Results 1  10
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1,008
Multiclass spectral clustering
 In Proc. Int. Conf. Computer Vision
, 2003
"... We propose a principled account on multiclass spectral clustering. Given a discrete clustering formulation, we first solve a relaxed continuous optimization problem by eigendecomposition. We clarify the role of eigenvectors as a generator of all optimal solutions through orthonormal transforms. We t ..."
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Cited by 265 (7 self)
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We propose a principled account on multiclass spectral clustering. Given a discrete clustering formulation, we first solve a relaxed continuous optimization problem by eigendecomposition. We clarify the role of eigenvectors as a generator of all optimal solutions through orthonormal transforms. We
ImplicitExplicit Methods For TimeDependent PDEs
 SIAM J. NUMER. ANAL
, 1997
"... Implicitexplicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized PDEs of diffusionconvection type. Typically, an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection ..."
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Cited by 178 (6 self)
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Implicitexplicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized PDEs of diffusionconvection type. Typically, an implicit scheme is used for the diffusion term and an explicit scheme is used
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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complementary to Fourier preparation by linear field gradients. Thus, by using multiple receiver coils in parallel scan time in Fourier imaging can be considerably reduced. The problem of image reconstruction from sensitivity encoded data is formulated in a general fashion and solved for arbitrary coil
Efficient spectralGalerkin method I. Direct solvers for second and fourthorder equations by using Legendre polynomials
 SIAM J. SCI. COMPUT
, 1994
"... We present some efficient algorithms based on the LegendreGalerkin approximations for the direct solution of the second and fourth order elliptic equations. The key to the efficiency of our algorithms is to construct appropriate base functions, which lead to systems with sparse matrices for the dis ..."
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Cited by 128 (64 self)
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for the discrete variational formulations. The complexities of the algorithms are a small multiple of N d+1 operations for a d dimensional domain with (N − 1) d unknowns, while the convergence rates of the algorithms are exponential for problems with smooth solutions. In addition, the algorithms can be effectively
ImplicitExplicit RungeKutta Methods for TimeDependent Partial Differential Equations
 Appl. Numer. Math
, 1997
"... Implicitexplicit (IMEX) linear multistep timediscretization schemes for partial differential equations have proved useful in many applications. However, they tend to have undesirable timestep restrictions when applied to convectiondiffusion problems, unless diffusion strongly dominates and an ap ..."
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Cited by 156 (7 self)
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Implicitexplicit (IMEX) linear multistep timediscretization schemes for partial differential equations have proved useful in many applications. However, they tend to have undesirable timestep restrictions when applied to convectiondiffusion problems, unless diffusion strongly dominates
From theory to practice: SubNyquist sampling of sparse wideband analog signals
 IEEE J. SEL. TOPICS SIGNAL PROCESS
, 2010
"... Conventional subNyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind subNyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. ..."
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Cited by 153 (55 self)
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Conventional subNyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind subNyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum
Dynamic Spectrum Management: Complexity and Duality
, 2007
"... Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectral densities dynamically in response to physical channel conditions. Due to cochannel interference, the achievable data rate of each user depends on not only the power spe ..."
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Cited by 129 (8 self)
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spectral density of its own, but also those of others in the system. Given any channel condition and assuming Gaussian signaling, we consider the problem to jointly determine all users ’ power spectral densities so as to maximize a systemwide utility function (e.g., weighted sumrate of all users
Wavelets on graphs via spectral graph theory
, 2009
"... We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian L. ..."
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Cited by 90 (8 self)
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We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian L
A spectral algorithm for envelope reduction of sparse matrices
 ACM/IEEE CONFERENCE ON SUPERCOMPUTING
, 1993
"... The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelopereducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the ..."
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Cited by 85 (5 self)
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of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results
Spectral bounds for sparse PCA: Exact and greedy algorithms
 Advances in Neural Information Processing Systems 18
, 2006
"... Sparse PCA seeks approximate sparse “eigenvectors ” whose projections capture the maximal variance of data. As a cardinalityconstrained and nonconvex optimization problem, it is NPhard and yet it is encountered in a wide range of applied fields, from bioinformatics to finance. Recent progress ha ..."
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Cited by 79 (4 self)
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has focused mainly on continuous approximation and convex relaxation of the hard cardinality constraint. In contrast, we consider an alternative discrete spectral formulation based on variational eigenvalue bounds and provide an effective greedy strategy as well as provably optimal solutions using
Results 1  10
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1,008