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In systems biology, it is common to measure biochemical entities at different levels of the same biological system. One of the central problems for the data fusion of such data sets is the heterogeneity of the data. This thesis discusses two types of heterogeneity. The first one is the type of data, such as metabolomics, proteomics and RNAseq data in genomics. These different omics data reflect the properties of the studied biological system from different perspectives. The second one is the type of scale, which indicates the measurements obtained at different scales, such as binary, ordinal, interval and ratio-scaled variables. In this thesis, we developed several statistical methods capable to fuse data sets of these two types of heterogeneity. The advantages of the proposed methods in comparison with other approaches are assessed using comprehensive simulations as well as the analysis of real biological data sets., Comment: PhD thesis, 173 pages, 60 figures

In systems biology, it is becoming increasingly common to measure biochemical entities at different levels of the same biological system. Hence, data fusion problems are abundant in the life sciences. With the availability of a multitude of measuring techniques, one of the central problems is the heterogeneity of the data. In this paper, we discuss a specific form of heterogeneity, namely that of measurements obtained at different measurement scales, such as binary, ordinal, interval and ratio-scaled variables. Three generic fusion approaches are presented of which two are new to the systems biology community. The methods are presented, put in context and illustrated with a real-life genomics example.

Multivariate binary data is becoming abundant in current biological research. Logistic principal component analysis (PCA) is one of the commonly used tools to explore the relationships inside a multivariate binary data set by exploiting the underlying low rank structure. We re-expressed the logistic PCA model based on the latent variable interpretation of the generalized linear model on binary data. The multivariate binary data set is assumed to be the sign observation of an unobserved quantitative data set, on which a low rank structure is assumed to exist. However, the standard logistic PCA model (using exact low rank constraint) is prone to overfitting, which could lead to divergence of some estimated parameters towards infinity. We propose to fit a logistic PCA model through non-convex singular value thresholding to alleviate the overfitting issue. An efficient Majorization-Minimization algorithm is implemented to fit the model and a missing value based cross validation (CV) procedure is introduced for the model selection. Our experiments on realistic simulations of imbalanced binary data and low signal to noise ratio show that the CV error based model selection procedure is successful in selecting the proposed model. Furthermore, the selected model demonstrates superior performance in recovering the underlying low rank structure compared to models with convex nuclear norm penalty and exact low rank constraint. A binary copy number aberration data set is used to illustrate the proposed methodology in practice., Comment: 19 pages, 14 figures

Multiple sets of measurements on the same objects obtained from different platforms may reflect partially complementary information of the studied system. The integrative analysis of such data sets not only provides us with the opportunity of a deeper understanding of the studied system, but also introduces some new statistical challenges. First, the separation of information that is common across all or some of the data sets, and the information that is specific to each data set is problematic. Furthermore, these data sets are often a mix of quantitative and discrete (binary or categorical) data types, while commonly used data fusion methods require all data sets to be quantitative. In this paper, we propose an exponential family simultaneous component analysis (ESCA) model to tackle the potential mixed data types problem of multiple data sets. In addition, a structured sparse pattern of the loading matrix is induced through a nearly unbiased group concave penalty to disentangle the global, local common and distinct information of the multiple data sets. A Majorization-Minimization based algorithm is derived to fit the proposed model. Analytic solutions are derived for updating all the parameters of the model in each iteration, and the algorithm will decrease the objective function in each iteration monotonically. For model selection, a missing value based cross validation procedure is implemented. The advantages of the proposed method in comparison with other approaches are assessed using comprehensive simulations as well as the analysis of real data from a chronic lymphocytic leukaemia (CLL) study. Availability: the codes to reproduce the results in this article are available at https://gitlab.com/uvabda., Comment: 32 pages, 14 figures

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. One standard tool of exploring the underlying dependence structure present in multiple quantitative data sets is simultaneous component analysis (SCA) model. However, it does not have any provisions when a part of the data are binary. To this end, we propose the generalized SCA (GSCA) model, which takes into account the distinct mathematical properties of binary and quantitative measurements in the maximum likelihood framework. Like in the SCA model, a common low dimensional subspace is assumed to represent the shared information between these two distinct types of measurements. However, the GSCA model can easily be overfitted when a rank larger than one is used, leading to some of the estimated parameters to become very large. To achieve a low rank solution and combat overfitting, we propose to use a concave variant of the nuclear norm penalty. 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 recovering the underlying structure. Also, a missing value based cross validation procedure is implemented for model selection. We illustrate the usefulness of the GSCA model for exploratory data analysis of quantitative gene expression and binary copy number aberration (CNA) measurements obtained from the GDSC1000 data sets., Comment: 19 pages, 10 figures