The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Qingjiang Chen - One of the best experts on this subject based on the ideXlab platform.
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The Presentation of a Class of Orthogonal Vector-Valued Multivariate Wavelet Packets Associated with an Integer-Valued Dilation Matrix
2009 International Conference on Environmental Science and Information Application Technology, 2009Co-Authors: Qingjiang Chen, Yongfeng PangAbstract:The notion of vector-valued multiresolution analysis of space of vector-valued higher-dimensional functions is introduced. An approach for constructing Orthogonal vector-valued higher-dimensional wavelet packets is presented and their properties are discussed by means of time-frequency analysis method, Matrix theory and functional analysis method. Three Orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal bases of L2(Rp,Cr) are obtained by constructing a series of subspaces of Orthogonal Matrix-valued wavelet packets.
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construction and properties of Orthogonal Matrix valued wavelets and wavelet packets
Chaos Solitons & Fractals, 2008Co-Authors: Qingjiang ChenAbstract:Abstract In this paper, we introduce Matrix-valued multiresolution analysis and Orthogonal Matrix-valued wavelets with arbitrary integer dilation factor m. A necessary and sufficient condition on the existence of Orthogonal Matrix-valued wavelets is derived by virtue of paraunitary vector filter bank theory. An algorithm for constructing compactly supported m-scale Orthogonal Matrix-valued wavelets is presented. The notion of Orthogonal Matrix-valued wavelet packets is proposed. Their properties are investigated by means of time–frequency method, operator theory and Matrix theory. In particular, it is shown how to construct various orthonormal bases of space L2(R, Cr×r) from these wavelet packets, and the Orthogonal decomposition relation is also given.
David F Gleich - One of the best experts on this subject based on the ideXlab platform.
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scalable methods for nonnegative Matrix factorizations of near separable tall and skinny matrices
Neural Information Processing Systems, 2014Co-Authors: Austin R Benson, Bartek Rajwa, David F GleichAbstract:Numerous algorithms are used for nonnegative Matrix factorization under the assumption that the Matrix is nearly separable. In this paper, we show how to make these algorithms scalable for data matrices that have many more rows than columns, so-called "tall-and-skinny matrices." One key component to these improved methods is an Orthogonal Matrix transformation that preserves the separability of the NMF problem. Our final methods need to read the data Matrix only once and are suitable for streaming, multi-core, and MapReduce architectures. We demonstrate the efficacy of these algorithms on terabyte-sized matrices from scientific computing and bioinformatics.
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scalable methods for nonnegative Matrix factorizations of near separable tall and skinny matrices
arXiv: Learning, 2014Co-Authors: Austin R Benson, Bartek Rajwa, David F GleichAbstract:Numerous algorithms are used for nonnegative Matrix factorization under the assumption that the Matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than columns, so-called "tall-and-skinny matrices". One key component to these improved methods is an Orthogonal Matrix transformation that preserves the separability of the NMF problem. Our final methods need a single pass over the data Matrix and are suitable for streaming, multi-core, and MapReduce architectures. We demonstrate the efficacy of these algorithms on terabyte-sized synthetic matrices and real-world matrices from scientific computing and bioinformatics.
Austin R Benson - One of the best experts on this subject based on the ideXlab platform.
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scalable methods for nonnegative Matrix factorizations of near separable tall and skinny matrices
Neural Information Processing Systems, 2014Co-Authors: Austin R Benson, Bartek Rajwa, David F GleichAbstract:Numerous algorithms are used for nonnegative Matrix factorization under the assumption that the Matrix is nearly separable. In this paper, we show how to make these algorithms scalable for data matrices that have many more rows than columns, so-called "tall-and-skinny matrices." One key component to these improved methods is an Orthogonal Matrix transformation that preserves the separability of the NMF problem. Our final methods need to read the data Matrix only once and are suitable for streaming, multi-core, and MapReduce architectures. We demonstrate the efficacy of these algorithms on terabyte-sized matrices from scientific computing and bioinformatics.
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scalable methods for nonnegative Matrix factorizations of near separable tall and skinny matrices
arXiv: Learning, 2014Co-Authors: Austin R Benson, Bartek Rajwa, David F GleichAbstract:Numerous algorithms are used for nonnegative Matrix factorization under the assumption that the Matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than columns, so-called "tall-and-skinny matrices". One key component to these improved methods is an Orthogonal Matrix transformation that preserves the separability of the NMF problem. Our final methods need a single pass over the data Matrix and are suitable for streaming, multi-core, and MapReduce architectures. We demonstrate the efficacy of these algorithms on terabyte-sized synthetic matrices and real-world matrices from scientific computing and bioinformatics.
Van Schagen F. - One of the best experts on this subject based on the ideXlab platform.
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The discrete twofold Ellis-Gohberg inverse problem
'Elsevier BV', 2018Co-Authors: Ter Horst S., Kaashoek M. A., Van Schagen F.Abstract:In this paper a twofold inverse problem for Orthogonal Matrix functions in the Wiener class is considered. The scalar-valued version of this problem was solved by Ellis and Gohberg in 1992. Under reasonable conditions, the problem is reduced to an invertibility condition on an operator that is defined using the Hankel and Toeplitz operators associated to the Wiener class functions that comprise the data set of the inverse problem. It is also shown that in this case the solution is unique. Special attention is given to the case that the Hankel operator of the solution is a strict contraction and the case where the functions are Matrix polynomials.Comment: 15 page
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The discrete twofold Ellis-Gohberg inverse problem
2017Co-Authors: Ter Horst S., Van Schagen F.Abstract:In this paper a twofold inverse problem for Orthogonal Matrix functions in the Wiener class is considered. The scalar-valued version of this problem was solved by Ellis and Gohberg in 1992. Under reasonable conditions, the problem is reduced to an invertibility condition on an operator that is defined using the Hankel and Toeplitz operators associated to the Wiener class functions that comprise the data set of the inverse problem. It is also shown that in this case the solution is unique. Special attention is given to the case that the Hankel operator of the solution is a strict contraction and the case where the functions are Matrix polynomials
Benoit Collins - One of the best experts on this subject based on the ideXlab platform.
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asymptotics of unitary and Orthogonal Matrix integrals
Advances in Mathematics, 2009Co-Authors: Benoit Collins, Alice Guionnet, Edouard MaurelsegalaAbstract:Abstract In this paper, we prove that in small parameter regions, arbitrary unitary Matrix integrals converge in the large N limit and match their formal expansion. Secondly we give a combinatorial model for our Matrix integral asymptotics and investigate examples related to free probability and the HCIZ integral. Our convergence result also leads us to new results of smoothness of microstates. We finally generalize our approach to integrals over the Orthogonal group.
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spectral analysis of the free Orthogonal Matrix
International Mathematics Research Notices, 2009Co-Authors: Teodor Banica, Benoit Collins, Paul ZinnjustinAbstract:We compute the spectral measure of the standard generators uij of the Wang algebra Ao(n). We show in particular that this measure has support (−2/ √ n + 2,2/ √ n + 2), and that it has no atoms. The computation is done by using various techniques, involving the general Wang algebra Ao(F), a representation of SU q 2 due to Woronowicz, and several calculations with Orthogonal polynomials.
