Expert Systems With Applications, ISSN 0957-4174, 07/2019, Volume 125, pp. 233 - 248

•A multi-objective optimization based kernel metric learning technique is developed.•This approach utilizes only few labeled data for generating...

Semi supervised classification | Clustering | Multi objective optimization | Bregman projection | Metric learning | FEATURE-SELECTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | GENETIC ALGORITHM | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer science | Usage | Algorithms | Data mining | Machine learning | Cluster analysis | Euclidean geometry | Data points | Human motion | Similarity | Vector quantization | Labelling | Smartphones | Kernels | Activity recognition | Multiple objective

Semi supervised classification | Clustering | Multi objective optimization | Bregman projection | Metric learning | FEATURE-SELECTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | GENETIC ALGORITHM | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer science | Usage | Algorithms | Data mining | Machine learning | Cluster analysis | Euclidean geometry | Data points | Human motion | Similarity | Vector quantization | Labelling | Smartphones | Kernels | Activity recognition | Multiple objective

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 8/2019, Volume 109, Issue 8, pp. 1777 - 1804

On the space of positive definite matrices, we consider distance functions of the form $$d(A,B)=\left[ \mathrm{tr}\mathcal {A}(A,B)-\mathrm{tr}\mathcal...

Theoretical, Mathematical and Computational Physics | Complex Systems | Barycentre | 15B48 | Physics | Geometry | Relative entropy | Strict convexity | 81P45 | Geometric mean | Bregman divergence | 94A17 | Matrix divergence | Group Theory and Generalizations | 49K35 | POSITIVE-DEFINITE MATRICES | INEQUALITIES | CONVEXITY | PHYSICS, MATHEMATICAL | DIVERGENCE | GEOMETRY | ENTROPY | Metric Geometry | Mathematical Physics | Mathematics

Theoretical, Mathematical and Computational Physics | Complex Systems | Barycentre | 15B48 | Physics | Geometry | Relative entropy | Strict convexity | 81P45 | Geometric mean | Bregman divergence | 94A17 | Matrix divergence | Group Theory and Generalizations | 49K35 | POSITIVE-DEFINITE MATRICES | INEQUALITIES | CONVEXITY | PHYSICS, MATHEMATICAL | DIVERGENCE | GEOMETRY | ENTROPY | Metric Geometry | Mathematical Physics | Mathematics

Journal Article

IEEE Transactions on Knowledge and Data Engineering, ISSN 1041-4347, 09/2017, Volume 29, Issue 9, pp. 1916 - 1927

We study content-based learning to rank from the perspective of learning distance functions. Standardly, the two key issues of learning to rank, feature...

Support vector machines | Training | Measurement | Analytical models | Semantics | structural SVM | Robustness | Data models | Learning to rank | robust structural learning | Bregman distance | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Geometry | Robust statistics | Usage | Artificial intelligence | Analysis | Learning | State of the art | Ranking | Outliers (statistics) | Nonlinearity | Mathematical models | Modelling

Support vector machines | Training | Measurement | Analytical models | Semantics | structural SVM | Robustness | Data models | Learning to rank | robust structural learning | Bregman distance | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Geometry | Robust statistics | Usage | Artificial intelligence | Analysis | Learning | State of the art | Ranking | Outliers (statistics) | Nonlinearity | Mathematical models | Modelling

Journal Article

IEEE Transactions on Knowledge and Data Engineering, ISSN 1041-4347, 03/2012, Volume 24, Issue 3, pp. 478 - 491

Learning distance functions with side information plays a key role in many data mining applications. Conventional distance metric learning approaches often...

Measurement | Training | metric learning | Clustering algorithms | Training data | Convex functions | Linear matrix inequalities | Bregman distance | distance functions | Kernel | convex functions | SCHEME | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Technology application | Usage | Kernel functions | Innovations | Machine learning | Data mining | Hessian matrices | Mathematical optimization

Measurement | Training | metric learning | Clustering algorithms | Training data | Convex functions | Linear matrix inequalities | Bregman distance | distance functions | Kernel | convex functions | SCHEME | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Technology application | Usage | Kernel functions | Innovations | Machine learning | Data mining | Hessian matrices | Mathematical optimization

Journal Article

Signal Processing: Image Communication, ISSN 0923-5965, 10/2017, Volume 58, pp. 24 - 34

The aim of super-resolution (SR) algorithms is to recover high-resolution (HR) images and videos from low-resolution (LR) ones. Since the SR is considered as...

Huber-Norm | Super-resolution | Regularization | Primal–dual | Bilateral total variation | Bregman distances | VIDEO | EXAMPLE-BASED SUPERRESOLUTION | RESTORATION | NOISE | ENGINEERING, ELECTRICAL & ELECTRONIC | MOTION ESTIMATION | ENHANCEMENT | RECONSTRUCTION METHOD | MULTIFRAME SUPERRESOLUTION | Primal dual | SUPER RESOLUTION | Analysis | Algorithms

Huber-Norm | Super-resolution | Regularization | Primal–dual | Bilateral total variation | Bregman distances | VIDEO | EXAMPLE-BASED SUPERRESOLUTION | RESTORATION | NOISE | ENGINEERING, ELECTRICAL & ELECTRONIC | MOTION ESTIMATION | ENHANCEMENT | RECONSTRUCTION METHOD | MULTIFRAME SUPERRESOLUTION | Primal dual | SUPER RESOLUTION | Analysis | Algorithms

Journal Article

Inverse Problems, ISSN 0266-5611, 10/2018, Volume 34, Issue 12, p. 124003

In this paper, we address the resolution of material decomposition, which is a nonlinear inverse problem encountered in spectral computed tomography (CT). The...

Bregman distance | convexity | spectral computerized tomography | SPARSITY CONSTRAINTS | MATHEMATICS, APPLIED | IMAGE-RESTORATION | ILL-POSED PROBLEMS | RECONSTRUCTION | ALGORITHM | SPECTRAL CT DATA | PHYSICS, MATHEMATICAL | COMPUTED-TOMOGRAPHY | X-RAY CT | DIFFUSION | Signal and Image Processing | Mathematics | Medical Imaging | Optimization and Control | Image Processing | Computer Science

Bregman distance | convexity | spectral computerized tomography | SPARSITY CONSTRAINTS | MATHEMATICS, APPLIED | IMAGE-RESTORATION | ILL-POSED PROBLEMS | RECONSTRUCTION | ALGORITHM | SPECTRAL CT DATA | PHYSICS, MATHEMATICAL | COMPUTED-TOMOGRAPHY | X-RAY CT | DIFFUSION | Signal and Image Processing | Mathematics | Medical Imaging | Optimization and Control | Image Processing | Computer Science

Journal Article

Machine Learning, ISSN 0885-6125, 7/2002, Volume 48, Issue 1, pp. 253 - 285

We give a unified account of boosting and logistic regression in which each learning problem is cast in terms of optimization of Bregman distances. The...

AdaBoost | maximum-entropy methods | boosting | iterative scaling | information geometry | Automation and Robotics | Computer Science | Artificial Intelligence (incl. Robotics) | convex optimization | Computer Science, general | logistic regression | Bregman distances | Iterative scaling | Information geometry | Logistic regression | Convex optimization | Boosting | Maximum-entropy methods | ALGORITHMS | DESCENT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algorithms | Studies

AdaBoost | maximum-entropy methods | boosting | iterative scaling | information geometry | Automation and Robotics | Computer Science | Artificial Intelligence (incl. Robotics) | convex optimization | Computer Science, general | logistic regression | Bregman distances | Iterative scaling | Information geometry | Logistic regression | Convex optimization | Boosting | Maximum-entropy methods | ALGORITHMS | DESCENT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algorithms | Studies

Journal Article

Journal of Multivariate Analysis, ISSN 0047-259X, 11/2018, Volume 168, pp. 276 - 289

The average squared volume of simplices formed by k independent copies from the same probability measure μ on Rd defines an integral measure of dispersion...

Generalized variance | Bregman divergence | Characteristic polynomial | Potential | Scatter | Dispersion | Mahalanobis distance | STATISTICS & PROBABILITY | Statistics | Mathematics

Generalized variance | Bregman divergence | Characteristic polynomial | Potential | Scatter | Dispersion | Mahalanobis distance | STATISTICS & PROBABILITY | Statistics | Mathematics

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 08/2010, Volume 6, Issue 4, pp. 1 - 26

We study a generalization of the k -median problem with respect to an arbitrary dissimilarity measure D. Given a finite set P of size n , our goal is to find a...

k -median clustering | Bregman divergences | k -means clustering | Itakura-Saito divergence | random sampling | Kullback-Leibler divergence | Approximation algorithm | Mahalanobis distance | κ-means clustering | Random sampling | κ-median clustering | k-median clustering | MATHEMATICS, APPLIED | k-means clustering | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Approximation | Divergence | Error analysis | Metric space | Mathematical analysis | Entropy | Clustering

k -median clustering | Bregman divergences | k -means clustering | Itakura-Saito divergence | random sampling | Kullback-Leibler divergence | Approximation algorithm | Mahalanobis distance | κ-means clustering | Random sampling | κ-median clustering | k-median clustering | MATHEMATICS, APPLIED | k-means clustering | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Approximation | Divergence | Error analysis | Metric space | Mathematical analysis | Entropy | Clustering

Journal Article

ENTROPY, ISSN 1099-4300, 05/2019, Volume 21, Issue 5, p. 485

The Jensen-Shannon divergence is a renowned bounded symmetrization of the unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler...

Jensen | Jeffreys divergence | PHYSICS, MULTIDISCIPLINARY | resistor average distance | mixture family | BHATTACHARYYA | REPRESENTATION | statistical M-mixture | METRIC DIVERGENCES | Burbea-Rao divergence | abstract weighted mean | quasi-arithmetic mean | Gaussian family | Cauchy scale family | MODELS | Bregman divergence | Jensen-Shannon divergence | HISTOGRAMS | clustering | f-divergence | INFORMATION GEOMETRY | Bhattacharyya distance | exponential family | BREGMAN | Jensen/Burbea–Rao divergence | Jensen–Shannon divergence

Jensen | Jeffreys divergence | PHYSICS, MULTIDISCIPLINARY | resistor average distance | mixture family | BHATTACHARYYA | REPRESENTATION | statistical M-mixture | METRIC DIVERGENCES | Burbea-Rao divergence | abstract weighted mean | quasi-arithmetic mean | Gaussian family | Cauchy scale family | MODELS | Bregman divergence | Jensen-Shannon divergence | HISTOGRAMS | clustering | f-divergence | INFORMATION GEOMETRY | Bhattacharyya distance | exponential family | BREGMAN | Jensen/Burbea–Rao divergence | Jensen–Shannon divergence

Journal Article

Vietnam Journal of Mathematics, ISSN 2305-221X, 9/2017, Volume 45, Issue 3, pp. 519 - 539

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The...

Variable quasi-Bregman monotonicity | 90C25 | Mathematics, general | Mathematics | Legendre function | Banach space | Bregman distance | Forward-backward algorithm | Multivariate minimization

Variable quasi-Bregman monotonicity | 90C25 | Mathematics, general | Mathematics | Legendre function | Banach space | Bregman distance | Forward-backward algorithm | Multivariate minimization

Journal Article

JOURNAL OF CONVEX ANALYSIS, ISSN 0944-6532, 2019, Volume 26, Issue 3, pp. 991 - 999

The Bregman distance B-xi x(y, x), xi(x) is an element of partial derivative J(y), associated to a convex sub-differentiable functional J is known to be in...

MATHEMATICS | strong monotonicity | symmetry | CONVEX | Bregman distance | REGULARIZATION | convexity | CONVERGENCE-RATES

MATHEMATICS | strong monotonicity | symmetry | CONVEX | Bregman distance | REGULARIZATION | convexity | CONVERGENCE-RATES

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2012, Volume 58, Issue 3, pp. 1277 - 1288

This paper introduces scaled Bregman distances of probability distributions which admit nonuniform contributions of observed events. They are introduced in a...

Context | Measurement | statistical decision | information retrieval | Probability | Vectors | exponential processes | classification | exponential distributions | machine learning | sufficiency | Convex functions | Concrete | divergences | Information theory | Bregman distances | STATISTICS | COMPUTER SCIENCE, INFORMATION SYSTEMS | INFERENCE | LEAST-SQUARES | ENGINEERING, ELECTRICAL & ELECTRONIC | REGULARIZATION | ENTROPY | Information storage and retrieval | Machine learning | Research | Concretes | Theorems | Nonuniform | Coding | Transformations | Recognition | Three dimensional

Context | Measurement | statistical decision | information retrieval | Probability | Vectors | exponential processes | classification | exponential distributions | machine learning | sufficiency | Convex functions | Concrete | divergences | Information theory | Bregman distances | STATISTICS | COMPUTER SCIENCE, INFORMATION SYSTEMS | INFERENCE | LEAST-SQUARES | ENGINEERING, ELECTRICAL & ELECTRONIC | REGULARIZATION | ENTROPY | Information storage and retrieval | Machine learning | Research | Concretes | Theorems | Nonuniform | Coding | Transformations | Recognition | Three dimensional

Journal Article

SIAM journal on imaging sciences, ISSN 1936-4954, 02/2017, Volume 10, Issue 1, pp. 111 - 146

In biomedical imaging reliable segmentation of objects (e.g., from small cells up to large organs) is of fundamental importance for automated medical...

nonlinear spectral methods | Chan-Vese method | Wulff shapes | circulating tumor cells | MSC-65K10 | eigenfunctions | inverse scale space | EWI-27772 | MSC-68U10 | multiscale segmentation | METIS-318833 | MSC-35A15 | Bregman iteration | total variation | IR-103647 | Inverse scale space | Multiscale segmentation | Nonlinear spectral methods | Total variation | Eigenfunctions | Circulating tumor cells | Chan–Vese method | SURVIVAL | MATHEMATICS, APPLIED | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | IMAGE SEGMENTATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | CIRCULATING TUMOR-CELLS | PREDICT | FRAMEWORK | SCALE | VARIATION REGULARIZATION | ACTIVE CONTOURS | BLOOD

nonlinear spectral methods | Chan-Vese method | Wulff shapes | circulating tumor cells | MSC-65K10 | eigenfunctions | inverse scale space | EWI-27772 | MSC-68U10 | multiscale segmentation | METIS-318833 | MSC-35A15 | Bregman iteration | total variation | IR-103647 | Inverse scale space | Multiscale segmentation | Nonlinear spectral methods | Total variation | Eigenfunctions | Circulating tumor cells | Chan–Vese method | SURVIVAL | MATHEMATICS, APPLIED | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | IMAGE SEGMENTATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | CIRCULATING TUMOR-CELLS | PREDICT | FRAMEWORK | SCALE | VARIATION REGULARIZATION | ACTIVE CONTOURS | BLOOD

Journal Article

Sankhya B, ISSN 0976-8386, 07/2018, Volume 80, Issue S1, pp. 1 - 12

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 2009, Volume 159, Issue 1, pp. 3 - 25

A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is...

Chebyshev set with respect to a Bregman distance | Subdifferential operators | Legendre function | Maximal monotone operator | Bregman distance | Bregman projection | Nearest point | MATHEMATICS | OPTIMIZATION

Chebyshev set with respect to a Bregman distance | Subdifferential operators | Legendre function | Maximal monotone operator | Bregman distance | Bregman projection | Nearest point | MATHEMATICS | OPTIMIZATION

Journal Article

17.
Full Text
The Moreau envelope function and proximal mapping in the sense of the Bregman distance

Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 3, pp. 1385 - 1399

In this paper, we explore some properties of the Moreau envelope function e λ f ( x ) of f and the associated proximal mapping P λ f ( x ) in the sense of the...

Proximal mapping | Continuity | Clarke regularity | Convexity | Bregman distance | Moreau envelope | MATHEMATICS | MATHEMATICS, APPLIED | PROJECTIONS | Envelopes | Nonlinearity | Mapping | Regularity

Proximal mapping | Continuity | Clarke regularity | Convexity | Bregman distance | Moreau envelope | MATHEMATICS | MATHEMATICS, APPLIED | PROJECTIONS | Envelopes | Nonlinearity | Mapping | Regularity

Journal Article

Signal Processing, ISSN 0165-1684, 04/2013, Volume 93, Issue 4, pp. 621 - 633

This paper provides an annotated bibliography for investigations based on or related to divergence measures for statistical data processing and inference...

Learning | Compression | Divergence | Bregman divergence | Estimation | Classification | f-Divergence | Information | Detection | Distance | Recognition | Indexing | SPECTRAL DISTANCE MEASURES | MAXIMUM-ENTROPY | CROSS-ENTROPY | KULLBACK-LEIBLER APPROXIMATION | BHATTACHARYYA DISTANCE | ENGINEERING, ELECTRICAL & ELECTRONIC | PATTERN-CLASSIFICATION | ALPHA-EM ALGORITHM | INFORMATION GEOMETRY | NONNEGATIVE MATRIX FACTORIZATION | Electronic data processing | Bibliography | Signal and Image Processing | Computer Science

Learning | Compression | Divergence | Bregman divergence | Estimation | Classification | f-Divergence | Information | Detection | Distance | Recognition | Indexing | SPECTRAL DISTANCE MEASURES | MAXIMUM-ENTROPY | CROSS-ENTROPY | KULLBACK-LEIBLER APPROXIMATION | BHATTACHARYYA DISTANCE | ENGINEERING, ELECTRICAL & ELECTRONIC | PATTERN-CLASSIFICATION | ALPHA-EM ALGORITHM | INFORMATION GEOMETRY | NONNEGATIVE MATRIX FACTORIZATION | Electronic data processing | Bibliography | Signal and Image Processing | Computer Science

Journal Article