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Matrix completion by deep matrix factorization
Neural Networks, 2018Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations.
Jicong Fan 0001, Jieyu Cheng
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Matrix Isomorphism of Matrix Lie Algebras
2012 IEEE 27th Conference on Computational Complexity, 2012We study the problem of matrix isomorphism of matrix Lie algebras (MatIsoLie). Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley -- Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices that is closed under linear combinations and the operation [
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From the matrix-geometric to the matrix-exponential
Queueing Systems, 1990The paper is concerned with the single server queues N/G/1 and GI/NI/1, respectively, in which the arrival process or the service process is a Neuts process, and derives the matrix-exponential forms of the solution of relevant nonlinear matrix equations for such queues. It generalises the matrix-exponential results of \textit{B. Sengupta} [Adv.
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Optical Implementation Of Matrix-Vector And Matrix-Matrix Multiplication
Journal of Optics, 1992From the viewpoint of information processing, the main advantage of an optical processor is its ability to operate in a highly parallel way. One of the most important applications of an optical processor, where its parallelism is efficiently used, is considered to be linear transformation because it involves many multiplications and additions in ...
M. Seth, K. Bhattacharya, A. Basuray
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Nonnegative matrix factorization with matrix exponentiation
2010 IEEE International Conference on Acoustics, Speech and Signal Processing, 2010Nonnegative matrix factorization (NMF) has been successfully applied to different domains as a technique able to find part-based linear representations for nonnegative data. However, when extra constraints are incorporated into NMF, simple gradient descent optimization can be inefficient for high-dimensional problems, due to the overhead to enforce the
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The anti-adjacency matrix of a graph: Eccentricity matrix
Discrete Applied Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianfeng Wang 0002 +3 more
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Adaptive sparse matrix-matrix multiplication on the GPU
Proceedings of the 24th Symposium on Principles and Practice of Parallel Programming, 2019In the ongoing efforts targeting the vectorization of linear algebra primitives, sparse matrix-matrix multiplication (SpGEMM) has received considerably less attention than sparse Matrix-Vector multiplication (SpMV). While both are equally important, this disparity can be attributed mainly to the additional formidable challenges raised by SpGEMM.
Martin Winter +4 more
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The derivative of the Riccati matrix with respect to a matrix
IEEE Transactions on Automatic Control, 1977The derivative of the solution of the Riccati matrix differential equation is described in this correspondence. Extensive use is made of the calculus of Vetter [8] and the formula for the derivative of the exponential matrix [5]. Additionally the differentiation of partitioned matrices and the differentiation with respect to a symmetric matrix are ...
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Practical criteria for positive-definite matrix, M-matrix and Hurwitz matrix
Applied Mathematics and Computation, 2007A new simple criterion is presented to verify if a matrix is positive definite, an \(M\)-matrix, or a Hurwitz matrix. It is based on the Gauss row elimination using inner and sign-preserving row operations. The computation of only one determinant is necessary.
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