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Matrix resconstruction: Skeleton decomposition versus singular value decomposition

Koku, Ahmet Buğra
HAMM, Keaton
In this work, Skeleton Decomposition (SD) and Singular Value Decomposition (SVD) are compared and evaluated for reconstruction of data matrices whose columns come from a union of subspaces. Specifically, an original data matrix is reconstructed from noise-contaminated version of it. First, matrix reconstruction using SD iteratively is introduced and alternative methods for forming SD-based reconstruction are discussed. Then, through exhaustive simulations, effects of process parameters such as noise level, data size, number of subspaces and their dimensions are evaluated for reconstruction performance. It is also shown that SD-based reconstruction is more effective when data is drawn from a union of low dimensional subspaces compared to a single space of the same dimension.