Nonnegative factorization of completely positive matrices
نویسندگان
چکیده
منابع مشابه
Separating doubly nonnegative and completely positive matrices
The cone of Completely Positive (CP) matrices can be used to exactly formulate a variety of NP-Hard optimization problems. A tractable relaxation for CP matrices is provided by the cone of Doubly Nonnegative (DNN) matrices; that is, matrices that are both positive semidefinite and componentwise nonnegative. A natural problem in the optimization setting is then to separate a given DNN but non-CP...
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Let M = [ttUiSi /_i be completely nonnegative (CNN), i.e., every minor of Mis nonnegative. Two methods for reducing the eigenvalue problem for M to that of a CNN, tridiagonal matrix, T = [?,-,] (r,-,= 0 when |i — j\ > 1), are presented in this paper. In the particular case that M is nonsingular it is shown for one of the methods that there exists a CNN nonsingular 5 such that SM = TS.
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It is shown that a sufficient condition for a nonnegative real symmetric matrix to be completely positive is that the matrix is diagonally dominant.
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Using a bordering approach, and building upon an already known factorization of a principal block, we establish sufficient conditions under which we can extend this factorization to the full matrix. Simulations show that the approach is promising also in higher dimensions.
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Let V ∈ R be a nonnegative matrix. The nonnegative matrix factorization (NNMF) problem consists of finding nonnegative matrix factors W ∈ R and H ∈ R such that V ≈ WH. Lee and Seung proposed two algorithms which find nonnegative W and H such that ‖V −WH‖F is minimized. After examining the case in which r = 1 about which a complete characterization of the solution is possible, we consider the ca...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1983
ISSN: 0024-3795
DOI: 10.1016/0024-3795(83)90162-3