  Modern data collection in many data paradigms, including bioinformatics,
often incorporates multiple traits derived from different data types (i.e.
platforms). We call this data multi-block, multi-view, or multi-omics data. The
emergent field of data integration develops and applies new methods for
studying multi-block data and identifying how different data types relate and
differ. One major frontier in contemporary data integration research is
methodology that can identify partially-shared structure between
sub-collections of data types. This work presents a new approach: Data
Integration Via Analysis of Subspaces (DIVAS). DIVAS combines new insights in
angular subspace perturbation theory with recent developments in matrix signal
processing and convex-concave optimization into one algorithm for exploring
partially-shared structure. Based on principal angles between subspaces, DIVAS
provides built-in inference on the results of the analysis, and is effective
even in high-dimension-low-sample-size (HDLSS) situations.
