Statistical analysis of unlabeled point sets: Comparing molecules in chemoinformatics

Biometrics

Volumn 63, Issue 1, 2007, Pages 237-251

  Dryden, Ian L ^a   Hirst, Jonathan D ^a   Melville, James L ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Alignment; Bayesian; Bioinformatics; Chemoinformatics; Markov chain Monte Carlo; Mixture model; Procrustes; Riemannian metric; Rigid body transformations; Shape; Size and shape; Steroids

Indexed keywords

APPROXIMATION ALGORITHMS; BAYESIAN NETWORKS; BIOINFORMATICS; CHAINS; GEOMETRY; INFERENCE ENGINES; INTELLIGENT SYSTEMS; MARKOV PROCESSES; MONTE CARLO METHODS;

BAYESIAN; CHEMOINFORMATICS; MARKOV CHAIN MONTE CARLO; MARKOV CHAIN MONTE-CARLO; MIXTURE MODELING; PROCRUSTES; RIEMANNIAN METRICS; RIGID BODY TRANSFORMATION; SHAPE; SIZE AND SHAPE; STEROID;

MOLECULES;

STEROID;

ALGORITHM; BAYESIAN ANALYSIS; COMPARATIVE STUDY; DATA PROCESSING; MARKOV CHAIN; MODELING; MOLECULAR ANALYSIS; MONTE CARLO ANALYSIS; STATISTICAL ANALYSIS; STEROID;

ALGORITHM; ARTICLE; ATOMIC PARTICLE; BAYES THEOREM; BIOINFORMATICS; CONCENTRATION (PARAMETERS); DATA ANALYSIS; MATHEMATICAL ANALYSIS; MOLECULE; MONTE CARLO METHOD; STATISTICAL ANALYSIS; STRUCTURE ANALYSIS;

EID: 34247277089     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2006.00622.x     Document Type: Article

References (36)

1. Bookstein, F. L. (1991). Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge, U.K.: Cambridge University Press.
2. Chui, H. and Rangarajan, A. (2000). A feature registration framework using mixture models. In IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA), 190-197. Washington, DC: IEEE Computer Society.
3. Chui, H. and Rangarajan, A. (2003). A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding 89, 114-141.
4. Coats, E. A. (1998). The CoMFA steroids as a benchmark data set for development of 3D QSAR methods. Perspectives in Drug Discovery and Design 12, 119-213.
5. Cross, A. D. J. and Hancock, E. R. (1998). Graph matching with a dual-step EM algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 20, 1236-1253.
6. Dryden, I. L. and Mardia, K. V. (1992). Size and shape analysis of landmark data. Biometrika 79, 57-68.
7. Dryden, I. L. and Mardia, K. V. (1998). Statistical Shape Analysis. Chichester: Wiley.
8. Esposito, E. X., Hopfinger, A. J., and Madura, J. D. (2004). Methods for applying the quantitative structure-activity relationship paradigm. In Chemoinformatics. Concepts, Methods, and Tools for Drug Discovery, J. Bajorath (ed), 131-214. Totowa, New Jersey: Humana Press.
9. Gold, S., Rangarajan, A., Lu, C.-P., Pappu, S., and Mjolsness, E. (1998). New algorithms for 2d and 3d point matching: Pose estimation and correspondence. Pattern Recognition 31, 1019-1031.
10. Good, A. C., So, S., and Richards, W. G. (1993). Structureactivity relationships from molecular similarity matrices. Journal of Medicinal Chemistry 36, 433-438.
11. Goodall, C. R. (1991). Procrustes methods in the statistical analysis of shape (with discussion). Journal of the Royal Statistical Society, Series B 53, 285-339.
12. Gower, J. C. (1975). Generalized Procrustes analysis. Psychometrika 40, 33-50.
13. Green, P. J. and Mardia, K. V. (2006). Bayesian alignment using hierarchical models, with applications in protein bioinformatics. Biometrika 93, 235-254.
14. Gross, J. and Yellen, J. (1999). Graph Theory and Its Applications. Boca Raton, Florida: CRC.
15. Humphrey, W., Dalke, A., and Schulten, K. (1996). VMD - Visual molecular dynamics. Journal of Molecular Graphics 14, 33-38.
16. Kendall, D. G. (1984). Shape manifolds, Procrustean metrics and complex projective spaces. Bulletin of the London Mathematical Society 16, 81-121.
17. Kendall, D. G., Barden, D., Carne, T. K., and Le, H. (1999). Shape and Shape Theory. Chichester: Wiley.
18. Kent, J. T. and Mardia, K. V. (2001). Shape, tangent projections and bilateral symmetry. Biometrika 88, 469-485.
19. Kent, J. T., Mardia, K. V., and Taylor, C. C. (2004). Matching problems for unlabeled configurations. In LASR2004 Proceedings: Bioinformatics, Images and Wavelets, R. G. Aykroyd, S. Barber, and K. V. Mardia (eds), 33-36, University of Leeds, U.K.
20. Le, H.-L. and Kendall, D. G. (1993). The Riemannian structure of Euclidean shape spaces: A novel environment for statistics. Annals of Statistics 21, 1225-1271.
21. Lemmen, C. and Lengauer, T. (2000). Computational methods for the structural alignment of molecules. Journal of Computer-Aided Molecular Design 14, 215-232.
22. Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979). Multivariate Analysis. London: Academic Press.
23. Melville, J. L. and Hirst, J. D. (2004). On the stability of CoMFA models. Journal of Chemical Information and Computer Science 44, 1294-1300.
24. Melville, J. L., Andrews, B. I., Lygo, B., and Hirst, J. D. (2004). Computational screening of combinatorial catalyst libraries. Chemical Communications 1410-1411.
25. Moss, S. and Hancock, E. R. (1996). Registering incomplete radar images using the EM algorithm. In Proceedings of the Seventh British Machine Vision Conference, R. B. Fisher and E. Trucco (eds), 685-694. Malvern, U.K.: British Machine Vision Association.
26. R Development Core Team. (2005). R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing.
27. Rangarajan, A., Chui, H., and Bookstein, F. L. (1997). The Softassign Procrustes matching algorithm. In Information Processing in Medical Imaging, J. Duncan and G. Gindi (eds), 29-42. Berlin: Springer.
28. Richmond, N. J., Willett, P., and Clark, R. D. (2004). Alignment of three-dimensional molecules using an image recognition algorithm. Journal of Molecular Graphics and Modelling 23, 199-209.
29. Small, C. G. (1996). The Statistical Theory of Shape. New York: Springer.
30. Stoyan, D. and Stoyan, H. (1994). Fractals, Random Shapes and Point Fields: Methods of Geometric Statistics. Chichester: Wiley.
31. Taylor, C. C., Mardia, K. V., and Kent, J. T. (2003). Matching unlabeled configurations using the EM algorithm. In LASR2003 Proceedings: Stochastic Geometry, Biological Structure and Images, R. G. Aykroyd, K. V. Mardia, and M. J. Langdon (eds), 19-21, University of Leeds, U.K.
32. Van Drie, J. H. (1997). Strategies for the determination of pharmacophoric 3D database queries. Journal of Computer-Aided Molecular Design 11, 39-52.
33. Wagener, M., Sadowski, J., and Gasteiger, J. (1995). Autocorrelation of molecular surface properties for modeling corticosteroid binding globulin and cytosolic Ah receptor activity by neural networks. Journal of the American Chemical Society 117, 7769-7775.
34. Walker, G. (1999). Robust, non-parametric and automatic methods for matching spatial point patterns. Ph.D. Thesis, University of Leeds, U.K.
35. Ward, J. H., Jr. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association 58, 236-244.
36. Wu, T. D., Schmidler, S. C., Hastie, T., and Brutlag, D. L. (1998). Regression analysis of multiple protein structures. Journal of Computational Biology 5, 585-595.