2013, De Gruyter studies in mathematics, ISBN 9783110263404, Volume 49, xi, 372

Book

Pattern Recognition, ISSN 0031-3203, 05/2015, Volume 48, Issue 5, pp. 1904 - 1912

...? To address this problem, we propose a novel criterion named Hilbert Space Embedding (HSE) Nyström criterion which directly minimizes the eigenvector approximation error...

Sampling methods | Eigenvalues and eigenfunctions | Spectral analysis | DIMENSIONALITY REDUCTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Kernels | Errors | Approximation | Mathematical analysis | Eigenvectors | Hilbert space | Mathematical models | Criteria | Density

Sampling methods | Eigenvalues and eigenfunctions | Spectral analysis | DIMENSIONALITY REDUCTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Kernels | Errors | Approximation | Mathematical analysis | Eigenvectors | Hilbert space | Mathematical models | Criteria | Density

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2017, Volume 272, Issue 5, pp. 1852 - 1875

In these notes, we study the relation between uniform and coarse embeddings between Banach spaces as well as uniform and coarse equivalences...

Nonlinear geometry of Banach spaces | Coarse embeddings | Uniform embeddings | MATHEMATICS | METRIC-SPACES | BANACH-SPACES | HILBERT-SPACE | Mathematics - Functional Analysis

Nonlinear geometry of Banach spaces | Coarse embeddings | Uniform embeddings | MATHEMATICS | METRIC-SPACES | BANACH-SPACES | HILBERT-SPACE | Mathematics - Functional Analysis

Journal Article

Journal of Mathematical Physics, ISSN 1089-7658, 2011, Volume 52, Issue 1, pp. 012102 - 012102-12

We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras...

ALGEBRAS | STATES | INEQUALITIES | INDEPENDENCE | PRODUCTS | PHYSICS, MATHEMATICAL | VIOLATION | TENSORS | APPROXIMATIONS | CALCULATION METHODS | ALGEBRA | CORRELATIONS | QUANTUM MECHANICS | HILBERT SPACE | MATHEMATICS | SPACE | MECHANICS | MATHEMATICAL SPACE | MATRICES | BANACH SPACE | MATHEMATICAL METHODS AND COMPUTING

ALGEBRAS | STATES | INEQUALITIES | INDEPENDENCE | PRODUCTS | PHYSICS, MATHEMATICAL | VIOLATION | TENSORS | APPROXIMATIONS | CALCULATION METHODS | ALGEBRA | CORRELATIONS | QUANTUM MECHANICS | HILBERT SPACE | MATHEMATICS | SPACE | MECHANICS | MATHEMATICAL SPACE | MATRICES | BANACH SPACE | MATHEMATICAL METHODS AND COMPUTING

Journal Article

Journal of Machine Learning Research, ISSN 1532-4435, 07/2011, Volume 12, pp. 2389 - 2410

... of distinguishing probability measures by embedding them into a reproducing kernel Hilbert space (RKHS). However, the relation between these two notions is not well understood...

Characteristic kernels | Conditionally strictly positive definite kernels | Kernel methods | Translation invariant kernels | Strictly positive definite kernels | Homogeneity testing | Hilbert space embeddings | Integrally strictly positive definite kernels | Universal kernels | Radial kernels | Binary classification | homogeneity testing | translation invariant kernels | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | radial kernels | characteristic kernels | conditionally strictly positive definite kernels | kernel methods | universal kernels | strictly positive definite kernels | binary classification | integrally strictly positive definite kernels | AUTOMATION & CONTROL SYSTEMS

Characteristic kernels | Conditionally strictly positive definite kernels | Kernel methods | Translation invariant kernels | Strictly positive definite kernels | Homogeneity testing | Hilbert space embeddings | Integrally strictly positive definite kernels | Universal kernels | Radial kernels | Binary classification | homogeneity testing | translation invariant kernels | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | radial kernels | characteristic kernels | conditionally strictly positive definite kernels | kernel methods | universal kernels | strictly positive definite kernels | binary classification | integrally strictly positive definite kernels | AUTOMATION & CONTROL SYSTEMS

Journal Article

6.
Full Text
Composition operators and embedding theorems for some function spaces of Dirichlet series

Mathematische Zeitschrift, ISSN 1432-1823, 2019, Volume 293, Issue 3-4, pp. 989 - 1014

We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators...

Mathematics, general | Primary 47B33 | Mathematics | 30H20 | Secondary 30B50 | 30H10 | MATHEMATICS | BERGMAN SPACES | H-2 SPACE | APPROXIMATION NUMBERS

Mathematics, general | Primary 47B33 | Mathematics | 30H20 | Secondary 30B50 | 30H10 | MATHEMATICS | BERGMAN SPACES | H-2 SPACE | APPROXIMATION NUMBERS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 06/2018, Volume 274, Issue 11, pp. 3149 - 3169

In this paper, we study nonlinear embeddings between Banach spaces. More specifically, the goal of this paper is to study weaker versions of coarse and uniform...

Nonlinear geometry of Banach spaces | Coarse embeddings | Property [formula omitted] of Kalton | Uniform embeddings | Property Q of Kalton | MATHEMATICS | COARSE | METRIC-SPACES | LIPSCHITZ | HILBERT-SPACE | GEOMETRY

Nonlinear geometry of Banach spaces | Coarse embeddings | Property [formula omitted] of Kalton | Uniform embeddings | Property Q of Kalton | MATHEMATICS | COARSE | METRIC-SPACES | LIPSCHITZ | HILBERT-SPACE | GEOMETRY

Journal Article

Neural Computation, ISSN 0899-7667, 2014, Volume 26, Issue 7, pp. 1484 - 1517

Causal discovery via the asymmetry between the cause and the effect has proved to be a promising way to infer the causal direction from observations. The basic...

Kernels | Asymmetry | Mathematical analysis | Preserves | Hilbert space | Transformations | Abbreviations | Complexity

Kernels | Asymmetry | Mathematical analysis | Preserves | Hilbert space | Transformations | Abbreviations | Complexity

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2015, Volume 276, Issue 2, pp. 347 - 367

.... We demonstrate that any simply connected smooth complete surface with curvature bounded above by a negative constant admits a smooth isometric embedding into the Lorentz...

Hilbert-efimov theorem | Isometric embedding | Lorentz-minkowski space | MATHEMATICS | isometric embedding | Hilbert-Efimov theorem | Lorentz-Minkowski space | DIMENSIONAL RIEMANNIAN-MANIFOLDS | DISKS | CONSTANT GAUSS CURVATURE

Hilbert-efimov theorem | Isometric embedding | Lorentz-minkowski space | MATHEMATICS | isometric embedding | Hilbert-Efimov theorem | Lorentz-Minkowski space | DIMENSIONAL RIEMANNIAN-MANIFOLDS | DISKS | CONSTANT GAUSS CURVATURE

Journal Article

Neurocomputing, ISSN 0925-2312, 11/2017, Volume 266, pp. 595 - 605

.... Motivated by the powerful framework of Hilbert space embeddings of distributions, in this paper we apply this methodology for the kernel embedding of an autoregressive process of order p...

Autoregressive process | Hilbert space embeddings | time series forecasting | cross-covariance operator | NEURAL-NETWORKS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Usage | Models | Stochastic processes | Analysis

Autoregressive process | Hilbert space embeddings | time series forecasting | cross-covariance operator | NEURAL-NETWORKS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Usage | Models | Stochastic processes | Analysis

Journal Article

ACM Transactions on Information Systems (TOIS), ISSN 1046-8188, 06/2017, Volume 35, Issue 3, pp. 1 - 27

...: In essence, these spaces allow an isometric embedding of any four points in three-dimensional Euclidean space, as well as any three points in two-dimensional Euclidean space...

metric space | Hilbert embedding | four-point property | metric indexing | Similarity search | Metric indexing | Four-point property | Metric Space | SPACES | COMPUTER SCIENCE, INFORMATION SYSTEMS | Information storage and retrieval | Data structures | Research | Search theory | Analysis | Computer Science - Information Retrieval

metric space | Hilbert embedding | four-point property | metric indexing | Similarity search | Metric indexing | Four-point property | Metric Space | SPACES | COMPUTER SCIENCE, INFORMATION SYSTEMS | Information storage and retrieval | Data structures | Research | Search theory | Analysis | Computer Science - Information Retrieval

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 6/2014, Volume 200, Issue 1, pp. 419 - 422

...-Lipschitz embeddings into uniformly convex Banach spaces.

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | MARKOV CONVEXITY | Trees (Graph theory) | Convex functions | Research | Banach spaces | Mathematical research | Functional Analysis | Metric Geometry

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | MARKOV CONVEXITY | Trees (Graph theory) | Convex functions | Research | Banach spaces | Mathematical research | Functional Analysis | Metric Geometry

Journal Article

JOURNAL OF MACHINE LEARNING RESEARCH, ISSN 1532-4435, 2017, Volume 18

In this paper, we study the minimax estimation of the Bochner integral mu(k)(P) := integral x(k)(.,x) dP(x) also called as the kernel mean embedding, based on random samples drawn...

translation invariant kernel | minimax lower bounds | kernel mean embeddings | Bochner integral | Bochner's theorem | reproducing kernel Hilbert space | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

translation invariant kernel | minimax lower bounds | kernel mean embeddings | Bochner integral | Bochner's theorem | reproducing kernel Hilbert space | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 06/2013, Volume 162, Issue 9, pp. 1621 - 1648

...) whenever H also shares those conditions. We also discuss some applications to compression functions of Lipschitz embeddings into uniformly convex Banach spaces, Folner...

MATHEMATICS | DISCRETE-GROUPS | EMBEDDABILITY | UNIFORM EMBEDDINGS | AMENABLE-GROUPS | COMPRESSION | HILBERT-SPACE | CONJECTURE | Mathematics - Group Theory | 20F65 | 20E22 | 20F16 | 20F69

MATHEMATICS | DISCRETE-GROUPS | EMBEDDABILITY | UNIFORM EMBEDDINGS | AMENABLE-GROUPS | COMPRESSION | HILBERT-SPACE | CONJECTURE | Mathematics - Group Theory | 20F65 | 20E22 | 20F16 | 20F69

Journal Article

Computer Graphics Forum, ISSN 0167-7055, 06/2013, Volume 32, Issue 3pt1, pp. 121 - 130

.... In this work, we propose a new visualization of the fiber probability distribution. It is based on embedding the probability measure into a particular reproducing kernel Hilbert space...

I.3.8 [Computer Graphics]: Applications | G.3 [Probability and Statistics]: Distribution functions | COMPUTER SCIENCE, SOFTWARE ENGINEERING | TENSOR | TRACTOGRAPHY | ORIENTATION | DIFFUSION MRI | METRICS | WILD BOOTSTRAP | Graphics software | Models | Fibers | Studies | Visualization | Analysis | Computer graphics | Hilbert space | Estimating techniques | Deltas | Uncertainty | Imaging | Diffusion | Estimates

I.3.8 [Computer Graphics]: Applications | G.3 [Probability and Statistics]: Distribution functions | COMPUTER SCIENCE, SOFTWARE ENGINEERING | TENSOR | TRACTOGRAPHY | ORIENTATION | DIFFUSION MRI | METRICS | WILD BOOTSTRAP | Graphics software | Models | Fibers | Studies | Visualization | Analysis | Computer graphics | Hilbert space | Estimating techniques | Deltas | Uncertainty | Imaging | Diffusion | Estimates

Journal Article

数学年刊：B辑英文版, ISSN 0252-9599, 2014, Volume 35, Issue 5, pp. 733 - 742

In this paper, the author studies the coarse embedding into uniformly convex Banach spaces...

一致凸空间 | 嵌入 | 度量空间 | 一致凸Banach空间 | 证明 | 子群 | Coarse embedding | Uniformly convex Banach spaces | 46B20 | 51F99 | Mathematics, general | Mathematics | Applications of Mathematics | Relative hyperbolic groups | MATHEMATICS | EMBEDDABILITY | BAUM-CONNES CONJECTURE | HILBERT-SPACE | RELATIVELY HYPERBOLIC GROUPS | Computer science

一致凸空间 | 嵌入 | 度量空间 | 一致凸Banach空间 | 证明 | 子群 | Coarse embedding | Uniformly convex Banach spaces | 46B20 | 51F99 | Mathematics, general | Mathematics | Applications of Mathematics | Relative hyperbolic groups | MATHEMATICS | EMBEDDABILITY | BAUM-CONNES CONJECTURE | HILBERT-SPACE | RELATIVELY HYPERBOLIC GROUPS | Computer science

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 369, Issue 1, pp. 60 - 75

Motivated by questions related to embeddings of homogeneous Sobolev spaces and to comparison of function spaces and operator ranges, we introduce the notion of closely embedded Hilbert spaces...

Operator range | Absolute continuity | Kernel operator | Continuous embedding | Closed embedding | Homogeneous Sobolev space | Hilbert space | MATHEMATICS | MATHEMATICS, APPLIED | LEBESGUE-TYPE DECOMPOSITION | POSITIVE OPERATORS

Operator range | Absolute continuity | Kernel operator | Continuous embedding | Closed embedding | Homogeneous Sobolev space | Hilbert space | MATHEMATICS | MATHEMATICS, APPLIED | LEBESGUE-TYPE DECOMPOSITION | POSITIVE OPERATORS

Journal Article

Journal of Complexity, ISSN 0885-064X, 06/2015, Volume 31, Issue 3, pp. 405 - 423

We study embeddings between tensor products of weighted reproducing kernel Hilbert spaces...

Reproducing kernel Hilbert space | Functions of infinitely many variables | Embeddings | Tensor product | MATHEMATICS | MATHEMATICS, APPLIED

Reproducing kernel Hilbert space | Functions of infinitely many variables | Embeddings | Tensor product | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Geometric and Functional Analysis, ISSN 1016-443X, 8/2013, Volume 23, Issue 4, pp. 1207 - 1229

For two metric spaces X and Y, say that X threshold-embeds into Y if there exist a number K...

Analysis | Mathematics | MARTINGALES | MATHEMATICS | DISTORTION | INEQUALITIES | DIMENSION | SMOOTH BANACH-SPACES | FINITE METRIC-SPACES | HILBERT-SPACE | UNIFORMLY CONVEX | GEOMETRY | GRAPHS | Computer science

Analysis | Mathematics | MARTINGALES | MATHEMATICS | DISTORTION | INEQUALITIES | DIMENSION | SMOOTH BANACH-SPACES | FINITE METRIC-SPACES | HILBERT-SPACE | UNIFORMLY CONVEX | GEOMETRY | GRAPHS | Computer science

Journal Article

Data mining and knowledge discovery, ISSN 1573-756X, 2019, Volume 33, Issue 2, pp. 499 - 525

... intervals are interpreted as samples drawn from unknown (conditional) distributions. In order to statistically distinguish them, we propose a novel method using Reproducing Kernel Hilbert Space embeddings...

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | Edge inference | Artificial Intelligence | Computer Science | Data Mining and Knowledge Discovery | Information Storage and Retrieval | Kernel embeddings | Diffusion networks | Clustering | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Cluster analysis | Models | Kernel functions | Analysis | Intervals | State of the art | Statistical analysis | Cascades | Statistical methods | Hilbert space | Batch processing | Diffusion | Information dissemination

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | Edge inference | Artificial Intelligence | Computer Science | Data Mining and Knowledge Discovery | Information Storage and Retrieval | Kernel embeddings | Diffusion networks | Clustering | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Cluster analysis | Models | Kernel functions | Analysis | Intervals | State of the art | Statistical analysis | Cascades | Statistical methods | Hilbert space | Batch processing | Diffusion | Information dissemination

Journal Article

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