Analysis of coupled data

In many fields of research problems often result in the collection of coupled data, which consist of different N-way N-mode data blocks that have one or more modes in common. To reveal the structure underlying such data an integrated modeling strategy, with a single set of parameters for the common mode(s), that is estimated based on the information in all data blocks, may be most appropriate. Such a strategy implies a global model, consisting of different N-way N-mode submodels, and a global loss function that is a (weighted) sum of the partial loss functions associated with the different submodels. In this dissertation a global model for an integrated analysis of a three-way three-mode binary data array and a two-way two-mode binary data matrix that have one mode in common is developed. Further, three questions concerning the analysis of coupled data are tackled. The first question deals with coupled data sets that consist of several data blocks that differ (considerably) in size, while the second question focuses on coupled data sets for which the different data blocks may be subject to different amounts of noise. To tackle these problems in the analysis weights could be applied to the different data blocks, with each weight indicating the importance of the corresponding data block in the analysis. The challenge then is to find optimal weights with respect to uncovering the underlying structure of the common mode(s). The third question deals with the problem of redundant or masking information in the coupled data set that may obfuscate its underlying structure. Procedures for variable selection are developed that try to remove this information from the analysis.status: publishe