Computing symmetric nonnegative rank factorizations
نویسندگان
چکیده
منابع مشابه
Computing Symmetric Nonnegative Rank Factorizations
An algorithm is described for the nonnegative rank factorization (NRF) of some completely positive (CP) matrices whose rank is equal to their CP-rank. The algorithm can compute the symmetric NRF of any nonnegative symmetric rank-r matrix that contains a diagonal principal submatrix of that rank and size with leading cost O(rm) operations in the dense case. The algorithm is based on geometric co...
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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...
متن کاملAppendix for ``On Mixed Memberships and Symmetric Nonnegative Matrix Factorizations''
1. If a communication class has at least two nodes and is aperiodic, then the rows corresponding to those nodes in T∞ are the stationary distribution for that class. Hence, T∞ has identical rows, so it cannot be full rank. 2. The probability of a Markov chain ending in a transient node goes to zero as the number of iterations k grows, so the column of T∞ corresponding to any transient node is i...
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The problem of finding overlapping communities in networks has gained much attention recently. Optimization-based approaches use nonnegative matrix factorization (NMF) or variants, but the global optimum cannot be provably attained in general. Model-based approaches, such as the popular mixed membership stochastic blockmodel or MMSB (Airoldi et al., 2008), use parameters for each node to specif...
متن کاملComputing symmetric rank for symmetric tensors
We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algebraic geometry approach. We give algorithms for computing the symmetric rank for 2 × · · · × 2 tensors and for tensors of small border rank. From a geometric point of view, we describe the symmetric rank strata for some secant varieties of Veronese varieties.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.03.016