Weighted Low-Rank Approximation of General Complex Matrices and Its Application in the Design of 2-D Digital Filters

By Wu-Sheng Lu, Soo-Chang Pei, Paul S. Wang. 1997

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Recovery guarantee of weighted low-rank approximation via alternating minimization (2016, background): “Being a common practical problem (e.g., [Lu et al., 1997, Srebro and Jaakkola, 2003, Li et al., 2010, Eriksson and van den Hengel, 2012]), multiple heuristics for non-convexoptimization such as alternating minimization have been developed, but they come with no guarantees.”
Weighted Low-Rank Approximations (2003, methodology): “Shpak (1990) and Lu et al. (1997) studied weighted-norm low-rank approximations for the design of two-dimensional digital filters where the weights arise from constraints of varying importance .”
Weighted low rank approximations with provable guarantees (2016, unknown): “[40, 39] looked at alternating minimization methods.”
Low-Rank Matrix Approximation with Weights or Missing Data Is NP-Hard (2010, unknown): “D digital ﬁlter design [19] and microarray data analysis [20].”
Correcting systematic effects in a large set of photometric light curves (2005, methodology): “Very similar algorithms were developed and applied for signal and image processing (e.g., Lu et al. 1997).”
Optimization algorithms exploiting unitary constraints (2002, background): “The weighted low-rank approximation problem [12] is to find a matrix having a prespecified rank and that best approximates a given matrix under a weighted norm.”