
Arun S. Konagurthu,
Parthan Kasarapu,
Lloyd Allison,
James H. Collier, and
Arthur M. Lesk
RECOMB 2014, Springer Verlag, LNBI 8394,
pp.144159, 2014.
Superposition by orthogonal transformation of vector sets by minimizing
the leastsquares 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 solns 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 leastsquares orthogonal transformation problem.
These sufficient statistics are additive. This property allows for the
superposition parameters (rotation, translation, & 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.
[doi:10.1007/9783319052694_11]

