Three dissimilarity measures to contrast dendrograms

Journal of Chemical Information and Modeling

Volumn 47, Issue 3, 2007, Pages 761-770

  Restrepo, Guillermo ^a,b   Mesa, Héber ^c   Llanos, Eugenio J ^d  

^a UNIVERSIDAD DE PAMPLONA   (Colombia)

^b UNIVERSITY OF BAYREUTH   (Germany)

^c UNIVERSIDAD DEL VALLE   (Colombia)

^d Grupo Chima   (Colombia)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTERING ALGORITHMS; DATABASE SYSTEMS; HIERARCHICAL SYSTEMS; SECURITY OF DATA;

CHEMICAL APPLICATIONS; CHEMICAL INVESTIGATION; CLUSTER INDICES; DENDROGRAMS;

DISSIMILAR MATERIALS;

EID: 34250850867     PISSN: 15499596     EISSN: 1549960X     Source Type: Journal    
DOI: 10.1021/ci6005189     Document Type: Article

References (53)

1. Everitt, B. S. Cluster Analysis; Edward Arnold: Bristol, U. K., 1993; Chapter 1, pp 1-10.
2. Downs, G. M.; Barnard, J. M. Clustering Methods and Their Uses in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; WileyVCH: Weinheim, Germany, 2002; Vol. 18, pp 1-40.
3. Handl, J.; Knowles, J.; Kell, D. B. Computational Cluster Validation in Post-Genomic Data Analysis. Bioinformatics 2005, 21, 3201-3212.
4. Willett, P.; Barnard, J. M.; Downs, G. M. Chemical Similarity Searching. J. Chem. Inf. Comput. Sci. 1998, 38, 983-996.
5. Potter, M. Set Theory and Its Philosophy; Oxford University press: Oxford, U. K., 2004; p 72.
6. Restrepo, G.; Mesa, H.; Llanos, E. J.; Villaveces, J. L. Topological Study of the Periodic System. J. Chem. Inf. Comput. Sci. 2004, 44, 68-75.
7. Restrepo, G.; Villaveces, J. L. From Trees (Dendrograms and Consensus Trees) to Topology. Croat. Chem. Acta 2005, 78, 275-281.
8. Restrepo, G.; Mesa, H.; Villaveces, J. L. On the Topological Sense of Chemical Sets. J. Math. Chem. 2006, 39, 363-376.
9. Restrepo, G.; Llanos, E. J.; Mesa, H. Topological Space of the Chemical Elements and Its Properties. J. Math. Chem. 2006, 39, 401 -416.
10. Restrepo, G.; Mesa, H.; Llanos, E. J.; Villaveces, J. L. Topological Study of the Periodic System. In The Mathematics of the Periodic Table; King, R. B., Rouvray, D. H., Eds.; Nova: New York, 2006; pp 75-100.
11. Daza, M. C.; Restrepo, G.; Uribe, E. A.; Villaveces, J. L. Quantum Chemical and Chemotopological Study of Fourth Row Monohydrides. Chem. Phys. Lett. 2006, 428, 55-61.
12. Mesa, H.; Restrepo, G. On Dendrograms and Topologies. J, Math. Chem. 2007, Submitted.
13. Felsenstein, J. The Number of Evolutionary Trees. Syst. Zool. 1978, 27, 27-33.
14. Estabrook, G. F.; McMorris, F. R.; Meacham, C. A. Comparison of Undirected Phylogenetic Trees Based on Subtrees of Four Evolutionary Units. Syst. Zool. 1985, 34, 193-200.
15. Felsenstein, J. Inferring Phylogenies; Sinauer Associates: Sunderland, MA, 2004; Chapter 30, pp 528-535.
16. Day, W. H. E. Optimal Algorithms for Comparing Trees with Labeled Leaves. J. Class. 1985, 2, 7-28.
17. Penny, D.; Hendy, M. D. The Use of Tree Comparison Metrics. Syst. Zool. 1985, 34, 75-82.
18. Steel, M. A.; Penny, D. Distributions of Tree Comparison MetricsSome New Results. Syst. Biol. 1993, 42, 126-141.
19. Penny, D.; Foulds, L. R.; Hendy, M. D. Testing the Theory of Evolution by Comparing Phylogenetic Trees Constructed from Five Different Protein Sequences. Nature 1982, 297, 197-200.
20. Critchlow, D. E.; Pearl, D. K.; Qian, C. The Triples Distance for Rooted Bifurcating Phylogenetic Trees. Syst. Biol. 1996, 45, 323-334.
21. Robinson, D. F. Comparison of Labeled Trees with Valency Three. J. Comb. Theory 1971, 11, 105-119.
22. Waterman, M. S.; Smith, T. F. On the Similarity of Dendrograms. J. Theor. Biol. 1978, 73, 789-800.
23. Boorman, S. A.; Olivier, D. C. Metrics on Spaces of Finite Trees. J. Math. Psychol. 1973, 10, 26-59.
24. Rouvray, D. H. Definition and Role of Similarity Concepts in the Chemical and Physical Sciences. J. Chem. Inf. Comput. Sci. 1992, 32, 580-586.
25. Restrepo, G.; Brüggemann, R. Ranking Regions through Cluster Analysis and Posets. WSEAS Trans. Inf. Sci. Appl. 2005, 2, 976-981.
26. Chartrand, G.; Lesniak, L. Graphs & Digraphs.; Wadsworth & Brooks/ Cole: Monterey, CA, 1986; pp 77-83.
27. Deza, M. M.; Deza, E. Dictionary of Distances; Elsevier: Amsterdam, 2006; p 6.
28. Page, R. D. M. COMPONENT User's Manual (Release 1.5); University of Auckland: Auckland, New Zealand, 1989; Chapter 4, pp 4.1-4.7. URL: http://taxonomy.zoology.gla.ac.uk/rod/cpw.html (accessed Apr 2007).
29. Slowinski, J. B. Review. Cladistics 1993, 9, 351-353.
30. Felsenstein, J. PHYLIP - Phylogeny Inference Package (Version 3.2). Cladistics 1989, 5, 164-166.
31. Swofford, D. L. PAUP: Phylogenetic Analysis Using Parsimony, Version 3.1; Illinois Natural History Survey: Champaign, IL, 1993; p 53.
32. Gusfield, D. Efficient Algorithms for Inferring Evolutionary Trees. Networks 1991, 21, 19-28.
33. Golumbic, M. C.; Trenk, A. N. Tolerance Graphs; Cambridge University Press: Cambridge, U. K., 2004; Chapter 1, p 4.
34. Bollobás, B. Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability; Cambridge University Press: Cambridge, U. K., 1988; p 1.
35. Gross, J.; Yellen, J. Graph Theory and Its Applications; CRC Press: Boca Raton, FL, 1999; Chapter 2, pp 64-65.
36. Chartrand, G.; Lesniak, L. Graphs & Digraphs; Chapman & Hall: London, 1996; pp 50-51.
37. Kratsch, D.; Hemaspaandra, L. A. On the Complexity of Graph Reconstruction. Math. Syst. Theory 1994, 27, 257-273.
38. Kelly, P. J. A Congruence Theorem for Trees. Pac. J. Math. 1957, 7, 961-968.
39. Restrepo, G.; Brüggemann, R. Ranking Regions Through Cluster Analysis and Posets. WSEAS Trans. Inf. Sci. Appl. 2005, 2, 976-981.
40. Gower, J. C. A General Coefficient of Similarity and Some of Its Properties. Biometrics 1971, 27, 857-874.
41. The NCI database is available at URL http://dtp.nci.nih.gov/ (accessed Apr 2007).
42. Barnard, J. M.; Downs, G. M. Clustering of Chemical Structures on the Basis of Two-Dimensional Similarity Measures. J. Chem. Inf. Comput. Sci. 1992, 32, 644-649.
43. Barnard, J. M.; Downs, G. M. Chemical Fragment Generation and Clustering Software. J. Chem. Inf. Comput. Sci. 1997, 37, 141-142.
44. The BCI software is available from Digital Chemistry Ltd. at URL http://www.digitalchemistry.co.uk (accessed Apr 2007).
45. Sneath, P. H. A.; Sokal, R. R. Numerical Taxonomy; WH Freeman: San Francisco, CA, 1973.
46. Gower, J. C. Measures of Similarity, Dissimilarity and Distance. In Encyclopaedia of Statistical Sciences; Kotz, S., Johnson, N. L., Read, C. B., Eds.; Wiley: Chichester, U. K., 1982; pp 397-405.
47. Brüggemann, R.; Halfon, E.; Welzl, G.; Voigt, K.; Steinberg, C. E. W. Applying the Concept of Partially Ordered Sets on the Ranking of Near-Shore Sediments by a Battery of Tests. J. Chem. Inf. Comput. Sci. 2001, 41, 918-925.
48. Adamson, G. W.; Bawden, D. Comparison of Hierarchical Cluster Analysis Techniques for Automatic Classification of Chemical Structures. J. Chem. Inf. Comput. Sci. 1981, 21, 204-209.
49. Downs, G. M.; Willett, P. Similarity Searching in Databases of Chemical Structures; Lipkowitz, K. B., Boyd, D. B., Eds.; WileyVCH: New York, U.S.A., 1996; Vol. 7, pp 1-66.
50. MacCuish, J.; Nicolaou, C.; MacCuish, N. E. Ties in Proximity and Clustering Compounds. J. Chem. Inf. Comput. Sci. 2001, 41, 134-146.
51. Kvasnicka, V.; Pospichal, J. Fast Evaluation of Chemical Distance by Tabu Search Algorithm. J. Chem. Inf. Comput. Sci. 1994, 34, 1109-1112.
52. Diudea, M. V. Molecular Topology. 16. Layer Matrices in Molecular Graphs. J. Chem. Inf. Comput. Sci. 1994, 34, 1064-1071.
53. Rücker, C; Rücker, G.; Meringer, M. Exploring the Limits of Graph Invariant- and Spectrum-Based Discrimination of (Sub)structures. J. Chem. Inf. Comput. Sci. 2002, 42, 640-650.