Biclustering Models Under Collinearity in Simulated Biological Experiments

Biclustering models allow simultaneous detection of group observations that are related to variables in a data matrix. Such methods have been applied in biological data for classification. Collinearity is a common feature in biological data as there exist interactions between genes and proteins in their respective pathways. Such relationships could seriously reduce the efficiency of biclustering models. In this study, synthetic data are generated to investigate the effect of collinearity on the performance of biclustering models. Specifically, the data are generated and induced with varying degrees of collinearity using Cholesky decomposition, and are implanted with biclusters to produce different sets of synthetic data. The effectiveness of three models namely Biclustering by Cheng and Church (BCCC), Spectral Bicluster (BCSpectral) and Plaid Model in correctly detecting three types of biclusters in the generated data matrix were compared. The results show that all the models investigated are sensitive to changes in the level of collinearity. At low collinearity, all biclustering models were able to detect the implanted biclusters in the data correctly. As the level of collinearity in the data rise, the proportion of detected biclusters captured by the models reduces. In particular, BCC outperformed the other two models for moderate to high collinearity with a Jaccard coefficient of 0.499 to 0.875 and 0.746 to 0.936 for one and two implanted biclusters respectively.