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

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Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making

International journal of intelligent systems, ISSN 0884-8173, 2018, Volume 33, Issue 7, pp. 1426 - 1458

The generalized Heronian mean and geometric Heronian mean operators provide two aggregation operators that consider the interdependent phenomena among the aggregated arguments...

multiple attribute decision making | q‐rung orthopair fuzzy sets | Pythagorean fuzzy set | q‐rung orthopair fuzzy weighted geometric Heronian mean operator | enterprise resource planning system | q‐rung orthopair fuzzy generalized weighted Heronian mean operator | q‐rung orthopair 2‐tuple linguistic sets | q-rung orthopair fuzzy generalized weighted Heronian mean operator | q-rung orthopair fuzzy weighted geometric Heronian mean operator | q-rung orthopair 2-tuple linguistic sets | q-rung orthopair fuzzy sets | INFORMATION | LINGUISTIC AGGREGATION OPERATORS | RELATIONAL ANALYSIS METHOD | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | REPRESENTATION MODEL | SETS | EINSTEIN OPERATIONS | SIMILARITY MEASURES | TOPSIS | ENTROPY | Decision-making | Human resource departments | Computer programs | Fuzzy sets | Operators | Enterprise resource planning | Hierarchies | Decision making | Internet resources

multiple attribute decision making | q‐rung orthopair fuzzy sets | Pythagorean fuzzy set | q‐rung orthopair fuzzy weighted geometric Heronian mean operator | enterprise resource planning system | q‐rung orthopair fuzzy generalized weighted Heronian mean operator | q‐rung orthopair 2‐tuple linguistic sets | q-rung orthopair fuzzy generalized weighted Heronian mean operator | q-rung orthopair fuzzy weighted geometric Heronian mean operator | q-rung orthopair 2-tuple linguistic sets | q-rung orthopair fuzzy sets | INFORMATION | LINGUISTIC AGGREGATION OPERATORS | RELATIONAL ANALYSIS METHOD | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | REPRESENTATION MODEL | SETS | EINSTEIN OPERATIONS | SIMILARITY MEASURES | TOPSIS | ENTROPY | Decision-making | Human resource departments | Computer programs | Fuzzy sets | Operators | Enterprise resource planning | Hierarchies | Decision making | Internet resources

Journal Article

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Lévy–Khintchine Representations of the Weighted Geometric Mean and the Logarithmic Mean

Mediterranean journal of mathematics, ISSN 1660-5454, 2013, Volume 11, Issue 2, pp. 315 - 327

...”, establish Lévy–Khintchine representations of the weighted geometric mean and the logarithmic mean by Cauchy integral formula, and obtain that the weighted geometric mean and the logarithmic mean are complete...

26E60 | Bernstein function | degree | Mathematics | 44A20 | Primary 30E20 | complete Bernstein function | Secondary 26A48 | Cauchy integral formula | Mathematics, general | weighted geometric mean | logarithmic mean | Lévy–Khintchine representation | completely monotonic degree | Lévy-Khintchine representation | MATHEMATICS | MATHEMATICS, APPLIED | Levy-Khintchine representation | GAMMA FUNCTION

26E60 | Bernstein function | degree | Mathematics | 44A20 | Primary 30E20 | complete Bernstein function | Secondary 26A48 | Cauchy integral formula | Mathematics, general | weighted geometric mean | logarithmic mean | Lévy–Khintchine representation | completely monotonic degree | Lévy-Khintchine representation | MATHEMATICS | MATHEMATICS, APPLIED | Levy-Khintchine representation | GAMMA FUNCTION

Journal Article

Annals of mathematics, ISSN 0003-486X, 2012, Volume 175, Issue 2, pp. 755 - 833

It has long been conjectured that starting at a generic smooth closed embedded surface in R 3 , the mean curvature flow remains smooth until it arrives at a singularity in a neighborhood of which the...

Tangents | Varifolds | Critical points | Hypersurfaces | Eigenvalues | Eigenfunctions | Polynomials | Mathematics | Entropy | Curvature | SPACE | MATHEMATICS | REGULARITY | THEOREM | SHAPES | CONSTRUCTION | MONOTONICITY | SELF-SIMILAR SURFACES | EMBEDDED MINIMAL-SURFACES | FIXED GENUS

Tangents | Varifolds | Critical points | Hypersurfaces | Eigenvalues | Eigenfunctions | Polynomials | Mathematics | Entropy | Curvature | SPACE | MATHEMATICS | REGULARITY | THEOREM | SHAPES | CONSTRUCTION | MONOTONICITY | SELF-SIMILAR SURFACES | EMBEDDED MINIMAL-SURFACES | FIXED GENUS

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2004, Volume 385, Issue 1-3, pp. 305 - 334

We propose a definition for geometric mean of k positive (semi) definite matrices. We show that our definition is the only one in the literature that has the...

Positive semidefinite matrix | Matrix inequality | Geometric mean | Matrix square root | Spectral radius | matrix square root | MATHEMATICS, APPLIED | positive semidefinite matrix | spectral radius | geometric mean | matrix inequality

Positive semidefinite matrix | Matrix inequality | Geometric mean | Matrix square root | Spectral radius | matrix square root | MATHEMATICS, APPLIED | positive semidefinite matrix | spectral radius | geometric mean | matrix inequality

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

Applied soft computing, ISSN 1568-4946, 2019, Volume 78, pp. 595 - 613

The geometric Bonferroni mean (GeoBM), which was designed as a primitive attempt to extend the Bonferroni mean (BM...

Linguistic 2-tuple | Aggregation function | Geometric Bonferroni mean | Generalized Bonferroni mean | Generalized extended Bonferroni mean | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OWA OPERATOR | INFORMATION | MODEL | AGGREGATION FUNCTIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Decision-making | Analysis

Linguistic 2-tuple | Aggregation function | Geometric Bonferroni mean | Generalized Bonferroni mean | Generalized extended Bonferroni mean | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OWA OPERATOR | INFORMATION | MODEL | AGGREGATION FUNCTIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Decision-making | Analysis

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 9

This note aims to generalize the reverse weighted arithmetic–geometric mean inequality of n positive invertible operators due to Lawson and Lim...

Lawson–Lim geometric mean | Kantorovich constant | 15A45 | Analysis | Ando–Li–Mathias geometric mean | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | Karcher mean | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | Ando-Li-Mathias geometric mean | KANTOROVICH INEQUALITY | Lawson-Lim geometric mean | Operators | Research

Lawson–Lim geometric mean | Kantorovich constant | 15A45 | Analysis | Ando–Li–Mathias geometric mean | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | Karcher mean | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | Ando-Li-Mathias geometric mean | KANTOROVICH INEQUALITY | Lawson-Lim geometric mean | Operators | Research

Journal Article

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Pythagorean Fuzzy Maclaurin Symmetric Mean Operators in Multiple Attribute Decision Making

International journal of intelligent systems, ISSN 0884-8173, 2018, Volume 33, Issue 5, pp. 1043 - 1070

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values...

GEOMETRIC AGGREGATION OPERATORS | TOPSIS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | SETS | ENTROPY | Decision-making | Fuzzy logic | Fuzzy sets | Operators | Decision making | Multisensor fusion | Data integration | Feasibility studies | Comparative analysis

GEOMETRIC AGGREGATION OPERATORS | TOPSIS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | SETS | ENTROPY | Decision-making | Fuzzy logic | Fuzzy sets | Operators | Decision making | Multisensor fusion | Data integration | Feasibility studies | Comparative analysis

Journal Article

Pattern Recognition, ISSN 0031-3203, 03/2018, Volume 75, pp. 188 - 198

•We developed a geometric mean distance metric learning algorithm for high-dimensional multi-modal data...

Efficiency | Geometric mean | Multi-modality | Metric learning | FACE RECOGNITION | SIMILARITY | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer science | Distance education | Algorithms | Data mining | Machine learning

Efficiency | Geometric mean | Multi-modality | Metric learning | FACE RECOGNITION | SIMILARITY | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer science | Distance education | Algorithms | Data mining | Machine learning

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 03/2015, Volume 63, Issue 3, pp. 636 - 649

In this paper, from the viewpoint of the Ando-Hiai inequality, we make a comparison among three geometric means...

unitarily invariant norm | Specht ratio | matrix geometric mean | Kantorovich constant | Ando-Li-Mathias geometric mean | Ando-Hiai inequality | Karcher mean | chaotic geometric mean | Ando–Li–Mathias geometric mean | Ando–Hiai inequality | INEQUALITIES | 47A64 | 47A30 | 47A63 | MATHEMATICS | Inequality | Constants | Complement | Algebra | Chaos theory | Inequalities | Images

unitarily invariant norm | Specht ratio | matrix geometric mean | Kantorovich constant | Ando-Li-Mathias geometric mean | Ando-Hiai inequality | Karcher mean | chaotic geometric mean | Ando–Li–Mathias geometric mean | Ando–Hiai inequality | INEQUALITIES | 47A64 | 47A30 | 47A63 | MATHEMATICS | Inequality | Constants | Complement | Algebra | Chaos theory | Inequalities | Images

Journal Article

The Annals of statistics, ISSN 0090-5364, 2005, Volume 33, Issue 3, pp. 1225 - 1259

This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds...

Glaucoma | Riemann manifold | Statistical theories | Geometric shapes | Coordinate systems | Landmarks | Sample mean | Mathematical vectors | Nonparametric Theory and Methods | Covariance matrices | Bootstrap resampling | Bootstrapping | Confidence regions | Central limit theorem | Extrinsic mean | Fréchet mean | LOCATION | bootstrapping | central limit theorem | SHAPE | BOOTSTRAP | IMAGE | STATISTICS & PROBABILITY | extrinsic mean | Frechet mean | confidence regions | 62H10 | 62H11

Glaucoma | Riemann manifold | Statistical theories | Geometric shapes | Coordinate systems | Landmarks | Sample mean | Mathematical vectors | Nonparametric Theory and Methods | Covariance matrices | Bootstrap resampling | Bootstrapping | Confidence regions | Central limit theorem | Extrinsic mean | Fréchet mean | LOCATION | bootstrapping | central limit theorem | SHAPE | BOOTSTRAP | IMAGE | STATISTICS & PROBABILITY | extrinsic mean | Frechet mean | confidence regions | 62H10 | 62H11

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

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Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean

Expert systems with applications, ISSN 0957-4174, 2009, Volume 36, Issue 2, pp. 1195 - 1207

Failure mode and effects analysis (FMEA) has been extensively used for examining potential failures in products, processes, designs and services. An important...

Fuzzy logic | Fuzzy weighted geometric mean | Failure mode and effects analysis | Centroid defuzzification | Fuzzy risk priority numbers | SYSTEM | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FMEA | PROGRAMMING APPROACH | INFERENCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Risk assessment

Fuzzy logic | Fuzzy weighted geometric mean | Failure mode and effects analysis | Centroid defuzzification | Fuzzy risk priority numbers | SYSTEM | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FMEA | PROGRAMMING APPROACH | INFERENCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Risk assessment

Journal Article