On sufficient statistics of least-squares superposition of vector sets

Arun S. Konagurthu, Parthan Kasarapu, Lloyd Allison, James H. Collier, Arthur M. Lesk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

Superposition by orthogonal transformation of vector sets by minimizing the least-squares error is a fundamental task in many areas of science, notably in structural molecular biology. Its widespread use for structural analyses is facilitated by exact solutions of this problem, computable in linear time. However, in several of these analyses it is common to invoke this superposition routine a very large number of times, often operating (through addition or deletion) on previously superposed vector sets. This paper derives a set of sufficient statistics for the least-squares orthogonal transformation problem. These sufficient statistics are additive. This property allows for the superposition parameters (rotation, translation, and root mean square deviation) to be computable as constant time updates from the statistics of partial solutions. We demonstrate that this results in a massive speed up in the computational effort, when compared to the method that recomputes superpositions ab initio. Among others, protein structural alignment algorithms stand to benefit from our results.

Original languageEnglish (US)
Title of host publicationResearch in Computational Molecular Biology - 18th Annual International Conference, RECOMB 2014, Proceedings
PublisherSpringer Verlag
Pages144-159
Number of pages16
ISBN (Print)9783319052687
DOIs
StatePublished - Jan 1 2014
Event18th Annual International Conference on Research in Computational Molecular Biology, RECOMB 2014 - Pittsburgh, PA, United States
Duration: Apr 2 2014Apr 5 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8394 LNBI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other18th Annual International Conference on Research in Computational Molecular Biology, RECOMB 2014
CountryUnited States
CityPittsburgh, PA
Period4/2/144/5/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Konagurthu, A. S., Kasarapu, P., Allison, L., Collier, J. H., & Lesk, A. M. (2014). On sufficient statistics of least-squares superposition of vector sets. In Research in Computational Molecular Biology - 18th Annual International Conference, RECOMB 2014, Proceedings (pp. 144-159). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8394 LNBI). Springer Verlag. https://doi.org/10.1007/978-3-319-05269-4_11