Improved Deterministic Conditions for Sparse and Low-Rank Matrix Decomposition
نویسندگان
چکیده
In this paper, the problem of splitting a given matrix into sparse and low-rank matrices is investigated. The problem is when and how we can exactly do this decomposition. This problem is ill-posed in general and we need to impose some (sufficient) conditions to be able to decompose a matrix into sparse and low-rank matrices. This conditions can be categorized into two general classes: (a) deterministic conditions and (b) probabilistic conditions. Deterministic conditions guarantee the success of decomposition for a given fixed matrix. In contrast, proabilistic conditions guarantee the success of the decomposition with certain probability for a certain class of random matrices. We improved the best existing result for deterministic conditions in this paper by introducing alternative projection method for dual matrix construction.
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