Generalized Simultaneous Component Analysis of Binary and Quantitative data
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In the current era of systems biological research there is a need for the integrative analysis of binary and quantitative genomics data sets measured on the same objects. We generalize the simultaneous component analysis (SCA) model, a canonical tool for the integrative analysis of multiple quantitative data sets, from the probabilistic perspective to explore the underlying dependence structure present in both these distinct measurements. Similar as in the SCA model, a common low dimensional subspace is assumed to represent the shared information between these two distinct measurements. However, the generalized SCA model can easily be overfit by using exact low rank constraint, leading to very large estimated parameters. We propose to use concave penalties in the low rank matrix approximation framework to mitigate this problem of overfitting and to achieve a low rank constraint simultaneously. An efficient majorization algorithm is developed to fit this model with different concave penalties. Realistic simulations (low signal to noise ratio and highly imbalanced binary data) are used to evaluate the performance of the proposed model in exactly recovering the underlying structure. Also, a missing value based cross validation procedure is implemented for model selection. In addition, exploratory data analysis of the quantitative gene expression and binary copy number aberrations (CNA) measurement obtained from the same 160 cell lines of the GDSC1000 data sets successfully show the utility of the proposed method.
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