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On the weighted geometric mean of accretive matrices
Annals of Functional Analysis, 2020In this paper, we discuss new inequalities for accretive matrices through non-standard domains. In particular, we present several relations for Ar\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage ...
Yassine Bedrani +2 more
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Geometric-Mean Policy Optimization
arXiv.orgGroup Relative Policy Optimization (GRPO) has significantly enhanced the reasoning capability of large language models by optimizing the arithmetic mean of token-level rewards.
Yuzhong Zhao +11 more
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Enhancing the structural performance of engineering components using the geometric mean optimizer
Materials TestingIn this article, a newly developed optimization approach based on a mathematics technique named the geometric mean optimization algorithm is employed to address the optimization challenge of the robot gripper, airplane bracket, and suspension arm of ...
Pranav Mehta +3 more
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Forum Mathematicum, 2012
In the recent years, many authors have discussed the geometric mean of \(n\) positive definite matrices. We have three types of geometric means which have at least ten nice properties. One of them is called BMP mean, which is defined by using symmetrization procedures [\textit{D. A. Bini}, \textit{B. Meini} and \textit{F. Poloni}, Math. Comput. 79, No.
Lawson, Jimmie, Lee, Hosoo, Lim, Yongdo
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In the recent years, many authors have discussed the geometric mean of \(n\) positive definite matrices. We have three types of geometric means which have at least ten nice properties. One of them is called BMP mean, which is defined by using symmetrization procedures [\textit{D. A. Bini}, \textit{B. Meini} and \textit{F. Poloni}, Math. Comput. 79, No.
Lawson, Jimmie, Lee, Hosoo, Lim, Yongdo
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The Journal of Financial and Quantitative Analysis, 1983
In 1959, Henry Latana [2] proposed an approximation to the geometric mean that was a simple function of the arithmetic mean and variance, thereby indicating a mathematical relationship between the risky investment choice model of Bernoulli and the Markowitz mean-variance model. In 1969, Young and Trent [4] presented empirical test results of the Latane
William H. Jean, Billy P. Helms
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In 1959, Henry Latana [2] proposed an approximation to the geometric mean that was a simple function of the arithmetic mean and variance, thereby indicating a mathematical relationship between the risky investment choice model of Bernoulli and the Markowitz mean-variance model. In 1969, Young and Trent [4] presented empirical test results of the Latane
William H. Jean, Billy P. Helms
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Multi-View Geometric Mean Metric Learning for Kinship Verification
International Conference on Information Photonics, 2019This paper proposes a multi-view geometric mean metric learning (MvGMML) method for the real-world kinship verification from facial images. Unlike existing kinship verification methods which dramatically degrade their performance when facial images are ...
Junlin Hu, Jiwen Lu, Li Liu, Jie Zhou
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Instance selection improves geometric mean accuracy: a study on imbalanced data classification
Progress in Artificial Intelligence, 2018A natural way of handling imbalanced data is to attempt to equalise the class frequencies and train the classifier of choice on balanced data. For two-class imbalanced problems, the classification success is typically measured by the geometric mean (GM ...
L. Kuncheva +3 more
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Noncommutative geometric means
The Mathematical Intelligencer, 2006This is an excellent article on the problems met in extending the notion of means to positive definite matrices. It should be read by all interested in means. A reasonable set of conditions that a mean \(M\) should satisfy are: (i) \(M(A_1, \dots,M_n)\) is invariant under any permutation of the matrices \(A_i, i\leq i\leq n\); (ii) \(M\) is increasing ...
Bhatia, Rajendra, Holbrook, John
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Canadian Mathematical Bulletin, 1989
AbstractThe aim of this paper is two-fold: First we prove the Radotype inequality Here denote the weighted geometric means of with where the pi are positive weights. Thereafter we investigate under which conditions the sequence is convergent as n → ∞
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AbstractThe aim of this paper is two-fold: First we prove the Radotype inequality Here denote the weighted geometric means of with where the pi are positive weights. Thereafter we investigate under which conditions the sequence is convergent as n → ∞
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Geometric Mean for Subspace Selection
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia ...
Dacheng, Tao +3 more
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