Exhaustive Signature Algorithm

1. Exhaustive Signature Algorithm Guy Harari

2. Outline • ISA biclustering algorithm • Bimax biclustering algorithm • Exhaustive Signature Algorithm • Results and future work

3. ISA algorithm • Was developed by Sven Bergmann in 2003. • Goal: find genes/conditions having correlated expression. • Frequently used, compared and improved. • Good results in real data.

4. ISA - details • Input – expression matrix , initial gene set. • Compute by normalizing each column. • For each condition • z-test avg. normalized expression in gene subset against avg. expression in condition. • If above a threshold, select the condition. • Do the same for resulting condition set. • Repeat until convergence of gene set.

5. ISA - drawbacks • Initial gene set should be given. • Few biclusters for specific parameter value. • Parameter values are hard to optimize. • Expression values aren’t normally distributed. • Genes might not be independent.

6. Exhaustive approach • Use Bimax algorithm to find seeds. • For each seed apply ISA with random parameters. • Drop similar seeds while running. • Drop similar biclusters from ISA. • Observation: applying the algorithm separately for positive and negative values improves results.

7. Bimax algorithm • Input – expression matrix • Binarize matrix (1 value for b% highest and lowest values). • Goal – find all submatrices which: • Contain only 1’s. • Are inclusion-maximal. • Method: • Drop areas in matrix with 0’s only. • Recursively apply Bimax on other areas.

8. Bimax - illustration

9. Bimax - illustration

10. Bimax - illustration

11. Bimax - illustration

12. Bimax - illustration

13. Bimax - drawbacks • Information loss due to binarization. • Binarization parameter is hard to control. • Runtime depends linearly on no. of biclusters. • Usually returns millions of biclusters. • Poor results on real data.

14. Exhaustive Signature Algorithm • Apply Bimax on the input expression matrix. • Keep biclusters that: • Do not overlap with other biclusters. • Have low p-value w.r.t abicluster score. • Sort resulting biclusters by size. • Begin with the largest, apply ISA for each one. • Keep new biclusters that do not overlap with previous ones. • Stop if more than N biclusters found.

15. ESA – details • Overlaps – use Jaccard index, take the larger. • Score – average abs. Pearson correlation between gene pairs. • P-value: • Randomize input matrix using edge shuffling. • Apply ESA on randomized matrix. • Keep score distribution of all biclusters found. • P-value = right tail of score distribution of resulting biclusters.

16. ESA – details • Observation: anti-correlated genes usually do not pass enrichment tests simultaneously. • So apply ESA separately on positive and negative expression values. • Also change ISA: • For positive run, test: score>threshold • For negative run, test: –score>threshold

17. ESA - experiments • Apply the algorithms: SAMBA, Bimax, ISA,ESA and ESANP (negative and positive values separately). • Datasets: • Gasch 2001 (yeast heat shock) • Whitfield 2002 (human cell cycle) • Evaluation: GO, TF and KEGG enrichment tests

18. Results – Yeast, GO

19. Results – Yeast, TF

20. Results – Yeast, KEGG

21. Results – Human, GO

22. Results – Human, KEGG

23. Conclusions • ESA exploits both Bimax’s power and ISA’s accuracy. • ESA avoids ISA’s parameter selection. • ESA avoids ISA’s seed generation. • ESA reduces #biclusters from Bimax. • ESA shows good resultson real data.

24. Future work • Test the algorithm on other datasets. • Initiate binarization parameter automatically. • Evaluate results with other criteria. • Avoid bias towards large biclusters.