Clustering on trees

Computational Statistics and Data Analysis

Volumn 24, Issue 2, 1997, Pages 217-234

  Maravalle, Maurizio ^a   Simeone, Bruno ^b   Naldini, Rosella ^b  

^a UNIVERSITY OF L'AQUILA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Computational complexity; Contiguity constrained clustering; Districting; Heuristics; Submodular functions; Trees

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; ERROR ANALYSIS; FUNCTIONS; HEURISTIC METHODS; POLYNOMIALS; SET THEORY;

CONTIGUITY CONSTRAINED CLUSTERING;

TREES (MATHEMATICS);

CLUSTER ANALYSIS; TREE PARTITIONING;

EID: 0031550921     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(96)00062-X     Document Type: Article

References (30)

1. Aho, A.V., J.E. Hopcroft and J.D. Ullman, The design and analysis of computer algorithms (Addison-Wesley, Reading, MA, 1975).
2. Anderberg, M.R., Cluster analysis for applications (Academic Press, New York, 1973).
3. Ben-Bassat, M. and L. Zaidenberg, Contextual template matching: a distance measure for patterns with hierarchically dependent features, IEEE Trans. PAMI, 6 (1984) 201-211.
4. Day, W.H.E., Complexity theory: an introduction for practitioners of classification, in: P. Arabie, L.J. Hubert and G. De Soete (Eds.), Clustering and classification (World Scientific, Singapore, 1996).
5. Delattre, M. and P. Hansen, Bicriterion cluster analysis, IEEE Trans. Pattern Analysis Machine Intelligence, 2 (1980) 277-291.
6. Ferligoj, A. and V. Batagelj, Clustering with relational constraints, Psychometrika, 47 (1982) 413-426.
7. Fisher, R.D., On grouping for maximum homogeneity, J. Amer. Statist. Assoc., 53 (1958) 789-98.
8. Fisher, M.L., G.L. Nemhauser and L.A. Wolsey, Analysis of approximations for maximizing a submodular set function II, Math. Programming, 14 (1978) 265-294.
9. Garey, M.R. and D.S. Johnson, Computers and intractability: a guide to the theory of NP-completeness (Freeman, San Francisco, 1979).
10. Golumbic, M.C. and R.E. Jamison, Edge and vertex intersection of paths in trees, Discrete Math., 55 (1985) 151-159.
11. Gordon, A.D., Classification: methods for exploratory analysis of multivariate data (Chapman & Hall, New York, 1981).
12. Guthery, S.B., Partition regression, J. Amer. Statist. Assoc., 69 (1974) 945-947.
13. Hansen, P., B. Jaumard and K. Musitu, Weight-constrained maximum split clustering, J. Classification, 7 (1990) 217-240.
14. Hansen, P., B. Jaumard, B. Simeone and V. Doring, Maximum split clustering under connectivity constraints, Cahier G-93-06, GERAD (Montréal, 1993).
15. Hartigan, J.A., Clustering algorithms (Wiley, New York, 1975).
16. Jardine, N. and R. Sibson, Mathematical taxonomy (Wiley, London, 1971).
17. Kaufman, L. and P.T. Rousseeuw, Finding groups in data: an introduction to cluster analysis (Wiley, New York, 1989).
18. Lefkovitch, L.P., Conditional clustering, Biometrics, 36 (1980) 43-58.
19. Lovász, L., Combinatorial problems and exercises (North-Holland, Amsterdam, 1979).
20. Maravalle, M. and B. Simeone, A greedy algorithm for maximum split clustering on trees, Research Report 4 (Series A) (Dipartimento di Statistica, Probabilità e Statistiche Applicate, Universitädi Roma "La Sapienza" (1984).
21. Maravalle, M. and B. Simeone, A spanning tree heuristic for regional clustering, Comm. Statist. Theory Methods, 24 (1995) 625-639.
22. Mulvey, J.M. and M.P. Beck, Solving capacitated clustering problems, Technical Report EES-82-2 (School of Engineering and Applied Science, Princeton University, 1982).
23. Mulvey, J.M. and H.P. Crowder, Cluster analysis: an application of lagrangian relaxation, Management Sci., 25 (1979) 329-340.
24. Murtagh, F., A survey of algorithms for contiguity-constrained clustering and related problems, Comput. J., 28 (1985) 82-88.
25. Perruchet, C., Constrained agglomerative hierarchical classification. Pattern Recognition, 16 (1983) 213-217.
26. Rao, M.R., Cluster analysis and mathematical programming, J. Amer. Statist. Assoc., 66 (1971) 622-626.
27. Schkolnick, M., A clustering algorithm for hierarchical structures, ACM Trans. Database Systems, 2 (1977) 27-44.
28. Scott, A.J., Combinatorial programming, spatial analysis and planning (Methuen, London, 1971).
29. Späth, H., Cluster analysis algorithms for data reduction and classification of objects (Chichester, Horwood, 1980).
30. Späth, H., Anticlustering: maximizing the variance criterion. Control Cybernet., 15 (1986) 213-218.