Applied Mathematics and Computation, ISSN 0096-3003, 11/2014, Volume 247, pp. 233 - 234

In this note, a technical error is pointed out in the equality (2) of Lemma 2.2 in the above mentioned paper, and the corresponding correction is presented.

Submatrix constraint | Orthogonal direct sum | Central principal submatrix | MATHEMATICS, APPLIED

Submatrix constraint | Orthogonal direct sum | Central principal submatrix | MATHEMATICS, APPLIED

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 12/2017, Volume 534, pp. 97 - 101

We give a new short proof of a version of a Hankel matrix rank theorem. That version expresses the rank of H by the smallest possible rank of an infinite...

Hankel matrix | Submatrix | Rank | MATHEMATICS | MATHEMATICS, APPLIED

Hankel matrix | Submatrix | Rank | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

3.
Full Text
The reflexive least squares solutions of the matrix equation with a submatrix constraint

NUMERICAL ALGORITHMS, ISSN 1017-1398, 11/2013, Volume 64, Issue 3, pp. 455 - 480

In this paper, an efficient algorithm is presented for minimizing where is the Frobenius norm, is a reflexive matrix with a specified central principal...

MATHEMATICS, APPLIED | Reflexive solutions | Submatrix constraint | Least squares solution | Central principal submatrix | SPECTRUM | Matrix equation | Algorithms

MATHEMATICS, APPLIED | Reflexive solutions | Submatrix constraint | Least squares solution | Central principal submatrix | SPECTRUM | Matrix equation | Algorithms

Journal Article

Journal of Machine Learning Research, ISSN 1532-4435, 04/2018, Volume 18, pp. 1 - 52

The principal submatrix localization problem deals with recovering a K x K principal submatrix of elevated mean j in a large n x n symmetric matrix subject to...

High-dimensional statistics | Biclustering | Message passing | Spectral algorithms computational complexity | Submatrix localization | GRAPH | message passing | spectral algorithms computational complexity | ALGORITHMS | MODEL | biclustering | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMMUNITY | DIMENSIONAL NOISY MATRIX | high-dimensional statistics | SPARSE SUBMATRIX | AUTOMATION & CONTROL SYSTEMS

High-dimensional statistics | Biclustering | Message passing | Spectral algorithms computational complexity | Submatrix localization | GRAPH | message passing | spectral algorithms computational complexity | ALGORITHMS | MODEL | biclustering | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMMUNITY | DIMENSIONAL NOISY MATRIX | high-dimensional statistics | SPARSE SUBMATRIX | AUTOMATION & CONTROL SYSTEMS

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2013, Volume 23, Issue 4, pp. 2502 - 2540

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 08/2017, Volume 63, Issue 8, pp. 4729 - 4745

We study the problem of recovering a hidden community of cardinality K from an n × n symmetric data matrix A, where for distinct indices i, j, A ij ~ P if i, j...

Algorithm design and analysis | Maximum likelihood estimation | Symmetric matrices | Computational modeling | Stochastic processes | submatrix localization | Community detection | rate distortion theory | stochastic block model | Q measurement | maximum likelihood | Cavity resonators | large deviation | COMPUTER SCIENCE, INFORMATION SYSTEMS | SPARSE SUBMATRIX | CLIQUES | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Computer simulation | Maximum likelihood estimates (Statistics) | Graph theory | Research | Design and construction | Computer-generated environments | Algorithms | Symmetric functions | Analysis | Gaussian processes | Voting | Communities | Asymptotic properties | Mathematical analysis | Classification | Likelihood ratio | Recovery | Matrix methods

Algorithm design and analysis | Maximum likelihood estimation | Symmetric matrices | Computational modeling | Stochastic processes | submatrix localization | Community detection | rate distortion theory | stochastic block model | Q measurement | maximum likelihood | Cavity resonators | large deviation | COMPUTER SCIENCE, INFORMATION SYSTEMS | SPARSE SUBMATRIX | CLIQUES | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Computer simulation | Maximum likelihood estimates (Statistics) | Graph theory | Research | Design and construction | Computer-generated environments | Algorithms | Symmetric functions | Analysis | Gaussian processes | Voting | Communities | Asymptotic properties | Mathematical analysis | Classification | Likelihood ratio | Recovery | Matrix methods

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 07/2019, Volume 165, pp. 32 - 43

An ordered graph H is a simple graph with a linear order on its vertex set. The corresponding Turán problem, first studied by Pach and Tardos, asks for the...

Turán problem | Ordered forest | Forbidden submatrix | MATHEMATICS | Turan problem | MATRICES

Turán problem | Ordered forest | Forbidden submatrix | MATHEMATICS | Turan problem | MATRICES

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 12/2013, Volume 225, pp. 425 - 445

In this paper, we construct an iterative method to solve the general coupled matrix equations∑j=1lAijXjBij=Ci,i=1,2,…,t,where Xj∈Rnj×nj(j=1,2,…,l) is a...

General coupled matrix equations | Least squares solution | Reflexive solutions | Central principal submatrix | Submatrix constraint | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | ITERATIVE SOLUTIONS | SYMMETRIC-SOLUTIONS | MULTIVARIABLE SYSTEMS | SPECTRUM | IDENTIFICATION | Algorithms | Construction | Mathematical models | Iterative methods | Computation | Least squares method | Mathematical analysis

General coupled matrix equations | Least squares solution | Reflexive solutions | Central principal submatrix | Submatrix constraint | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | ITERATIVE SOLUTIONS | SYMMETRIC-SOLUTIONS | MULTIVARIABLE SYSTEMS | SPECTRUM | IDENTIFICATION | Algorithms | Construction | Mathematical models | Iterative methods | Computation | Least squares method | Mathematical analysis

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 06/2008, Volume 19, Issue 2, pp. 655 - 673

Recently, a semidefinite programming (SDP) relaxation approach has been proposed to solve the sensor network localization problem. Although it achieves high...

Chordal graph | Semidefinite programming | Principal submatrix | Sensor network localization | Second-order cone programming | semidefinite programming | second-order cone programming | MATHEMATICS, APPLIED | DISTANCE GEOMETRY | ALGORITHM | RIGIDITY | chordal graph | sensor network localization | principal submatrix

Chordal graph | Semidefinite programming | Principal submatrix | Sensor network localization | Second-order cone programming | semidefinite programming | second-order cone programming | MATHEMATICS, APPLIED | DISTANCE GEOMETRY | ALGORITHM | RIGIDITY | chordal graph | sensor network localization | principal submatrix

Journal Article

The Annals of Statistics, ISSN 0090-5364, 6/2015, Volume 43, Issue 3, pp. 1089 - 1116

This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the...

Asymptotic equivalence | LARGE-AVERAGE | minimax rate | STATISTICS & PROBABILITY | high-dimensional statistics | submatrix detection | planted clique | CLIQUES | computational complexity | 62H15 | 62C20

Asymptotic equivalence | LARGE-AVERAGE | minimax rate | STATISTICS & PROBABILITY | high-dimensional statistics | submatrix detection | planted clique | CLIQUES | computational complexity | 62H15 | 62C20

Journal Article

Computacion y Sistemas, ISSN 1405-5546, 2016, Volume 20, Issue 2, pp. 251 - 262

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2013, Volume 439, Issue 10, pp. 2774 - 2783

In this paper, the inverse eigenvalue problem of reconstructing a Jacobi matrix from part of its eigenvalues and its leading principal submatrix is considered....

Eigenvalue | Submatrix | Jacobi matrix | Inverse problem | MATHEMATICS, APPLIED | ALGORITHM | Algorithms

Eigenvalue | Submatrix | Jacobi matrix | Inverse problem | MATHEMATICS, APPLIED | ALGORITHM | Algorithms

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2014, Volume 458, pp. 679 - 688

The problem of comparing the Perron roots of two n-by-n nonnegative matrices, that differ only in a particular k-by-k principal submatrix, is considered....

Comparing Perron roots | Nonnegative matrices | Variable submatrix | MATHEMATICS, APPLIED

Comparing Perron roots | Nonnegative matrices | Variable submatrix | MATHEMATICS, APPLIED

Journal Article

Ecological Modelling, ISSN 0304-3800, 02/2013, Volume 251, pp. 307 - 311

Life cycle graph for a size-structured population of Carapa guianensis. Straight arrows indicate survival transitions from one size class to the next in one...

Carapa guianensis | Strong components | Stochastic growth rate | Reproductive submatrix | Life cycle graph | False growth rate

Carapa guianensis | Strong components | Stochastic growth rate | Reproductive submatrix | Life cycle graph | False growth rate

Journal Article

Journal of Machine Learning Research, ISSN 1532-4435, 04/2016, Volume 17

We consider two closely related problems: planted clustering and submatrix localization. In the planted clustering problem, a random graph is generated based...

Graph clustering | Bi-clustering | Minimax recovery | Planted partition | Planted clique | Convex relaxation | Computational hardness | Planted coloring | Submatrix localization | minimax recovery | planted coloring | computational hardness | LARGE-AVERAGE | bi-clustering | submatrix localization | planted partition | HIDDEN CLIQUES | HARD | planted clique | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | graph clustering | GRAPHS | SEMIDEFINITE RELAXATIONS | COMMUNITY DETECTION | convex relaxation | AUTOMATION & CONTROL SYSTEMS

Graph clustering | Bi-clustering | Minimax recovery | Planted partition | Planted clique | Convex relaxation | Computational hardness | Planted coloring | Submatrix localization | minimax recovery | planted coloring | computational hardness | LARGE-AVERAGE | bi-clustering | submatrix localization | planted partition | HIDDEN CLIQUES | HARD | planted clique | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | graph clustering | GRAPHS | SEMIDEFINITE RELAXATIONS | COMMUNITY DETECTION | convex relaxation | AUTOMATION & CONTROL SYSTEMS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 07/2018, Volume 341, Issue 7, pp. 1987 - 1993

An order-sDavenport–Schinzel sequence over an n-letter alphabet is one avoiding immediate repetitions and alternating subsequences with length s+2. The main...

Zarankiewicz problem | Forbidden submatrix | Davenport–Schinzel problem | Forbidden subsequence | Davenport-Schinzel problem | MATHEMATICS | BIPARTITE TURAN NUMBERS | NONLINEARITY | GRAPHS

Zarankiewicz problem | Forbidden submatrix | Davenport–Schinzel problem | Forbidden subsequence | Davenport-Schinzel problem | MATHEMATICS | BIPARTITE TURAN NUMBERS | NONLINEARITY | GRAPHS

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2018, Volume 64, Issue 3, pp. 1666 - 1698

Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One...

non-convex optimization | restricted isometry property | Compressed sensing | sparse and low-rank matrix | alternating minimization | sample complexity | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | SUBMATRIX | PCA | ENGINEERING, ELECTRICAL & ELECTRONIC | BLIND | RECOVERY | PURSUIT | Decay rate | Noise measurement | Detection | Recovery | Matrix methods | Factorization | Optimization | Information theory

non-convex optimization | restricted isometry property | Compressed sensing | sparse and low-rank matrix | alternating minimization | sample complexity | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | SUBMATRIX | PCA | ENGINEERING, ELECTRICAL & ELECTRONIC | BLIND | RECOVERY | PURSUIT | Decay rate | Noise measurement | Detection | Recovery | Matrix methods | Factorization | Optimization | Information theory

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 02/2015, Volume 466, pp. 102 - 116

In this paper, the inverse eigenvalue problem of reconstructing a Jacobi matrix from its eigenvalues, its leading principal submatrix and part of the...

Eigenvalue | Submatrix | Jacobi matrix | Inverse problem | MATHEMATICS | MATHEMATICS, APPLIED | ALGORITHM | Algorithms

Eigenvalue | Submatrix | Jacobi matrix | Inverse problem | MATHEMATICS | MATHEMATICS, APPLIED | ALGORITHM | Algorithms

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 07/2018, Volume 64, Issue 7, pp. 4872 - 4894

We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture...

Upper bound | Clustering algorithms | submatrix localization | clustering | Sparse matrices | Noise measurement | information-theoretic bounds | Task analysis | sparse PCA | Method of moments | Principal component analysis | First and second moment methods | SEMIDEFINITE RELAXATIONS | LARGEST EIGENVALUE | PRINCIPAL-COMPONENTS | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Lower bounds | Random noise | Algorithms | Phase transformations | Upper bounds | Likelihood ratio | Position (location) | Localization | Clustering | Information theory | Mathematics | Computer Science

Upper bound | Clustering algorithms | submatrix localization | clustering | Sparse matrices | Noise measurement | information-theoretic bounds | Task analysis | sparse PCA | Method of moments | Principal component analysis | First and second moment methods | SEMIDEFINITE RELAXATIONS | LARGEST EIGENVALUE | PRINCIPAL-COMPONENTS | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Lower bounds | Random noise | Algorithms | Phase transformations | Upper bounds | Likelihood ratio | Position (location) | Localization | Clustering | Information theory | Mathematics | Computer Science

Journal Article

Annals of Statistics, ISSN 0090-5364, 08/2017, Volume 45, Issue 4, pp. 1403 - 1430

We study in this paper computational and statistical boundaries for submatrix localization. Given one observation of (one or multiple nonoverlapping) signal...

Lower bounds | Minimax | Statistical boundary | Planted clique | Signal-to-noise ratio | Computational boundary | Detection | Computational complexity | Submatrix localization | LOW-RANK APPROXIMATION | detection | submatrix localization | STATISTICS & PROBABILITY | ALGORITHMS | planted clique | PROBABILITY-INEQUALITIES | lower bounds | OPTIMAL RATES | SPARSE PCA | signal-to-noise ratio | statistical boundary | minimax | computational complexity

Lower bounds | Minimax | Statistical boundary | Planted clique | Signal-to-noise ratio | Computational boundary | Detection | Computational complexity | Submatrix localization | LOW-RANK APPROXIMATION | detection | submatrix localization | STATISTICS & PROBABILITY | ALGORITHMS | planted clique | PROBABILITY-INEQUALITIES | lower bounds | OPTIMAL RATES | SPARSE PCA | signal-to-noise ratio | statistical boundary | minimax | computational complexity

Journal Article

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