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Zuzanna Szancer - One of the best experts on this subject based on the ideXlab platform.
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On $$\widetilde{J}$$J~ -tangent Affine Hyperspheres
Results in Mathematics, 2020Co-Authors: Zuzanna SzancerAbstract:In this paper we study $$\widetilde{J}$$-tangent affine Hyperspheres, where $$\widetilde{J}$$ is the canonical para-complex structure on $$\mathbb {R}^{2n+2}$$. The main purpose of this paper is to give a classification of $$\widetilde{J}$$-tangent affine Hyperspheres of an arbitrary dimension with an involutive distribution $$\mathcal {D}$$. In particular, we classify all such Hyperspheres in the 3-dimensional case. We also show that there is a direct relation between $$\widetilde{J}$$-tangent affine Hyperspheres and Calabi products. As an application we obtain certain classification results. In particular, we show that, with one exception, all odd dimensional proper flat affine Hyperspheres are, after a suitable affine transformation, $$\widetilde{J}$$-tangent. Some examples of $$\widetilde{J}$$-tangent affine Hyperspheres are also given.
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On $\widetilde{J}$-tangent affine Hyperspheres
arXiv: Differential Geometry, 2018Co-Authors: Zuzanna SzancerAbstract:In this paper we study $\widetilde{J}$-tangent affine Hyperspheres, where $\widetilde{J}$ is the canonical para-complex structure on $\mathbb{R}^{2n+2}$. The main purpose of this paper is to give a classification of $\widetilde{J}$-tangent affine Hyperspheres of an arbitrary dimension with an involutive distribution $\mathcal{D}$. In particular, we classify all such Hyperspheres in the $3$-dimensional case. We also show that there is a direct relation between $\widetilde{J}$-tangent affine Hyperspheres and Calabi products. As an application we obtain certain classification results. In particular, we show that, with one exception, all odd dimensional proper flat affine Hyperspheres are, after a suitable affine transformation, $\widetilde{J}$-tangent. Some examples of $\widetilde{J}$-tangent affine Hyperspheres are also given.
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On Para-Complex Affine Hyperspheres
Results in Mathematics, 2017Co-Authors: Zuzanna SzancerAbstract:In this paper we introduce a notion of a para-complex affine Hypersphere. We give a complete local classification of such hypersurfaces and give several examples. It turns out that every para-complex affine Hypersphere can be constructed from (real) affine Hyperspheres. As an application, we classify all 2-dimensional para-complex affine Hyperspheres.
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J -Tangent Affine Hyperspheres
Results in Mathematics, 2014Co-Authors: Zuzanna SzancerAbstract:In this paper we study J-tangent affine Hyperspheres. Under some additional conditions we give a local characterization of 3-dimensional J-tangent affine Hyperspheres.
Luc Vrancken - One of the best experts on this subject based on the ideXlab platform.
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On product affine Hyperspheres in ℝ n+1
Science China Mathematics, 2019Co-Authors: Xiuxiu Cheng, Marilena Moruz, Luc VranckenAbstract:In this paper, we study locally strongly convex affine Hyperspheres in the unimodular affine space ℝn+1 which, as Riemannian manifolds, are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional curvature. As the main result, a complete classification of such affine Hyperspheres is established. Moreover, as direct consequences, 3- and 4-dimensional affine Hyperspheres with parallel Ricci tensor are also classified.
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On product affine Hyperspheres in $\mathbb{R}^{n+1}$
arXiv: Differential Geometry, 2018Co-Authors: Xiuxiu Cheng, Marilena Moruz, Luc VranckenAbstract:In this paper, we study locally strongly convex affine Hyperspheres in the unimodular affine space $\mathbb{R}^{n+1}$ which, as Riemannian manifolds, are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional curvatures. As the main result, a complete classification of such affine Hyperspheres is established. Moreover, as direct consequences, affine Hyperspheres of dimensions 3 and 4 with parallel Ricci tensor are also classified.
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WITH CONSTANT AFFINE SECTIONAL CURVATURE
2016Co-Authors: Marcus Kriele, Luc VranckenAbstract:We study affine Hyperspheres M with constant sectional curvature (with respect to the affine metric h). A conjecture by M. Magid and P. Ryan states that every such affine Hypersphere with nonzero Pick invariant is affinely equivalent to either (X2 ? X2)(X2 ? X2) ... (X2m_ X2m) 1 or (X2 ? X2)(X2 ? X2) ... (X2m_ ? Xm)X2m+1 1 where the dimension n satisfies n - 2m - 1 or n - 2m. Up to now, this conjecture was proved if M is positive definite or if M is a 3-dimensional Lorentz space. In this paper, we give an affirmative answer to this conjecture for arbitrary dimensional Lorentzian affine Hyperspheres.
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Characterizations of the Calabi Product of Hyperbolic Affine Hyperspheres
Results in Mathematics, 2008Co-Authors: Luc VranckenAbstract:There exists a well known construction which allows to associate with two hyperbolic affine Hyperspheres \(f_{i} : M^{n_{i}}_{i} \rightarrow {\mathbb{R}}^{n_{i}+1}\) a new hyperbolic affine Hypersphere immersion of \(I \times M_{1} \times M_{2}\) into \({\mathbb{R}}^{n_{1}+n_{2}+2}\). In this paper we deal with the inverse problem: how to determine from properties of the difference tensor whether a given hyperbolic affine Hypersphere immersion of a manifold \(M^{n} \rightarrow R^{n+1}\) can be decomposed in such a way.
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lorentzian affine Hyperspheres with constant affine sectional curvature
Transactions of the American Mathematical Society, 2000Co-Authors: Marcus Kriele, Luc VranckenAbstract:We study ane Hyperspheres M with constant sectional curvature (with respect to the ane metric h). A conjecture by M. Magid and P. Ryan states that every such ane Hypersphere with nonzero Pick invariant is anely equivalent to either where the dimension n satises n =2 m 1o rn =2 m .U p to now, this conjecture was proved if M is positive denite or if M is a 3-dimensional Lorentz space. In this paper, we give an armative answer to this conjecture for arbitrary dimensional Lorentzian ane Hyperspheres.
Xinjun Peng - One of the best experts on this subject based on the ideXlab platform.
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a structural information based twin Hypersphere support vector machine classifier
International Journal of Machine Learning and Cybernetics, 2017Co-Authors: Xinjun Peng, Lingyan Kong, Dongjing ChenAbstract:Twin-Hypersphere support vector machine (THSVM) for binary pattern recognition aims at generating two Hyperspheres in the feature space such that each Hypersphere contains as many as possible samples in one class and is as far as possible from the other one. THSVM has a fast learning speed since it solves two small sized support vector machine (SVM)-type quadratic programming problems (QPPs). However, it only simply considers the prior class-based structural information in the optimization problems. In this paper, a structural information-based THSVM (STHSVM) classifier for binary classification is presented. This proposed STHSVM focuses on the cluster-based structural information of the corresponding class in each optimization problem, which is vital for designing a good classifier in different real-world problems. In addition, it also leads to a fast learning speed since this STHSVM solves a series of smaller-sized QPPs compared with THSVM. Experimental results demonstrate that STHSVM is superior in generalization performance to other classifiers.
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twin support vector Hypersphere tsvh classifier for pattern recognition
Neural Computing and Applications, 2014Co-Authors: Xinjun PengAbstract:Motivated by the support vector data description, a classical one-class support vector machine, and the twin support vector machine classifier, this paper formulates a twin support vector Hypersphere (TSVH) classifier, a novel binary support vector machine (SVM) classifier that determines a pair of Hyperspheres by solving two related SVM-type quadratic programming problems, each of which is smaller than that of a conventional SVM, which means that this TSVH is more efficient than the classical SVM. In addition, the TSVH successfully avoids matrix inversion compared with the twin support vector machine, which indicates learning algorithms of the SVM can be easily extended to this TSVH. Computational results on several synthetic as well as benchmark data sets indicate that the proposed TSVH is not only faster, but also obtains better generalization.
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a twin Hypersphere support vector machine classifier and the fast learning algorithm
Information Sciences, 2013Co-Authors: Xinjun PengAbstract:This paper formulates a twin-Hypersphere support vector machine (THSVM) classifier for binary recognition. Similar to the twin support vector machine (TWSVM) classifier, this THSVM determines two Hyperspheres by solving two related support vector machine (SVM)-type problems, each one is smaller than the classical SVM, which makes the THSVM be more efficient than the classical SVM. In addition, the THSVM avoids the matrix inversions in its two dual quadratic programming problems (QPPs) compared with the TWSVM. By considering the characteristics of the dual QPPs of THSVM, an efficient Gilbert's algorithm for the THSVM based on the reduced convex hull (RCH) instead of directly optimizing its pair of QPPs is further presented. Computational results on several synthetic as well as benchmark datasets indicate the significant advantages of the THSVM classifier in the computational time and test accuracy.
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least squares twin support vector Hypersphere ls tsvh for pattern recognition
Expert Systems With Applications, 2010Co-Authors: Xinjun PengAbstract:The twin support vector Hypersphere (TSVH) is a novel efficient pattern recognition tool, because it determines a pair of Hyperspheres by solving two related SVM-type problems, each of which is smaller than in a classical SVM. In this paper we formulate a least squares version for this classifier, termed as the least squares twin support vector Hypersphere (LS-TSVH). This formulation leads to extremely simple and fast algorithm for generating binary classifier based on a pair of Hyperspheres. Due to equality type constraints in the formulation, the solution follows from solving two sets of nonlinear equations, instead of the two dual quadratic programming problems (QPPs) for TSVH. We show that the two sets of nonlinear equations are solved using the well-known Newton downhill algorithm. The effectiveness of proposed LS-TSVH is demonstrated by experimental results on several artificial and benchmark datasets.
Nicolas Le Bihan - One of the best experts on this subject based on the ideXlab platform.
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von Mises-Fisher approximation of multiple scattering process on the Hypersphere
2013Co-Authors: Florent Chatelain, Nicolas Le BihanAbstract:This paper presents a ''method of moments'' estimation technique for the study of multiple scattering on the Hypersphere. The proposed model is similar to a compound Poisson process evolving on a special manifold: the unit Hypersphere. The presented work makes use of an approximation result for multiply convolved von Mises-Fisher distributions on Hyperspheres. Comparison with other approximations show the accuracy of the proposed model to provide estimators for the mean free path and concentration parameters when studying a multiple scattering process. Such a process is classically used to model the propagation of waves or particules in random media.
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ICASSP - Von Mises-Fisher approximation of multiple scattering process on the Hypersphere
2013 IEEE International Conference on Acoustics Speech and Signal Processing, 2013Co-Authors: Florent Chatelain, Nicolas Le BihanAbstract:This paper presents a “method of moments” estimation technique for the study of multiple scattering on the Hypersphere. The proposed model is similar to a compound Poisson process evolving on a special manifold: the unit Hypersphere. The presented work makes use of an approximation result for multiply convolved von Mises-Fisher distributions on Hyperspheres. Comparison with other approximations show the accuracy of the proposed model to provide estimators for the mean free path and concentration parameters when studying a multiple scattering process. Such a process is classically used to model the propagation of waves or particles in random media.
Hailing Zhang - One of the best experts on this subject based on the ideXlab platform.
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State evaluation of Power-Shift Steering Transmission based on Hypersphere support vector machine
2010 IEEE International Conference on Mechatronics and Automation, 2010Co-Authors: Yingfeng Zhang, Lili Cui, Hailing ZhangAbstract:The Hypersphere support vector machine is an efficient method to evaluate the state of mechanism. The state of Power-Shift Steering Transmission (PSST) is studied using Hypersphere support vector machine. The theory of Hypersphere support vector machine is researched and an evaluation model is developed. The generalization of the model is analyzed. The spectrometric oil analysis data are processed using Principal Component Analysis (PCA) method and the selection of parameters is made. The influence of abnormal for performance of Hypersphere support vector machine is analyzed. On the basis of training samples, the state of test samples is evaluated. It has been proved that Hypersphere support vector machine is suitable for evaluating the state of PSST. Moreover, the correct rate of model can be improved greatly if abnormal samples are taken into account.