4.1 Synthetic data
We created synthetic datasets with different numbers of rows and columns. For each dataset, we generated biclusters by sampling subsets of rows and columns. For this experiment, we randomly generated the number of rows and columns and identifiers for the rows and columns; we did not need to generate values for the cells of the matrices. For each set of biclusters, we recorded the time required to run our layout algorithm and the number of rows and columns in the computed layout. For each layout, we estimated the efficiency of the layout as the ratio of the size of the layout to the size of the dataset. Lower values of efficiency are better than higher values, since they indicate that the algorithm is able to exploit overlaps between biclusters. For each choice of number of rows in the dataset, number of columns in the dataset, and number of biclusters, we averaged the results for 100 runs. Tables 1 and 2 display our results. Efficiency values may be less than one, e.g., when some rows or columns in the dataset do not belong to any bicluster.
Table 1  Execution times (in seconds) for the layout algorithm on synthetic matrices
#biclusters  #rows + #columns in the dataset
10  30  50  70  90
20  0.168  0.328  0.462  0.52  0.532
40  1.23  2.514  3.046  3.574  4.008
60  4.074  7.992  11.238  11.71  12.81
80  9.484  19.586  25.546  29.652  29.446
100  17.982  37.966  48.418  50.916  56.112
Table 2  Efficiency values for the layout algorithm on synthetic matrices.
# biclusters  #rows + #columns in the dataset
10  30  50  70  90
20  0.184  0.842  1.316  1.254  1.428
40  0.304  1.16  1.632  2.04  2.074
60  0.398  1.496  2.262  2.26  2.508
80  0.512  1.65  2.358  2.726  2.698
100  0.48  1.808  2.582  2.686  2.996