Simulation Results

Intensive tests of the algorithm on simulated data were performed. The simulation process computes artifical gene fingerprints (hybridized oligos) for each participating gene. For each gene and a given probe, the precise locations along the gene are generated in a realistic manner. Then, truncated clones of each gene are generated. Each clone inherits the probe fingerprints and their locations from its original gene (just the fingerprints with locations within the clone boundaries are inherited). Finally, each copy is incorporated with false positive and false negative errors, again, realistically. If we denote the total number of oligos by p and the total number of clones by N, then the result of the simulation is an $N \times p$ hybridization matrix H, where H_ij=1 if clone i hybridized with oligo j, and H_ij=0 otherwise. The simulation results are summarized in figure 11.10. A comparison of the Minkowski scores is given in figure 11.11.

  

Figure 11.10: Examples of results of HCS and Greedy clustering algorithms in high noise simulation. The fingerprint data consisted of 780 cDNAs from 12 genes, in clusters of sizes 10,20,...,120. The number of oligos is 200. The expected rate of false positive hybridizations is 25%. The expected false negative hybridization rate is 40%. A: The hybridization fingerprints matrix H. Each of the 780 rows is a fingerprint vector of one cDNA. White denotes positive hybridization. B: The binarized similarity matrix. Position i,j is black iff S_ij>50. Matrix coordinates are scrambled, as in realistic scenarios. C: Clustering solution generated by the greedy algorithm. Minkowski score is 1.32. cDNAs from the same true cluster appear consecutively, and the black lines are the borders between the different clusters. Position i,j is black if the solution puts cDNAs i and j in the same cluster. D: Clustering solution generated by the HCS algorithm. Minkowski score is 0.209.

  

Figure 11.11: Performance comparison of HCS (squares) and Greedy (diamonds) algorithms on simulation data (using Minkowski score).