The Complexity of Positive Semidefinite Matrix Factorization
نویسندگان
چکیده
منابع مشابه
The complexity of positive semidefinite matrix factorization
Let A be a matrix with nonnegative real entries. The PSD rank of A is the smallest integer k for which there exist k × k real PSD matrices B1, . . . , Bm, C1, . . . , Cn satisfying A(i|j) = tr(BiCj) for all i, j. This paper determines the computational complexity status of the PSD rank. Namely, we show that the problem of computing this function is polynomial-time equivalent to the existential ...
متن کاملAlgorithms for Positive Semidefinite Factorization
This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an m-by-n nonnegative matrix X and an integer k, the PSD factorization problem consists in finding, if possible, symmetric k-by-k positive semidefinite matrices {A, ..., A} and {B, ..., B} such that Xi,j = trace(AB) for i = 1, ...,m, and ...
متن کاملOn the complexity of nonnegative matrix factorization
Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases and other information retrieval and clustering applications. In this report, we define an exact version of NMF. Then we establish several results about exact NMF: (1) that it is equivalent to a problem in polyhedral combinatorics; (2) that it is NP-hard; and (3) that a pol...
متن کاملComplexity of the positive semidefinite matrix completion problem with a rank constraint
We consider the decision problem asking whether a partial rational symmetric matrix with an all-ones diagonal can be completed to a full positive semidefinite matrix of rank at most k. We show that this problem is NP -hard for any fixed integer k ≥ 2. Equivalently, for k ≥ 2, it is NP -hard to test membership in the rank constrained elliptope Ek(G), i.e., the set of all partial matrices with of...
متن کاملOn the Complexity of the Positive Semidefinite Zero Forcing Number
The positive zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring, and is related to a more conventional version of zero forcing. We establish a relation between the zero forcing and the fast-mixed searching, which implies some NP-completeness results for the zero forcing problem. For chordal graphs much is understood regarding the relat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2017
ISSN: 1052-6234,1095-7189
DOI: 10.1137/16m1080616