S-semigoodness for Low-Rank Semidefinite Matrix Recovery
نویسندگان
چکیده
We extend and characterize the concept of s-semigoodness for a sensing matrix in sparse nonnegative recovery (proposed by Juditsky , Karzan and Nemirovski [Math Program, 2011]) to the linear transformations in low-rank semidefinite matrix recovery. We show that ssemigoodness is not only a necessary and sufficient condition for exact s-rank semidefinite matrix recovery by a semidefinite program, but also provides a stable recovery under some conditions. We also show that both s-semigoodness and semiNSP are equivalent.
منابع مشابه
Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix
The positive semidefinite rank of a nonnegative (m×n)-matrix S is the minimum number q such that there exist positive semidefinite (q × q)-matrices A1, . . . , Am, B1, . . . , Bn such that S(k, l) = trA∗kBl. The most important lower bound technique on nonnegative rank only uses the zero/nonzero pattern of the matrix. We characterize the power of lower bounds on positive semidefinite rank based ...
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