Times series averaging from a probabilistic interpretation of time-elastic kernel

At the light of regularized dynamic time warping kernels, this paper reconsider the concept of time elastic centroid (TEC) for a set of time series. From this perspective, we show first how TEC can easily be addressed as a preimage problem. Unfortunately this preimage problem is ill-posed, may suffer from over-fitting especially for long time series and getting a sub-optimal solution involves heavy computational costs. We then derive two new algorithms based on a probabilistic interpretation of kernel alignment matrices that expresses in terms of probabilistic distributions over sets of alignment paths. The first algorithm is an iterative agglomerative heuristics inspired from the state of the art DTW barycenter averaging (DBA) algorithm proposed specifically for the Dynamic Time Warping measure. The second proposed algorithm achieves a classical averaging of the aligned samples but also implements an averaging of the time of occurrences of the aligned samples. It exploits a straightforward progressive agglomerative heuristics. An experimentation that compares for 45 time series datasets classification error rates obtained by first near neighbors classifiers exploiting a single medoid or centroid estimate to represent each categories show that: i) centroids based approaches significantly outperform medoids based approaches, ii) on the considered experience, the two proposed algorithms outperform the state of the art DBA algorithm, and iii) the second proposed algorithm that implements an averaging jointly in the sample space and along the time axes emerges as the most significantly robust time elastic averaging heuristic with an interesting noise reduction capability. Index Terms-Time series averaging Time elastic kernel Dynamic Time Warping Time series clustering and classification

Fr-TM-align: a new protein structural alignment method based on fragment alignments and the TM-score

©2008 Pandit and Skolnick; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is available from: http://www.biomedcentral.com/1471-2105/9/531doi:10.1186/1471-2105-9-531Background: Protein tertiary structure comparisons are employed in various fields of contemporary structural biology. Most structure comparison methods involve generation of an initial seed alignment, which is extended and/or refined to provide the best structural superposition between a pair of protein structures as assessed by a structure comparison metric. One such metric, the TM-score, was recently introduced to provide a combined structure quality measure of the coordinate root mean square deviation between a pair of structures and coverage. Using the TM-score, the TM-align structure alignment algorithm was developed that was often found to have better accuracy and coverage than the most commonly used structural alignment programs; however, there were a number of situations when this was not true. Results: To further improve structure alignment quality, the Fr-TM-align algorithm has been developed where aligned fragment pairs are used to generate the initial seed alignments that are then refined using dynamic programming to maximize the TM-score. For the assessment of the structural alignment quality from Fr-TM-align in comparison to other programs such as CE and TMalign, we examined various alignment quality assessment scores such as PSI and TM-score. The assessment showed that the structural alignment quality from Fr-TM-align is better in comparison to both CE and TM-align. On average, the structural alignments generated using Fr-TM-align have a higher TM-score (~9%) and coverage (~7%) in comparison to those generated by TM-align. Fr- TM-align uses an exhaustive procedure to generate initial seed alignments. Hence, the algorithm is computationally more expensive than TM-align. Conclusion: Fr-TM-align, a new algorithm that employs fragment alignment and assembly provides better structural alignments in comparison to TM-align. The source code and executables of Fr- TM-align are freely downloadable at: http://cssb.biology.gatech.edu/skolnick/files/FrTMalign/

New Algorithms for Protein Structure Comparison and Protein Structure Prediction

Proteins show a great variety of 3D conformations, which can be used to infer their evolutionary relationship and to classify them into more general groups; therefore algorithms of protein structure alignment, protein similarity search and protein structure prediction are very helpful for protein biologists. We developed new algorithms for the problems in this field. The algorithms are tested with structures from the Protein Data Bank (PDB) and SCOP, a Structure Classification of Protein Database. The experimental results show that our tools are more efficient than some well known systems for finding similar protein structures and predicting protein structures