Abstract
We present a novel algorithm for estimating the rigid-body transformation of a sequence of coordinates, aiming at the application to protein structures. Basically the sequence is modeled as a hidden Markov model where each state outputs an ellipsoidal Gaussian. Since maximum likelihood estimation requires to solve a complicated optimization problem, we introduce a variational estimation technique, which performs singular value decomposition in each step. Our probabilistic algorithm allows to superimpose a number of sequences which are rotated and translated in arbitrary ways.
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Bashford, D., Lesk, A.M., Chothia, C.: Determinants of a protein fold: unique features of the globin amino acid sequences. J. Mol. Biol. 196, 199–216 (1987)
Challis, J.H.: A procedure for determining rigid body transformation parameters. J. Biomechanics 28, 733–737 (1995)
Weng, Z., Szustakowski, J.D.: Protein structure alignment using a genetic algorithm. Proteins: structure, function, and genetics 38(4), 428–440 (2000)
Jaakkola, T., Haussler, D.: Exploiting generative models in discriminative classifiers. In: NIPS, vol. 11, pp. 487–493. MIT Press, Cambridge (1999)
Jordan, M.I., Ghahramani, Z., Jaakkola, T., Saul, L.: An introduction to variational methods for graphical methods. In: Jordan, M.I. (ed.) Learning in Graphical Models, pp. 105–161. MIT Press, Cambridge (1998)
Mount, D.W.: Bioinformatics: Sequence and Genome Analysis. Cold Spring Harbor Laboratory Press (March 2001)
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)
Rabiner, L.R.: A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE 77, 257–286 (1989)
Revow, M.D., Williams, C.K.I., Hinton, G.E.: Using generative models for handwritten digit recognition. IEEE T. PAMI 18(6), 592–606 (1996)
Seeger, M.: Learning with labeled and unlabeled data. Technical report, Institute for Adaptive and Neural Computation, University of Edinburgh (2001)
Shindyalov, I.N., Bourne, P.E.: Protein structure alignment by incremental combinatorial extension (CE) of the optimal path. Protein Engineering 11, 739–747 (1998)
Smyth, P.: Clustering sequences with hidden markov models. In: NIPS, vol. 9, pp. 648–654. The MIT Press, Cambridge (1997)
Tsuda, K., Kin, T., Asai, K.: Marginalized kernels for biological sequences. Bioinformatics 18 (Suppl. 1), S268–S275 (2002)
Wu, T.D., Hastie, T., Schmidler, S.C., Brutlag, D.L.: Regression analysis of multiple protein structures. J. Comput. Biol. 5(3), 585–595 (1998)
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© 2004 Springer-Verlag Berlin Heidelberg
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Kato, T., Tsuda, K., Tomii, K., Asai, K. (2004). A New Variational Framework for Rigid-Body Alignment. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2004. Lecture Notes in Computer Science, vol 3138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27868-9_17
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DOI: https://doi.org/10.1007/978-3-540-27868-9_17
Publisher Name: Springer, Berlin, Heidelberg
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