The rapid development and availability of cheap storage and sensing devices has quickly produced a deluge of high-dimensional data. While the dimensionality of modern datasets continues to grow, our saving grace is that these data often exhibit low-dimensional structure that can be exploited to compress, organize, and cluster massive collections of data.;Signal models such as linear subspace models, remain one of the most widely used models for high-dimensional data; however, in many settings of interest, finding a global model that can capture all the relevant structure in the data is not possible. Thus, an alternative to learning a global model is to instead learn a hybrid model or a union of low-dimensional subspaces that model different subsets of signals in the dataset as living on distinct subspaces.;This thesis develops new methods and theory for learning union of subspace models as well as exploiting multi-subspace structure in a wide range of signal processing and data analysis tasks. The main contributions of this thesis include new methods and theory for: (i) decomposing and subsampling datasets consisting of signals on unions of subspaces, (ii) subspace clustering for learning union of subspace models, and (iii) exploiting multi-subspace structure in order accelerate distributed computing and signal processing on massive collections of data. I demonstrate the utility of the proposed methods in a number of important imaging and computer vision applications including: illumination-invariant face recognition, segmentation of hyperspectral remote sensing data, and compression of video and lightfield data arising in 3D scene modeling and analysis.
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