Theory of Spectral Method for Union of Subspaces-Based Random Geometry Graph

Union of Subspaces (UoS) model serves as an important model i n statistical machine learning. Briefly speaking, UoS models those high-dimensional da ta, encountered in many real-world problems, which lie close to low-dimensional subspaces corresponding to several classes to which the data belong, such as handwritten digits (Hasti e and Simard, 1998), face images (Basri and Jacobs, 2003), DNA microarray data (Parvare sh et al., 2008), and hyper-spectral images (Chen et al., 2011), to name just a few. A fund amental task in processing data points in UoS is to cluster these data points, which is kn own as Subspace Clustering (SC). Applications of SC has spanned all over science and eng ineering, including motion segmentation (Costeira and Kanade, 1998; Kanatani, 2001), face recognition (Wright et al., 2008), and classification of diseases (McWilliams and Monta na, 2014) and so on. We refer the reader to the tutorial paper (Vidal, 2011) for a review of the development of SC. The authors are with Department of Electronic Engineering, Tsinghua University, Beijing 100084, China. The corresponding author of this paper is Y. Gu (gyt@tsinghu a.edu.cn).