1 / 23

Better Filtering with Gapped q -grams

Better Filtering with Gapped q -grams. S. Burkhardt. J. Kärkkäinen. Center for Bioinformatics, Saarbrücken Max-Planck Institut f. Informatik, Saarbrücken. Outline. Motivation The `classic` q -gram Lemma q -shapes Measuring Filter quality/speed Experimental Results Conclusion.

alfreda-burt
Download Presentation

Better Filtering with Gapped q -grams

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Better Filtering withGapped q-grams S. Burkhardt J. Kärkkäinen Center for Bioinformatics, Saarbrücken Max-Planck Institut f. Informatik, Saarbrücken

  2. Outline • Motivation • The `classic` q-gram Lemma • q-shapes • Measuring Filter quality/speed • Experimental Results • Conclusion

  3. The Problem The k-mismatches problem For a pattern P, a string S, a value k : find all occurences of P in S with at most k character replacements.

  4. A common Approach Filter Algorithms Filtration Stage: Examine S with a Filter Criterium Return areas with potential matches Verification Stage: Verify which areas have true matches

  5. Problem Definition String S G C A T T C G A T G G A C T G G A C T A G T G A T T G A G T Pattern P A C T C k = 1 • Find occurences of P with at most k errors

  6. q-gram Lemma The q-gram Lemma For a pattern P, a string S, a value k: Matches to P in S with at most k errors contain at least |P|-q+1-(kq) substrings of length q (q-grams) from S.

  7. q-gram Lemma T C G C G A G A T A T T T T A T A C T C G A T T A C T C G A T T A C q = 3 # of q-grams : |P| - q + 1 k = 1 |P| = 8 => t = 8-3+1-1 = 5 G C A T T C G A T G G A C T G G AC T A G T G A A TC A G T Error number k : at least t = |P| - q + 1 - (qk) common q-grams in |P| letters

  8. Some Definitions In the DP matrix, one can count the number of matching q-grams per diagonal

  9. q-shapes General idea: • Use substrings with gaps (q-shapes) • compute correct threshold t • total length s is called span |Q| = 11 k = 3 3-shape ##.# s = 4 1 gap t = 1 OOXOOXOOXOO OOX OXO XOO OOX OXO XOO OOX OXO XOO 3-gram ### t = 0 no filter! OOOXXOOXOOO OO.X OO.X OX.O XX.O XO.X OO.O OX.O XO.O O = match, X = mismatch

  10. q-shapes Judging the quality of q-shapes I We developed a DP based approach for computing the threshold t given a q-shape and a query length |P| Observation: The threshold t is not the only factor that influences the behaviour of a q-shape

  11. q-shapes Judging the quality of q-shapes II We define the minimum coverage as the minimum number of matching characters for any arrangement of t matching q-shapes in P and a substring of length |P| in S ##.# ##.# ----- For t=2 and the 3-shape ##.# the minimum coverage is 5

  12. q-shapes Judging the quality of q-shapes III The value q (i.e.the number of matching characters in a shape) determines the expected number of occurences in a random string S 3-shape: ##.# S = {A,C,G,T} Expected number of occurences of a single 3-shape in S: occ = |S| 1 |S|q

  13. q-shapes Judging the quality of q-shapes IV The speed of the filter step is influenced by the expected number of matching q-shapes in S. The efficiency of the filtration correlates closely with the minimum coverage Speed: value of q Efficiency: minimum coverage

  14. q-shapes Judging the quality of q-shapes V Shapes with maximal minimum coverage for: |Q| = 50, k=5 q=6 : ##......#..#..#.# q=9 : ###..#..#.#...#.## q=10: ###..#..#.#..###.# q=11: #######.##.## q=12: ###.#..###.#..###.# Good shapes are not neccessarily regular or predictable in their form.

  15. The Search Space

  16. The Search Space

  17. Experiments Evaluating q-shapes • Experimental setup for q-shapes: • 50 million character random (Bernoulli) string S • 1000 random queries of length 500 • queries have no approximate matches in S • compute threshold for |Q|=50 • actual value of |Q| is 500! (to reduce runtime of tests) • Experiments show 10x reduced filter efficiency; relative performance between shapes unaffected

  18. Experiments Evaluating q-shapes What we measured for every shape and all queries: A) The total number of occurrences of all shapes Good indicator of the total work for the filter phase B) The number of diagonals containing at least t shapes Good indicator of the filter efficiency The experiments show a good correlation between A and the predicted values as well as B and the minimum coverage

  19. Experiments

  20. Experiments

  21. Experiments

  22. Conclusion Our work…. • An analysis of q-grams with gaps (q-shapes) • Results include: • experimental evidence for their superiority • when compared to standard q-grams • a method to roughly judge their quality, the • minimum coverage • a way to calculate the parameters required to • us them in a filter algorithm

  23. Conclusion Todo…. • an algorithm to predict the best shapes • improve the quality measure for q-grams • extension to the k-differences problem (with • insertions and deletions) • a thorough analysis of filter behaviour for • > k differences (use as a heuristic filter)

More Related