High dimensional data consists of matrices with a large number of features and is common across many fields of study, including genetics, imaging, and toxicology. This type of data is challenging to analyze because of its size, and many traditional methods are difficult to implement or interpret with such data. One way of handling high dimensional data is dimension reduction, which aims to reduce high rank, high-dimensional data sets into low-rank approximations, which maintain important components of the structures of the matrices but are easier to use in models. The most common method for dimension reduction of a single matrix is principal components analysis (PCA). Multi-source data are high dimensional data in which multiple data sources share a dimension. When two or more data sets share a feature set, this is called horizontal integration. When two or more data sets share a sample set, this is called vertical integration. Traditionally, there are two ways to approach such a data set: either analyze each data source separately or treat them as one data set. However, these analyses may miss important features that are unique to each data source or miss important relationships between the data sources. A number of recent methods have been developed for analyzing multi-source data that are either vertically or horizontally integrated. One such method is Joint and Individual Variation Explained (JIVE), which decomposes the variation in multi-source data sets into structure that is shared between data sources (called joint structure) and structure that is unique to each of the data sources (called individual structure) (Lock et al. 2013). We have created an R package, r.jive, that implements the JIVE algorithm and provides visualization tools for multi-source data, making multi-source methods more accessible. While there are several methods for data sets with horizontal or vertical integration, there have been no previous methods for data sets with simultaneous horizontal and vertical integration (which we call bidimensional integration). We introduce a method called Linked Matrix Factorization that allows for simultaneous decomposition of multi-source data sets with bidimensional integration. We also introduce a method for bidimensionally integrated data that are not normally distributed, called Generalized Linked Matrix Factorization, which is based on generalized linear models rather than ordinary least squares.
University of Minnesota Ph.D. dissertation. July 2018. Major: Biostatistics. Advisor: Eric Lock. 1 computer file (PDF); viii, 86 pages.
Integrative Analyses for Multi-source Data with Multiple Shared Dimensions.
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