A Co-analysis Framework for Exploring Multivariate Scientific Data
Table 1: The computational time (seconds) of bicluster generation and the number of biclusters for three data sets.
['[ITALIC] δ', 'Isabel time', 'Isabel number', 'Combustion time', 'Combustion number', 'Asteroid time', 'Asteroid number']
Biclusters are generated in the preprocessing stage before the exploration process. The computational time ranges from less than 1 min to more than 1 h, and is roughly proportional to the number of biclusters, which depends on the number of variables and the complexity of the volume. The number of biclusters can be very large, especially for 10 variables such as the hurricane data. During visual exploration, users can filter small or large biclusters based on the number of voxels according to their analysis requirements, including the background feature. Because we assume that users have little prior knowledge about the data, biclusters in each combination of variables are extracted from the data. If users have prior knowledge, only variables of interest need to search for biclusters and this would greatly improve computational and analytical efficiency. In addition, the searching process can be accelerated by parallel computation because the expansion of each variable pair is independent. The biclustering method includes two parameters, the tolerance and the minimal number of voxels. The minimal number of voxels can be set to a very small number even zero to determine all biclusters. However, this would increase the computational time and generate many noisy and meaningless biclusters with only a few voxels. In our experiments, the minimal number of voxels is fixed to 0.2% of the total voxels of the explored volume, a relatively low value, to balance these factors. In this case, the resolution of multivariable data has little impact on the number of biclusters, although small biclusters may not be extracted when the resolution is low. The tolerance is related to the data range and meaning of the variables, and determines the maximum difference of scalar values to be considered as the same feature. In order to restrain the over-segmentation problem, the tolerance can be chosen from 10 to 30 depending on the application (20 by default in our experiments).