A reduction algorithm for approximating a (nonmetric) dissimilarity by a tree distance

Journal of Classification

Volumn 13, Issue 1, 1996, Pages 129-155

  Gascuel, Olivier ^a   Levy, Denise ^a  

^a LIRMM   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030555957     PISSN: 01764268     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01202585     Document Type: Article

References (41)

1. BANDELT, H. J., and DRESS, A. (1986), "Reconstructing the Shape of a Tree From Observed Dissimilarity Data," Advances in Applied Mathematics, 7, 309-343.
2. BARTHÉLEMY, J. P., and LUONG, X. (1986), "Représentations arborées de mesures de dissimilarité," Statistique et Analyse des Données, 11, 20-41.
3. BARTHÉLEMY, J. P., and GUENOCHE, A. (1988), Les arbres et les représentations des proximités, Paris: Masson.
4. BARTHÉLEMY, J. P., and GUENOCHE, A. (1991), Trees and Proximity Representations, Chichester: Wiley.
5. BROSSIER, G. (1985), "Approximation des dissimilarités par des arbres additifs," Mathématiques et Sciences Humaines, 91, 5-21.
6. BUNEMAN, P. (1971), "The Recovery of Trees From Measures of Dissimilarity," in Mathematics in Archeological and Historical Sciences, Eds., F. R. Hodson, D. G. Kendall and P. Tautu, Edinburgh: Edinburgh University Press, 387-395.
7. BUNEMAN, P. (1974), "A Note on Metric Properties of Trees," Journal of Combinatorial Theory, 17(B), 48-50.
8. CARROLL, J. D., and CHANG, J. J. (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's," in Proceedings, 81st Annual Convention, American Psychological Association, 8, 1097-1098.
9. CARROLL, J. D., and PRUZANSKY, S. (1980), "Discrete and Hybrid Scaling Models," in Similarity and choice, Eds.,E. B. Lantermann and H. Feger, Bern: Hans Huber, 108-139.
10. CASE, S. M. (1978), "Biochemical Systematics of Members of the Genus Rana native to Western North America," Systematic Zoology, 27, 299-311.
11. CAVALLI-SFORZA, L. L., and EDWARDS, A. W. F. (1967), "Phylogenetic Analysis: Models and Estimation Procedures," American Journal of Human Genetics, 19, 223-257.
12. CHANDON, J. L., LEMAIRE, J., and POUGET, J (1980), "Construction de l'ultramétrique la plus proche d'une dissimilarité au sens des moindres carrés," R.A.I.R.O. Recherche Opérationelle, 14, 157-170.
13. COLONIUS, H. and SCHULZE, H. H. (1981), "Tree Structures for Proximity Data," British Journal of Mathematical and Statistical Psychology, 34, 167-180.
14. CUNNIGHAM, J. P., and SHEPARD. R. N. (1974), "Monotone Mapping of Similarities into a General Metric Space," Journal of Mathematical Psychology, 11, 335-363.
15. CUNNINGHAM, J. P. (1978), "Free Trees as Representations of Psychological Distances," Journal of Mathematical Psychology, 17, 165-188.
16. DAY, W. H. E. (1987), "Computational Complexity of Inferring Phytogenies from Dissimilarity Matrices," Bulletin of Mathematical Biology, 49, 461-467.
17. DE SOETE, G. (1983), "A Least Squares Algorithm for Fitting Additive Trees to Proximity Data," Psychometrika, 48, 621-626.
18. DE SOETE, G., CARROLL, J. D., and DESARBO, W. S. (1987), "Least Squares Algorithms for Constructing Constrained Ultrametric and Additive Tree Representations of Symmetric Proximity Data," Journal of Classification, 4, 155-173.
19. FELSENSTEIN, J. (ed) (1983), Numerical Taxonomy, Berlin: Springer-Verlag.
20. FELSENSTEIN, J. (1984), "Distance Methods for Inferring Phylogenies: A Justification," Evolution, 38, 16-24.
21. FICHET, B. (1986), "Projection on an Acute Symmetrical Simplicial Closed Convex Cone and Its Application to Star Graphs," in Proceedings of COMPSTAT (Roma), eds., H. Caussinus, P. Ettinger and R. Tomassone, Wien: Physica-Verlag, 176-181.
22. FITCH, W. M., and MARGOLIASH, E. (1967), "Construction of Phylogenetic rees," Science, 155, 279-284.
23. FITCH, W. M. (1981), "A Non-Sequential Method for Constructing Trees and Hierarchical Classifications," Journal of Molecular Evolution, 18, 30-37.
24. GUENOCHE, A. (1986), "Représentations arborées des classifications," R.A.I.R.O Recherche opérationnelle, 20, 341-354.
25. HENLEY, N. M. (1969), "A Psychological Study of the Semantics of Animal Terms," Journal of Verbal Learning and Verbal Behavior, 8, 176-184.
26. HOPFIELD, J. J. (1982), "Neural Networks and Physical Systems with Emergent Collective Computational Abilities," Proceedings of the National Academy of Sciences USA, 79, 2554-2558.
27. KLAUER, K. C., and CARROLL, J. D. (1989), "A Mathematical Programming Approach to Fitting General Graphs," Journal of Classification, 6, 247-270.
28. LAWSON, C. M., and HANSON, R. J. (1974), Solving Least Squares Problems, Englewood Cliffs, NJ: Prentice Hall.
29. PRUZANSKY, S., TVERSKY, A., and CARROLL, J. D. (1982), "Spatial Versus Tree Representation of Proximity Data," Psychometrika, 47, 3-19.
30. ROBINSON, D. F., and FOULDS, L. R. (1981), "Comparison of Phylogenetic Trees," Mathematical Biosciences, 53, 131-147.
31. ROUX, M. (1988), "Techniques of Approximation for Building Two Tree Structures," in Recent Developments in Clustering and Data Analysis, Eds., C. Hayashi, E. Diday, M. Jambu, and N. Ohsumi, New York: Academic Press, 151-170.
32. RZHETSKY, A., and NEI, M. (1992), "Statistical Properties of the Ordinary Least-Squares, Generalized Least-Squares, and Minimum Evolution Methods of Phylogenetic Inference," Journal of Molecular Evolution, 35, 367-375.
33. SAITOU, N., and NEI, M. (1987), "The Neighbor-Joining Method: A New Method for Reconstruction of Phylogenetic Trees," Molecular Biology and Evolution, 4, 406-425.
34. SATTATH, S., and TVERSKY, A. (1977), "Additive Similarity Trees," Psychometrika, 42, 319-345.
35. SIMOES-PEREIRA, J. M. S. (1969), "A Note on Tree Realizability of a Distance Matrix," Journal of Combinatorial Theory, 6(B), 303-310.
36. SMOLENSKII, Y. A. (1969), "A Method for Linear Recording of Graphs," USSR Computational Mathematics and Mathematical Physics, 2, 396-397.
37. STOER, J. and WITZGALL, C. (1970), Convexity and Optimization in Finite Dimensions, New York: Academic Press.
38. STUDIER, J. A., and KEPPLER, K. J. (1988), "A Note on the Neighbor-Joining Method of Saitou and Nei," Molecular Biology and Evolution, 5, 729-731.
39. TENENHAUS, M. (1988), "Canonical Analysis of Two Convex Polyhedral Cones and Applications," Psychometrika, 53, 503-524.
40. TVERSKY, A. (1977), "Features of Similarity," Psychological Review, 84, 327-352.
41. ZARESTKII, K. (1965), "Reconstructing a Tree from the Distances Between Its Leaves," Uspehi Mathematicheskikh Nauk, 20, 90-92 (in Russian).