We start from a few examples of coupled behavioral sciences data, along with associated research questions and data-analytic methods. Linking up with these, we introduce a few concepts and distinctions, by means of which we specify the focus of this paper: 1) data that take the form of a collection of coupled matrices that are linked in either the experimental unit or the variable data mode; 2) associated with questions about the mechanisms underlying these data matrices; 3) which are to be addressed by data-analytic methods that rely on a submodel per data matrix, with a common parameterization of the shared data mode. Next, we outline the principles of two closely related families within this focus: the families of multiblock component- and factor-based models for data fusion (while considering both deterministic and stochastic model variants). Then, we review developments within these families to capture both similarities and differences between the different data matrices under study. We follow with a discussion on recent attempts to address quite a few challenges in data fusion based on multiblock component and factor models, including whether and how to differentially weigh the different data matrices under study, and problems such as dealing with large numbers of variables, outliers, and missing values. While the focus of this paper is on data and modeling contributions from the behavioral sciences, we point in a concluding section at their relevance for other domains and at the importance of related methods developed in those domains.

BACKGROUND: High throughput data are complex and methods that reveal structure underlying the data are most useful. Principal component analysis, frequently implemented as a singular value decomposition, is a popular technique in this respect. Nowadays often the challenge is to reveal structure in several sources of information (e.g., transcriptomics, proteomics) that are available for the same biological entities under study. Simultaneous component methods are most promising in this respect. However, the interpretation of the principal and simultaneous components is often daunting because contributions of each of the biomolecules (transcripts, proteins) have to be taken into account. RESULTS: We propose a sparse simultaneous component method that makes many of the parameters redundant by shrinking them to zero. It includes principal component analysis, sparse principal component analysis, and ordinary simultaneous component analysis as special cases. Several penalties can be tuned that account in different ways for the block structure present in the integrated data. This yields known sparse approaches as the lasso, the ridge penalty, the elastic net, the group lasso, sparse group lasso, and elitist lasso. In addition, the algorithmic results can be easily transposed to the context of regression. Metabolomics data obtained with two measurement platforms for the same set of Escherichia coli samples are used to illustrate the proposed methodology and the properties of different penalties with respect to sparseness across and within data blocks. CONCLUSION: Sparse simultaneous component analysis is a useful method for data integration: First, simultaneous analyses of multiple blocks offer advantages over sequential and separate analyses and second, interpretation of the results is highly facilitated by their sparseness. The approach offered is flexible and allows to take the block structure in different ways into account. As such, structures can be found that are exclusively tied to one data platform (group lasso approach) as well as structures that involve all data platforms (Elitist lasso approach). AVAILABILITY: The additional file contains a MATLAB implementation of the sparse simultaneous component method.

MOTIVATION: Finding genes that are preferentially expressed in a particular tissue or condition is a problem that cannot be solved by standard statistical testing procedures. A relatively unknown procedure that can be used is the intersection-union test (IUT). However, two disadvantages of the IUT are that it is conservative and it conveys only the information of the least differing target tissue-other tissue pair. RESULTS: We propose a Bayesian procedure that quantifies how much evidence there is in the overall expression profile for selective over-expression. In a small simulation study, it is shown that the proposed method outperforms the IUT when it comes to finding selectively expressed genes. An application to publicly available data consisting of 22 tissues shows that the Bayesian method indeed selects genes with functions that reflect the specific tissue functions. The proposed method can also be used to find genes that are underexpressed in a particular tissue. AVAILABILITY: Both MATLAB and R code that implement the IUT and the Bayesian procedure in an efficient way, can be downloaded at http://ppw.kuleuven.be/okp/software/BayesianIUT/.

BACKGROUND: In contemporary biology, complex biological processes are increasingly studied by collecting and analyzing measurements of the same entities that are collected with different analytical platforms. Such data comprise a number of data blocks that are coupled via a common mode. The goal of collecting this type of data is to discover biological mechanisms that underlie the behavior of the variables in the different data blocks. The simultaneous component analysis (SCA) family of data analysis methods is suited for this task. However, a SCA may be hampered by the data blocks being subjected to different amounts of measurement error, or noise. To unveil the true mechanisms underlying the data, it could be fruitful to take noise heterogeneity into consideration in the data analysis. Maximum likelihood based SCA (MxLSCA-P) was developed for this purpose. In a previous simulation study it outperformed normal SCA-P. This previous study, however, did not mimic in many respects typical functional genomics data sets, such as, data blocks coupled via the experimental mode, more variables than experimental units, and medium to high correlations between variables. Here, we present a new simulation study in which the usefulness of MxLSCA-P compared to ordinary SCA-P is evaluated within a typical functional genomics setting. Subsequently, the performance of the two methods is evaluated by analysis of a real life Escherichia coli metabolomics data set. RESULTS: In the simulation study, MxLSCA-P outperforms SCA-P in terms of recovery of the true underlying scores of the common mode and of the true values underlying the data entries. MxLSCA-P further performed especially better when the simulated data blocks were subject to different noise levels. In the analysis of an E. coli metabolomics data set, MxLSCA-P provided a slightly better and more consistent interpretation. CONCLUSION: MxLSCA-P is a promising addition to the SCA family. The analysis of coupled functional genomics data blocks could benefit from its ability to take different noise levels per data block into consideration and improve the recovery of the true patterns underlying the data. Moreover, the maximum likelihood based approach underlying MxLSCA-P could be extended to custom-made solutions to specific problems encountered.

BACKGROUND: Data integration is currently one of the main challenges in the biomedical sciences. Often different pieces of information are gathered on the same set of entities (e.g., tissues, culture samples, biomolecules) with the different pieces stemming, for example, from different measurement techniques. This implies that more and more data appear that consist of two or more data arrays that have a shared mode. An integrative analysis of such coupled data should be based on a simultaneous analysis of all data arrays. In this respect, the family of simultaneous component methods (e.g., SUM-PCA, unrestricted PCovR, MFA, STATIS, and SCA-P) is a natural choice. Yet, different simultaneous component methods may lead to quite different results. RESULTS: We offer a structured overview of simultaneous component methods that frames them in a principal components setting such that both the common core of the methods and the specific elements with regard to which they differ are highlighted. An overview of principles is given that may guide the data analyst in choosing an appropriate simultaneous component method. Several theoretical and practical issues are illustrated with an empirical example on metabolomics data for Escherichia coli as obtained with different analytical chemical measurement methods. CONCLUSION: Of the aspects in which the simultaneous component methods differ, pre-processing and weighting are consequential. Especially, the type of weighting of the different matrices is essential for simultaneous component analysis. These types are shown to be linked to different specifications of the idea of a fair integration of the different coupled arrays.

BACKGROUND: Microarray compendia profile the expression of genes in a number of experimental conditions. Such data compendia are useful not only to group genes and conditions based on their similarity in overall expression over profiles but also to gain information on more subtle relations between genes and conditions. Getting a clear visual overview of all these patterns in a single easy-to-grasp representation is a useful preliminary analysis step: We propose to use for this purpose an advanced exploratory method, called multidimensional unfolding. RESULTS: We present a novel algorithm for multidimensional unfolding that overcomes both general problems and problems that are specific for the analysis of gene expression data sets. Applying the algorithm to two publicly available microarray compendia illustrates its power as a tool for exploratory data analysis: The unfolding analysis of a first data set resulted in a two-dimensional representation which clearly reveals temporal regulation patterns for the genes and a meaningful structure for the time points, while the analysis of a second data set showed the algorithm's ability to go beyond a mere identification of those genes that discriminate between different patient or tissue types. CONCLUSION: Multidimensional unfolding offers a useful tool for preliminary explorations of microarray data: By relying on an easy-to-grasp low-dimensional geometric framework, relations among genes, among conditions and between genes and conditions are simultaneously represented in an accessible way which may reveal interesting patterns in the data. An additional advantage of the method is that it can be applied to the raw data without necessitating the choice of suitable genewise transformations of the data.