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ON MATRIX BALANCING AND EIGENVECTOR COMPUTATION
"... Abstract. Balancing a matrix is a preprocessing step while solving the nonsymmetric eigenvalue problem. Balancing a matrix reduces the norm of the matrix and hopefully this will improve the accuracy of the computation. Experiments have shown that balancing can improve the accuracy of the computed ei ..."
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Abstract. Balancing a matrix is a preprocessing step while solving the nonsymmetric eigenvalue problem. Balancing a matrix reduces the norm of the matrix and hopefully this will improve the accuracy of the computation. Experiments have shown that balancing can improve the accuracy of the computed
Privacy-preserving protocols for eigenvector computation
- In ECML/PKDD Workshop on Privacy and Security issues in Data Mining and Machine Learning
, 2010
"... Abstract. In this paper, we present a protocol for computing the principal eigenvector of a collection of data matrices belonging to multiple semi-honest parties with privacy constraints. Our proposed protocol is based on secure multi-party computation with a semi-honest arbitrator who deals with da ..."
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Cited by 2 (2 self)
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Abstract. In this paper, we present a protocol for computing the principal eigenvector of a collection of data matrices belonging to multiple semi-honest parties with privacy constraints. Our proposed protocol is based on secure multi-party computation with a semi-honest arbitrator who deals
Implementing regularization implicitly via approximate eigenvector computation
- In Proceedings of the 28th International Conference on Machine Learning
, 2011
"... Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective function. This procedure often leads to optimization problems that ..."
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Cited by 9 (5 self)
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have the side-effect of performing regularization implicitly. Thus, we consider the question: What is the regularized optimization objective that an approximation algorithm is exactly optimizing? We address this question in the context of computing approximations to the smallest nontrivial eigenvector
Adaptive Inner-Outer Inverse Iteration for Eigenvector Computations
, 1998
"... Inverse iteration is a standard technique for finding selected eigenvectors associated with eigenvalues which are known approximately. At each step the solution of a linear system of equations is required, which is usually done by factorizing the system matrix. When direct factorization is impractic ..."
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Inverse iteration is a standard technique for finding selected eigenvectors associated with eigenvalues which are known approximately. At each step the solution of a linear system of equations is required, which is usually done by factorizing the system matrix. When direct factorization
ACE: A Fast Multiscale Eigenvector Computation for Drawing Huge Graphs
, 2002
"... We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE finds an optimal drawing by minimizing a quadratic energy function due to Hall, using a novel algebraic multigrid technique. The algorithm exhibits ..."
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Cited by 73 (13 self)
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We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE finds an optimal drawing by minimizing a quadratic energy function due to Hall, using a novel algebraic multigrid technique. The algorithm
Solution of a Polynomial System of Equations Via the Eigenvector Computation
- Linear Algebra Appl
, 2001
"... We propose new techniques and algorithms for the solution of a polynomial system of equations by matrix methods. For such a system, we seek its specied root, at which a fixed polynomial takes its maximum or minimum absolute value on the set of roots. We unify several known approaches and simplify th ..."
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Cited by 3 (1 self)
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the solution substantially, in particular in the case of an overconstrained polynomial system having only a simple root or a few roots. We reduce the solution to the computation of the eigenvector of an associated dense matrix, but we dene this matrix implicitly, as a Schur complement in a sparse
Faster Eigenvector Computation via Shift-and-Invert Preconditioning
, 2016
"... Abstract We give faster algorithms and improved sample complexities for the fundamental problem of estimating the top eigenvector. Given an explicit matrix A ∈ R n×d , we show how to compute an approximate top eigenvector of · log 1/ . Here nnz(A) is the number of nonzeros in A, sr(A) is the stable ..."
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Abstract We give faster algorithms and improved sample complexities for the fundamental problem of estimating the top eigenvector. Given an explicit matrix A ∈ R n×d , we show how to compute an approximate top eigenvector of · log 1/ . Here nnz(A) is the number of nonzeros in A, sr
Segmentation using eigenvectors: A unifying view
- In ICCV
, 1999
"... Automatic grouping and segmentation of images remains a challenging problem in computer vision. Recently, a number of authors have demonstrated good performance on this task using methods that are based on eigenvectors of the a nity matrix. These approaches are extremely attractive in that they are ..."
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Cited by 380 (1 self)
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Automatic grouping and segmentation of images remains a challenging problem in computer vision. Recently, a number of authors have demonstrated good performance on this task using methods that are based on eigenvectors of the a nity matrix. These approaches are extremely attractive
PEST: Term-Propagation over Wiki Structures as Eigenvector Computation
, 2010
"... We present PEST, a novel approach to approximate querying of structured wiki data that exploits the structure of that data to propagate term weights between related wiki pages and tags. Based on the pest matrix, eigenvectors representing the distribution of a term after propagation are computed. T ..."
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We present PEST, a novel approach to approximate querying of structured wiki data that exploits the structure of that data to propagate term weights between related wiki pages and tags. Based on the pest matrix, eigenvectors representing the distribution of a term after propagation are computed
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