with a similarity measure-an additive clustering technique. Bulletin of Mathematical Biology 51(1): 133-166.
    • (1989) Bulletin of Mathematical Biology , vol.51 , Issue.1 , pp. 133-166
    • Bandelt, H.-J.1    Dress, W.M.2
  • 5
    • 0002527332 scopus 로고
    • An order theoretic framework for overlapping clustering
    • Bandelt H-J, Dress WM (1994) An order theoretic framework for overlapping clustering. Discrete Mathematics 136: 21-37.
    • (1994) Discrete Mathematics , vol.136 , pp. 21-37
    • Bandelt, H.-J.1    Dress, W.M.2
  • 6
    • 34250186783 scopus 로고    scopus 로고
    • Actes des Rencontres de la Société Francophone de Classification
    • Barthélemy J-P (2003) Classifications binaires. Actes des Rencontres de la Société Francophone de Classification: 67-69.
    • (2003) Classifications binaires , pp. 67-69
    • Barthélemy, J.-P.1
  • 7
    • 0035540988 scopus 로고    scopus 로고
    • NP-hard approximation problems in overlapping clustering
    • Barthélemy J-P, Brucker F (2001) NP-hard approximation problems in overlapping clustering. Journal of Classification 18(2): 159-183.
    • (2001) Journal of Classification , vol.18 , Issue.2 , pp. 159-183
    • Barthélemy, J.-P.1    Brucker, F.2
  • 10
    • 0007185382 scopus 로고
    • Les isomorphismes hte et hts, après la bijection de Benzécri-Johnson
    • Batbedat A (1988) Les isomorphismes hte et hts, après la bijection de Benzécri-Johnson. Metron 46: 47-59.
    • (1988) Metron , vol.46 , pp. 47-59
    • Batbedat, A.1
  • 12
    • 0015475519 scopus 로고
    • Symmetric binary b-trees: Data structures and maintenance
    • Bayer R (1972) Symmetric binary b-trees: Data structures and maintenance. Acta Informatica 1: 290-306.
    • (1972) Acta Informatica , vol.1 , pp. 290-306
    • Bayer, R.1
  • 15
    • 34250219602 scopus 로고    scopus 로고
    • Set systems for which each set properly intersects at most one other set-application to pyramidal clustering
    • 0202
    • Bertrand P (2002) Set systems for which each set properly intersects at most one other set-application to pyramidal clustering. Cahiers du Ceremade, 0202.
    • (2002) Cahiers du Ceremade
    • Bertrand, P.1
  • 16
    • 0037446987 scopus 로고    scopus 로고
    • The k-weak hierarchies: An extension of the weak hierarchical clustering structure
    • Bertrand P, JanowitzM (2003) The k-weak hierarchies: an extension of the weak hierarchical clustering structure. Discrete Applied Mathematics 127: 199-220.
    • (2003) Discrete Applied Mathematics , vol.127 , pp. 199-220
    • Bertrand, P.1    Janowitz, M.2
  • 17
    • 0004190631 scopus 로고
    • American Mathematical Society, Providence
    • Birkhoff G (1967) Lattice theory. American Mathematical Society, Providence.
    • (1967) Lattice theory
    • Birkhoff, G.1
  • 18
    • 0002173644 scopus 로고
    • O jistém problému minimálniím (about a certain minimal problem)
    • Borůvka O (1926a) O jistém problému minimálniím (about a certain minimal problem). Práce mor. přírodověd. spol. v Brně 3: 37-58.
    • (1926) Práce mor. přírodověd. spol. v Brně , vol.3 , pp. 37-58
    • Borůvka, O.1
  • 19
    • 0347740414 scopus 로고
    • Příspěvek k řešení otázky ekonomické stavby elektrovodných sítí (contribution to the solution of the problem of economical construction of electrical networks)
    • Borůvka O (1926b) Příspěvek k řešení otázky ekonomické stavby elektrovodných sítí (contribution to the solution of the problem of economical construction of electrical networks). Elektrotechnický obzor 15: 153-154.
    • (1926) Elektrotechnický obzor , vol.15 , pp. 153-154
    • Borůvka, O.1
  • 23
    • 34250162140 scopus 로고    scopus 로고
    • From hypertrees to arboreal quasi-ultrametrics
    • (forthcoming)
    • Brucker F (2004) From hypertrees to arboreal quasi-ultrametrics. Discrete Applied Mathematics (forthcoming).
    • (2004) Discrete Applied Mathematics
    • Brucker, F.1
  • 24
    • 34250201863 scopus 로고    scopus 로고
    • Rigid hypergraphs: Combinatorial optimization problem in clustering and similarity analysis
    • In
    • Brucker F, Osswald C, Barthélemy J-P (2003) Rigid hypergraphs: combinatorial optimization problem in clustering and similarity analysis. In: INOC 2003 Proceedings, pp 126-133.
    • (2003) INOC 2003 Proceedings , pp. 126-133
    • Brucker, F.1    Osswald, C.2    Barthélemy, J.-P.3
  • 25
    • 0001773546 scopus 로고
    • On the complexity of clustering problems
    • In: Beckman M, Kunzi HP (eds), Springer, Berlin Heidelberg NewYork
    • Brucker P (1978) On the complexity of clustering problems. In: Beckman M, Kunzi HP (eds) Optimization and operations research. Springer, Berlin Heidelberg NewYork, pp 45-54.
    • (1978) Optimization and operations research , pp. 45-54
    • Brucker, P.1
  • 26
    • 0000679777 scopus 로고
    • Spatial, non-spatial and hybrid models for scaling
    • Carroll JD (1976) Spatial, non-spatial and hybrid models for scaling. Psychometrika 41: 439-463.
    • (1976) Psychometrika , vol.41 , pp. 439-463
    • Carroll, J.D.1
  • 27
    • 0002307454 scopus 로고
    • A method for fitting a class of hierarchical tree structure models to dissimilarity data, and its application to some body part data of Miller
    • In
    • Carroll JD, Chang JJ (1973) A method for fitting a class of hierarchical tree structure models to dissimilarity data, and its application to some body part data of Miller. In: Proc. of the 81st Convention of the American Psychological Association, vol 8, pp 1097-1098.
    • (1973) Proc. of the 81st Convention of the American Psychological Association , vol.8 , pp. 1097-1098
    • Carroll, J.D.1    Chang, J.J.2
  • 28
    • 0002671655 scopus 로고
    • Discrete and hybrid scaling methods
    • In: Lauterman EB, Freger H (eds), Hans Huber, Bern
    • Carroll JD, Pruzansky S (1980) Discrete and hybrid scaling methods. In: Lauterman EB, Freger H (eds) Similarity and choice. Hans Huber, Bern.
    • (1980) Similarity and choice
    • Carroll, J.D.1    Pruzansky, S.2
  • 31
    • 0030550408 scopus 로고    scopus 로고
    • Space-conserving agglomerative algorithms
    • Chen Z (1996) Space-conserving agglomerative algorithms. Journal of Classification 13: 157-168.
    • (1996) Journal of Classification , vol.13 , pp. 157-168
    • Chen, Z.1
  • 32
    • 0031517186 scopus 로고    scopus 로고
    • Recognition of robinsonian dissimilarities
    • Chepoï V, Fichet B (1997) Recognition of robinsonian dissimilarities. Journal of Classification 14: 311-325.
    • (1997) Journal of Classification , vol.14 , pp. 311-325
    • Chepoï, V.1    Fichet, B.2
  • 36
    • 12144250562 scopus 로고
    • (ed), (Lecture Notes in Statistics), Springer, Berlin Heidelberg New-York
    • Van Cutsem B (ed) (1994) Classification and dissimilarity analysis (Lecture Notes in Statistics), vol 93. Springer, Berlin Heidelberg New-York.
    • (1994) Classification and dissimilarity analysis , vol.93
    • Van Cutsem, B.1
  • 38
    • 0041654378 scopus 로고    scopus 로고
    • Dissimilarités multivoies et généralisations d'hypergraphes sans triangles
    • Diatta J (1997) Dissimilarités multivoies et généralisations d'hypergraphes sans triangles. Mathématiques, Informatique et Sciences Humaines 138: 57-73.
    • (1997) Mathématiques, Informatique et Sciences Humaines , vol.138 , pp. 57-73
    • Diatta, J.1
  • 39
    • 0007264993 scopus 로고    scopus 로고
    • Approximating dissimilarities by quasi-ultrametrics
    • Diatta J (1998) Approximating dissimilarities by quasi-ultrametrics. Discrete Mathematics 192: 81-86.
    • (1998) Discrete Mathematics , vol.192 , pp. 81-86
    • Diatta, J.1
  • 40
    • 0002701045 scopus 로고
    • From Asprejan hierachies and Bandelt-Dress weak-hierarchies to quasihierarchies
    • In: Diday E et al. (eds), Springer, Berlin Heidelberg NewYork
    • Diatta J, Fichet B (1994) From Asprejan hierachies and Bandelt-Dress weak-hierarchies to quasihierarchies. In: Diday E et al. (eds) New approaches in classification and data analysis. Springer, Berlin Heidelberg NewYork, pp 111-118.
    • (1994) New approaches in classification and data analysis , pp. 111-118
    • Diatta, J.1    Fichet, B.2
  • 41
    • 0002579892 scopus 로고
    • Une nouvelle méthode en classification automatique et reconnaissance des formes: La méthode des nuées dynamiques
    • Diday E (1971) Une nouvelle méthode en classification automatique et reconnaissance des formes: la méthode des nuées dynamiques. Revue de Statistique Appliquée 19(2): 19-33.
    • (1971) Revue de Statistique Appliquée , vol.19 , Issue.2 , pp. 19-33
    • Diday, E.1
  • 42
    • 34250197555 scopus 로고
    • Inversions en classification automatique: Applications à la construction adaptative d'indices d'agrégation
    • Diday E (1983) Inversions en classification automatique: applications à la construction adaptative d'indices d'agrégation. Revue de Statistique Appliquée 31(1): 45-62.
    • (1983) Revue de Statistique Appliquée , vol.31 , Issue.1 , pp. 45-62
    • Diday, E.1
  • 44
    • 0007192980 scopus 로고
    • Orders and overlapping clusters in pyramids
    • In: de Leew J, et al. (eds)
    • Diday E (1986) Orders and overlapping clusters in pyramids. In: de Leew J, et al. (eds) Multidimentionnal data analysis proceedings, pp 201-234.
    • (1986) Multidimentionnal data analysis proceedings , pp. 201-234
    • Diday, E.1
  • 45
    • 34147120474 scopus 로고
    • Two problems in connection with graphs
    • Dijkstra E (1959) Two problems in connection with graphs. Numerische Mathematik 1: 269-271.
    • (1959) Numerische Mathematik , vol.1 , pp. 269-271
    • Dijkstra, E.1
  • 47
    • 85119733203 scopus 로고
    • chapter Classical perfect graphs. An introduction with emphasis on triangulated and interval graphs. North-Holland, Amsterdam
    • Duchet P (1984) Topics in perfect graphs, chapter Classical perfect graphs. An introduction with emphasis on triangulated and interval graphs. North-Holland, Amsterdam, pp 67-96.
    • (1984) Topics in perfect graphs , pp. 67-96
    • Duchet, P.1
  • 49
    • 84963036437 scopus 로고
    • On the cophenetic correlation coefficients
    • Farris JS (1969) On the cophenetic correlation coefficients. Systematic Zoology 18: 279-285.
    • (1969) Systematic Zoology , vol.18 , pp. 279-285
    • Farris, J.S.1
  • 50
    • 34250163221 scopus 로고
    • Sur une extension de la notion de hiérarchie et son équivalence avec quelques matrices de Robinson
    • Fichet B (1984) Sur une extension de la notion de hiérarchie et son équivalence avec quelques matrices de Robinson. Actes des "Journées de statistique de la Grande Motte": 12-12.
    • (1984) Actes des "Journées de statistique de la Grande Motte" , pp. 12
    • Fichet, B.1
  • 51
    • 85133987478 scopus 로고
    • Data analysis: Geometric and algebraic structures
    • In: Prohorov YA, et al. (eds), V.N.U. Science Press
    • Fichet B (1986) Data analysis: geometric and algebraic structures. In: Prohorov YA, et al. (eds) First world congress of the Bernoulli society proceedings. V. N. U. Science Press, pp 123-132.
    • (1986) First world congress of the Bernoulli society proceedings , pp. 123-132
    • Fichet, B.1
  • 55
    • 0043178365 scopus 로고
    • Hypergraphes arborés
    • Flament C (1978) Hypergraphes arborés. Discrete Mathematics 21: 223-227.
    • (1978) Discrete Mathematics , vol.21 , pp. 223-227
    • Flament, C.1
  • 62
    • 0001120850 scopus 로고
    • Minimal spanning trees and single linkage cluster analysis
    • Gower JC, Ross GJS (1969) Minimal spanning trees and single linkage cluster analysis. Applied Statistics 18: 54-64.
    • (1969) Applied Statistics , vol.18 , pp. 54-64
    • Gower, J.C.1    Ross, G.J.S.2
  • 63
    • 0000950204 scopus 로고    scopus 로고
    • Cluster analysis and mathematical programming
    • Hansen P, Jaumard B (1997) Cluster analysis and mathematical programming. Mathematical programming 79: 191-215.
    • (1997) Mathematical programming , vol.79 , pp. 191-215
    • Hansen, P.1    Jaumard, B.2
  • 64
    • 0007336159 scopus 로고
    • How to choose k entities among n
    • In: Cox I, Hansen P, Julesz B (eds), Providence
    • Hansen P, Jaumard B, Mladenovic N (1995) How to choose k entities among n. In: Cox I, Hansen P, Julesz B (eds) Partitioning data sets. Providence, pp 105-116.
    • (1995) Partitioning data sets , pp. 105-116
    • Hansen, P.1    Jaumard, B.2    Mladenovic, N.3
  • 65
    • 0004795618 scopus 로고
    • Partitionning problems in cluster analysis: A review of mathematical approaches
    • In: Diday E et al. (eds), Springer, Berlin Heidelberg NewYork
    • Hansen P, Jaumard B, Sanlaville E (1994) Partitionning problems in cluster analysis: a review of mathematical approaches. In: Diday E et al. (eds) New approaches in classification and data analysis. Springer, Berlin Heidelberg NewYork, pp 228-240.
    • (1994) New approaches in classification and data analysis , pp. 228-240
    • Hansen, P.1    Jaumard, B.2    Sanlaville, E.3
  • 70
    • 0032282322 scopus 로고    scopus 로고
    • Graph-theoretic representations for proximity matrices through strongly-anti-robinsonian or circular strongly-anti-robinsonian matrices
    • Hubert L, Arabie P, Meulman J (1998) Graph-theoretic representations for proximity matrices through strongly-anti-robinsonian or circular strongly-anti-robinsonian matrices. Psychometrica 63(4): 341-358.
    • (1998) Psychometrica , vol.63 , Issue.4 , pp. 341-358
    • Hubert, L.1    Arabie, P.2    Meulman, J.3
  • 77
    • 0014129195 scopus 로고
    • Hierarchical clustering schemes
    • Johnson SC (1967) Hierarchical clustering schemes. Psychometrika 32: 241-254.
    • (1967) Psychometrika , vol.32 , pp. 241-254
    • Johnson, S.C.1
  • 78
    • 0022735230 scopus 로고
    • NP-hard problems in hierarchical-tree clustering
    • Krivanek A, Moravek J (1986) NP-hard problems in hierarchical-tree clustering. Acta Informatica 23: 311-323.
    • (1986) Acta Informatica , vol.23 , pp. 311-323
    • Krivanek, A.1    Moravek, J.2
  • 79
    • 70350674995 scopus 로고
    • On the shortest spanning tree of a graph and the travelling salesman problem
    • Kruskal JB (1956) On the shortest spanning tree of a graph and the travelling salesman problem. Proceedings of the American Mathematical Society 7: 48-50.
    • (1956) Proceedings of the American Mathematical Society , vol.7 , pp. 48-50
    • Kruskal, J.B.1
  • 80
    • 0003126317 scopus 로고
    • A general theory of classificatory sorting strategies
    • Lance GN, Williams WT (1967a) A general theory of classificatory sorting strategies. The Computer Journal 9(4): 373-380.
    • (1967) The Computer Journal , vol.9 , Issue.4 , pp. 373-380
    • Lance, G.N.1    Williams, W.T.2
  • 81
    • 0003126321 scopus 로고
    • A general theory of classificatory sorting strategies
    • Lance GN, Williams WT (1967b) A general theory of classificatory sorting strategies. The Computer Journal 10(3): 271-277.
    • (1967) The Computer Journal , vol.10 , Issue.3 , pp. 271-277
    • Lance, G.N.1    Williams, W.T.2
  • 82
    • 0039824104 scopus 로고
    • Description combinatoire des ultramétriques
    • Leclerc B (1981) Description combinatoire des ultramétriques. Mathématiques et Sciences Humaines 73: 5-37.
    • (1981) Mathématiques et Sciences Humaines , vol.73 , pp. 5-37
    • Leclerc, B.1
  • 84
    • 0039232217 scopus 로고
    • Les hiérarchies de parties et leur demi-treillis
    • Leclerc B (1985a) Les hiérarchies de parties et leur demi-treillis. Mathématiques et Sciences Humaines 89: 5-34.
    • (1985) Mathématiques et Sciences Humaines , vol.89 , pp. 5-34
    • Leclerc, B.1
  • 85
    • 84934902118 scopus 로고
    • La comparaison de hiérarchies: Indices et métriques
    • Leclerc B (1985b) La comparaison de hiérarchies: indices et métriques. Mathématiques et Sciences Humaines 92: 5-40.
    • (1985) Mathématiques et Sciences Humaines , vol.92 , pp. 5-40
    • Leclerc, B.1
  • 86
    • 84976923621 scopus 로고
    • Elementary linkage analysis for isolating orthogonal and oblique types and typal relevancies
    • McQuitty LL (1957) Elementary linkage analysis for isolating orthogonal and oblique types and typal relevancies. Educational and Psychological Measurement 17: 207-229.
    • (1957) Educational and Psychological Measurement , vol.17 , pp. 207-229
    • McQuitty, L.L.1
  • 89
    • 34250163559 scopus 로고    scopus 로고
    • Robustesse aux variations de méthode pour la classification hiérarchique
    • In:, SFdS, Lyon
    • Osswald C (2003a) Robustesse aux variations de méthode pour la classification hiérarchique. In: XXXVèmes Journées de Statistiques. SFdS, Lyon, pp 751-754.
    • (2003) XXXVèmes Journées de Statistiques , pp. 751-754
    • Osswald, C.1
  • 90
    • 84911584312 scopus 로고
    • Shortest connection network and some generalizations
    • Prim RC (1957) Shortest connection network and some generalizations. Bell System Technical Journal 26: 1389-1401.
    • (1957) Bell System Technical Journal , vol.26 , pp. 1389-1401
    • Prim, R.C.1
  • 91
    • 0141636945 scopus 로고
    • Circular representation problem on hypergraphs
    • QuilliotA (1984) Circular representation problem on hypergraphs. Discrete Mathematics 51: 251-264.
    • (1984) Discrete Mathematics , vol.51 , pp. 251-264
    • Quilliot, A.1
  • 93
    • 70350573233 scopus 로고
    • Amethod for chronologically ordering archeological deposits
    • RobinsonWS (1951)Amethod for chronologically ordering archeological deposits. American Antiquity 16: 295-301.
    • (1951) American Antiquity , vol.16 , pp. 295-301
    • Robinson, W.S.1
  • 96
    • 0342693559 scopus 로고
    • Some observations of a paper by Lance and Williams
    • Sibson R (1971) Some observations of a paper by Lance and Williams. The Computer Journal 14: 156-157.
    • (1971) The Computer Journal , vol.14 , pp. 156-157
    • Sibson, R.1
  • 97
    • 9444222978 scopus 로고
    • The application of computers to taxonomy
    • Sneath PHA (1957) The application of computers to taxonomy. Journal of General Microbiology 17: 201-226.
    • (1957) Journal of General Microbiology , vol.17 , pp. 201-226
    • Sneath, P.H.A.1
  • 98
    • 0002471149 scopus 로고
    • The comparison of dendrograms by objective methods
    • Sokal RR, Rolf FJ (1962) The comparison of dendrograms by objective methods. Taxon 9: 33-40.
    • (1962) Taxon , vol.9 , pp. 33-40
    • Sokal, R.R.1    Rolf, F.J.2
  • 100
    • 0002969802 scopus 로고
    • A method to establish groups of equal amplitude in plant sociology based on the dissimilarity of species content and the applications of the analysis of the vegetation of danish common
    • Sorensen T (1948) A method to establish groups of equal amplitude in plant sociology based on the dissimilarity of species content and the applications of the analysis of the vegetation of danish common. Biologiske Skrifter 5(4): 1-34.
    • (1948) Biologiske Skrifter , vol.5 , Issue.4 , pp. 1-34
    • Sorensen, T.1


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