IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 02/2009, Volume 31, Issue 2, pp. 260 - 274

... step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the Geometric Mean for Subspace...

Biometrics | visualization | subspace selection (or dimensionality reduction) | Gaussian distribution | Information management | Covariance matrix | geometric mean | Information analysis | Pattern classification | Data visualization | Machine learning | Kullback-Leibler (KL) divergence | Linear discriminant analysis | Arithmetic mean | Bioinformatics | Fisher's linear discriminant analysis (FLDA) | Visualization | Geometric mean | Subspace selection (or dimensionality reduction) | DIMENSIONALITY REDUCTION | LINEAR DISCRIMINANT-ANALYSIS | FACE RECOGNITION | LDA | DECOMPOSITION | CLASSIFICATION | machine learning | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | IMAGE | CRITERION | Models, Theoretical | Data Interpretation, Statistical | Algorithms | Artificial Intelligence | Computer Simulation | Pattern Recognition, Automated - methods | Discriminant Analysis | Average | Evaluation | Methods | Studies | Discriminant analysis | Reduction | Maximization | Intelligence | Classification | Matrices | Criteria | Subspaces

Biometrics | visualization | subspace selection (or dimensionality reduction) | Gaussian distribution | Information management | Covariance matrix | geometric mean | Information analysis | Pattern classification | Data visualization | Machine learning | Kullback-Leibler (KL) divergence | Linear discriminant analysis | Arithmetic mean | Bioinformatics | Fisher's linear discriminant analysis (FLDA) | Visualization | Geometric mean | Subspace selection (or dimensionality reduction) | DIMENSIONALITY REDUCTION | LINEAR DISCRIMINANT-ANALYSIS | FACE RECOGNITION | LDA | DECOMPOSITION | CLASSIFICATION | machine learning | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | IMAGE | CRITERION | Models, Theoretical | Data Interpretation, Statistical | Algorithms | Artificial Intelligence | Computer Simulation | Pattern Recognition, Automated - methods | Discriminant Analysis | Average | Evaluation | Methods | Studies | Discriminant analysis | Reduction | Maximization | Intelligence | Classification | Matrices | Criteria | Subspaces

Journal Article

2.
Full Text
Sharp bounds for the Sándor–Yang means in terms of arithmetic and contra-harmonic means

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 13

In the article, we provide several sharp upper and lower bounds for two Sándor–Yang means in terms of combinations of arithmetic and contra-harmonic means.

26E60 | Analysis | Mathematics, general | Mathematics | 26D99 | Applications of Mathematics | Schwab–Borchardt mean | Arithmetic mean | Contra-harmonic mean | 26D07 | Quadratic mean | Sándor–Yang mean | MATHEMATICS | Schwab-Borchardt mean | MATHEMATICS, APPLIED | INEQUALITIES | POWER | SEIFFERT | Sandor-Yang mean | Lower bounds | Arithmetic | Research

26E60 | Analysis | Mathematics, general | Mathematics | 26D99 | Applications of Mathematics | Schwab–Borchardt mean | Arithmetic mean | Contra-harmonic mean | 26D07 | Quadratic mean | Sándor–Yang mean | MATHEMATICS | Schwab-Borchardt mean | MATHEMATICS, APPLIED | INEQUALITIES | POWER | SEIFFERT | Sandor-Yang mean | Lower bounds | Arithmetic | Research

Journal Article

Expert systems with applications, ISSN 0957-4174, 2018, Volume 114, pp. 97 - 106

•The results of aggregation by weighted arithmetic mean are normalization-dependent...

Aggregation | Weighted arithmetic mean | Normalization of priorities | Rank reversal | Weighted geometric mean | Analytic hierarchy process | DECISION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATRICES | RELATIVE IMPORTANCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Analysis | Business schools

Aggregation | Weighted arithmetic mean | Normalization of priorities | Rank reversal | Weighted geometric mean | Analytic hierarchy process | DECISION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATRICES | RELATIVE IMPORTANCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Analysis | Business schools

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 14

.... As applications, we find new inequalities for the arithmetic and generalized logarithmic means.

26E60 | 26A51 | Ostrowski inequality | 26A33 | Mathematics | Conformable derivative | Conformable integral | Analysis | Generalized logarithmic mean | Mathematics, general | Applications of Mathematics | Arithmetic mean | 26D15 | MATHEMATICS, APPLIED | CONVEXITY | TERMS | SHARP BOUNDS | SEIFFERT | COMPANION | MATHEMATICS | RESPECT | MAPPINGS | ELLIPTIC INTEGRALS | Integrals | Inequalities | Research

26E60 | 26A51 | Ostrowski inequality | 26A33 | Mathematics | Conformable derivative | Conformable integral | Analysis | Generalized logarithmic mean | Mathematics, general | Applications of Mathematics | Arithmetic mean | 26D15 | MATHEMATICS, APPLIED | CONVEXITY | TERMS | SHARP BOUNDS | SEIFFERT | COMPANION | MATHEMATICS | RESPECT | MAPPINGS | ELLIPTIC INTEGRALS | Integrals | Inequalities | Research

Journal Article

Journal of fluid mechanics, ISSN 0022-1120, 04/2019, Volume 865, pp. 363 - 380

This work demonstrates that the popular arithmetic mean conformation tensor frequently used in the analysis of turbulent viscoelastic flows is not a good representative of the ensemble...

JFM Papers | MECHANICS | turbulent flows | PHYSICS, FLUIDS & PLASMAS | channel flow | viscoelasticity | DRAG REDUCTION | Viscoelasticity | Turbulence | Euclidean geometry | Turbulent flow | Deformation | Computational fluid dynamics | Reynolds number | Mathematics | Velocity | Tensors | Simulation | Mathematical analysis | Modelling | Polymers | Channel flow | Arithmetic | Conformation | Eigen values | Physics - Fluid Dynamics

JFM Papers | MECHANICS | turbulent flows | PHYSICS, FLUIDS & PLASMAS | channel flow | viscoelasticity | DRAG REDUCTION | Viscoelasticity | Turbulence | Euclidean geometry | Turbulent flow | Deformation | Computational fluid dynamics | Reynolds number | Mathematics | Velocity | Tensors | Simulation | Mathematical analysis | Modelling | Polymers | Channel flow | Arithmetic | Conformation | Eigen values | Physics - Fluid Dynamics

Journal Article

PloS one, ISSN 1932-6203, 2017, Volume 12, Issue 1, p. e0168767

Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector...

GENERALIZED AGGREGATION OPERATORS | VAGUE SET-THEORY | LINGUISTIC INFORMATION | DISTANCE MEASURE | MULTIDISCIPLINARY SCIENCES | KNOWLEDGE | Decision Making | Group Processes | Models, Theoretical | Intuition | Fuzzy Logic | Humans | Decision-making | Fuzzy sets | Set theory | Usage | Research | Statistics | Decision support systems | Studies | Operators | Decision making | Linguistics | Values | Reliability analysis | Methods | Cybernetics

GENERALIZED AGGREGATION OPERATORS | VAGUE SET-THEORY | LINGUISTIC INFORMATION | DISTANCE MEASURE | MULTIDISCIPLINARY SCIENCES | KNOWLEDGE | Decision Making | Group Processes | Models, Theoretical | Intuition | Fuzzy Logic | Humans | Decision-making | Fuzzy sets | Set theory | Usage | Research | Statistics | Decision support systems | Studies | Operators | Decision making | Linguistics | Values | Reliability analysis | Methods | Cybernetics

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 10

.../\pi]^{2}$ are the arithmetic, geometric and special quasi-arithmetic means of a and b, respectively.

26E60 | quasi-arithmetic mean | Analysis | arithmetic mean | Mathematics, general | Mathematics | Applications of Mathematics | 33E05 | Gaussian hypergeometric function | geometric mean | complete elliptic integral | MATHEMATICS, APPLIED | FUNCTIONAL INEQUALITIES | CONVEXITY | APPROXIMATIONS | MONOTONICITY | MATHEMATICS | COMPLETE ELLIPTIC INTEGRALS | 1ST | RESPECT | KIND | TRANSFORMATION INEQUALITIES | Arithmetic | Research

26E60 | quasi-arithmetic mean | Analysis | arithmetic mean | Mathematics, general | Mathematics | Applications of Mathematics | 33E05 | Gaussian hypergeometric function | geometric mean | complete elliptic integral | MATHEMATICS, APPLIED | FUNCTIONAL INEQUALITIES | CONVEXITY | APPROXIMATIONS | MONOTONICITY | MATHEMATICS | COMPLETE ELLIPTIC INTEGRALS | 1ST | RESPECT | KIND | TRANSFORMATION INEQUALITIES | Arithmetic | Research

Journal Article

PloS one, ISSN 1932-6203, 2018, Volume 13, Issue 3, p. e0193027

...), and the Hamy mean (HM) operator is a good tool to deal with multiple attribute group decision making (MAGDM...

SYMMETRIC FUNCTION | MODEL | AGGREGATION OPERATORS | MULTIDISCIPLINARY SCIENCES | ENTROPY | Decision-making | Analysis

SYMMETRIC FUNCTION | MODEL | AGGREGATION OPERATORS | MULTIDISCIPLINARY SCIENCES | ENTROPY | Decision-making | Analysis

Journal Article

Journal of function spaces, ISSN 2314-8888, 2019, Volume 2019, pp. 1 - 7

In the article, we provide several sharp bounds for the Toader mean by use of certain combinations of the arithmetic, quadratic, contraharmonic, and Gaussian...

MATHEMATICS | COMPLETE ELLIPTIC INTEGRALS | MATHEMATICS, APPLIED | FUNCTIONAL INEQUALITIES | BOUNDS | Questions and answers | Bivariate analysis | Mathematics | Applied mathematics | Integrals | Arithmetic | Inequality

MATHEMATICS | COMPLETE ELLIPTIC INTEGRALS | MATHEMATICS, APPLIED | FUNCTIONAL INEQUALITIES | BOUNDS | Questions and answers | Bivariate analysis | Mathematics | Applied mathematics | Integrals | Arithmetic | Inequality

Journal Article

The American mathematical monthly, ISSN 1930-0972, 2018, Volume 108, Issue 9, pp. 797 - 812

Formulations of the geometric mean generalize to a rather remarkable variety of contexts and applications...

Algebra | Cones | Geometric mean | Eigenvalues | Hilbert spaces | Matrices | Mathematical inequalities | Arithmetic mean | Riccati equation | Symmetry | MATHEMATICS | JORDAN ALGEBRAS | POSITIVE-DEFINITE MATRICES | OPERATORS | INTERIOR-POINT ALGORITHMS | Geometry

Algebra | Cones | Geometric mean | Eigenvalues | Hilbert spaces | Matrices | Mathematical inequalities | Arithmetic mean | Riccati equation | Symmetry | MATHEMATICS | JORDAN ALGEBRAS | POSITIVE-DEFINITE MATRICES | OPERATORS | INTERIOR-POINT ALGORITHMS | Geometry

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2017, Volume 69, Issue 1, pp. 25 - 51

... if a related function is X-mean-periodic for some appropriate functional space X. Building on the work of Masatoshi Suzuki for modular elliptic curves, we will explore the dual...

Arithmetic schemes | Automorphic representations | Zeta functions | L-functions | Mean-periodicity | arithmetic schemes | MATHEMATICS | zeta functions | mean-periodicity | automorphic representations

Arithmetic schemes | Automorphic representations | Zeta functions | L-functions | Mean-periodicity | arithmetic schemes | MATHEMATICS | zeta functions | mean-periodicity | automorphic representations

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 6

In this paper, we refine and generalize some weighted arithmetic–geometric operator mean inequalities due to Lin (Stud. Math. 215:187–194, 2013) and Zhang (Banach J. Math. Anal. 9:166–172, 2015) as follows...

Positive linear map | Weighted geometric operator mean | Weighted arithmetic operator mean | Analysis | Operator inequality | Mathematics, general | Mathematics | Applications of Mathematics | 47A63 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Inequalities | Arithmetic | Research

Positive linear map | Weighted geometric operator mean | Weighted arithmetic operator mean | Analysis | Operator inequality | Mathematics, general | Mathematics | Applications of Mathematics | 47A63 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Inequalities | Arithmetic | Research

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2013, Volume 438, Issue 4, pp. 1564 - 1569

The weighted Riemannian mean of positive definite matrices is a kind of weighted geometric mean of n matrices...

Arithmetic–geometric mean inequality | Matrix inequality | The Riemannian mean | Geometric mean | Positive definite matrix | Arithmetic-geometric mean inequality | MATHEMATICS | MATHEMATICS, APPLIED | Equality

Arithmetic–geometric mean inequality | Matrix inequality | The Riemannian mean | Geometric mean | Positive definite matrix | Arithmetic-geometric mean inequality | MATHEMATICS | MATHEMATICS, APPLIED | Equality

Journal Article

International Journal of Theoretical and Applied Finance, ISSN 0219-0249, 03/2018, Volume 21, Issue 2

We solve the problems of mean–variance hedging (MVH) and mean–variance portfolio selection (MVPS...

deterministic strategies | Mean-variance hedging | quadratic optimization problems | partial information | restricted information | mean-variance portfolio selection | financial markets | type (A) semimartingales | Trading | Hedging | Transformation | Put & call options | Optimization | Arithmetic

deterministic strategies | Mean-variance hedging | quadratic optimization problems | partial information | restricted information | mean-variance portfolio selection | financial markets | type (A) semimartingales | Trading | Hedging | Transformation | Put & call options | Optimization | Arithmetic

Journal Article

Natural Hazards, ISSN 0921-030X, 2/2017, Volume 85, Issue 3, pp. 1297 - 1322

.... They found the equation fit observed data well both globally and for particular regions. In conventional G–R relation, N(M) represents an arithmetic mean...

Earth Sciences | Logarithmic mean | Hydrogeology | Natural Hazards | Logarithmic standard deviation | Civil Engineering | Geotechnical Engineering & Applied Earth Sciences | Geophysics/Geodesy | Arithmetic mean | Arithmetic standard deviation | Environmental Management | M-W MAGNITUDES | GEOSCIENCES, MULTIDISCIPLINARY | CATALOG | CALIFORNIA | WATER RESOURCES | EARTHQUAKES | METEOROLOGY & ATMOSPHERIC SCIENCES | Earthquakes | Seismology | Median | Standard deviation | Aftershocks | Mathematical analysis | Representations | Catalogs | Information centers | Seismicity | Arithmetic

Earth Sciences | Logarithmic mean | Hydrogeology | Natural Hazards | Logarithmic standard deviation | Civil Engineering | Geotechnical Engineering & Applied Earth Sciences | Geophysics/Geodesy | Arithmetic mean | Arithmetic standard deviation | Environmental Management | M-W MAGNITUDES | GEOSCIENCES, MULTIDISCIPLINARY | CATALOG | CALIFORNIA | WATER RESOURCES | EARTHQUAKES | METEOROLOGY & ATMOSPHERIC SCIENCES | Earthquakes | Seismology | Median | Standard deviation | Aftershocks | Mathematical analysis | Representations | Catalogs | Information centers | Seismicity | Arithmetic

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 22

In 2016 we proved that for every symmetric, repetition invariant and Jensen concave mean M the Kedlaya-type inequality A(x(1), M(x(1), x(2)), ... , M(x(1), ... , x(n))) <= M(x(1), A(x(1), x(2)), ... , A(x(1), ... , x(n...

Kedlaya inequality | MATHEMATICS, APPLIED | Jensen convexity | DEVIATION MEANS | Discrete mean | HARDYS INEQUALITY | Gini mean | Concavity | Quasi-arithmetic mean | MATHEMATICS | Weighted mean | VALUES | MIXED MEANS | Power mean | Deviation mean | Inequality | Mathematics - Classical Analysis and ODEs | 39B62 | Research | 26D15

Kedlaya inequality | MATHEMATICS, APPLIED | Jensen convexity | DEVIATION MEANS | Discrete mean | HARDYS INEQUALITY | Gini mean | Concavity | Quasi-arithmetic mean | MATHEMATICS | Weighted mean | VALUES | MIXED MEANS | Power mean | Deviation mean | Inequality | Mathematics - Classical Analysis and ODEs | 39B62 | Research | 26D15

Journal Article