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geometric algorithms for parametric-margin ν-support vector machine

NEUROCOMPUTING 2013年 99卷 197-205页

作者： Peng, Xinjun Xu, Dong Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China

The parametric-margin nu-support vector machine (par-nu-SVM) is a useful classifier in many cases, especially when the noise is heteroscedastic. In this paper, the geometric interpretation for the par-nu-SVM is described, which is equivalent to finding a couple of points in two disjoint mu-reduced convex hulls (mu-RCHs) by simultaneously minimizing the square distance and maximizing the square norm of their sum with a weight factor 1/(c nu) given by users. Motivated by the Gilbert-Schlesinger-Kozinec (GSK) and Mitchell-Dem'yanov-Malozemov (MDM) algorithms, two geometric algorithms, called the parametric mu-GSK (par-mu-GSK) and parametric mu-MDM (par-mu-MDM) algorithms, are introduced to solve the par-nu-SVM. Computational results on several synthetic as well as benchmark datasets demonstrate the significant performance of the proposed algorithms in terms of both kernel operations and classification accuracy. Crown Copyright (C) 2012 Published by Elsevier B.V. All rights reserved.

关键词： Support vector machine Parametric-margin Nearest point problem Reduced convex hull geometric algorithm

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A v-twin support vector machine (v-TSVM) classifier and its geometric algorithms

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INFORMATION SCIENCES 2010年第20期180卷 3863-3875页

作者： Peng Xinjun Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China Sci Comp Key Lab Shanghai Univ Shanghai 200234 Peoples R China

In this paper, a v-twin support vector machine (v-TSVM) is presented, improving upon the recently proposed twin support vector machine (TSVM). This v-TSVM introduces a pair of parameters (v) to control the bounds of the fractions of the support vectors and the error margins. The theoretical analysis shows that this v-TSVM can be interpreted as a pair of minimum generalized Mahalanobis-norm problems on two reduced convex hulls (RCHs). Based on the well-known Gilbert's algorithm, a geometric algorithm for TSVM (GA-TSVM) and its probabilistic speed-up version, named PGA-TSVM, are presented. Computational results on several synthetic as well as benchmark datasets demonstrate the significant advantages of the proposed algorithms in terms of both computation complexity and classification accuracy. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.

关键词： Pattern recognition Twin support vector machine geometric interpretation geometric algorithm Probabilistic speed-up strategy

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Point-tangent/point-normal B-spline curve interpolation by geometric algorithms

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COMPUTER-AIDED DESIGN 2009年第6期41卷 412-422页

作者： Gofuku, Shu-ichi Tamura, Shigefumi Maekawa, Takashi Yokohama Natl Univ Dept Mech Engn Digital Engn Lab Yokohama Kanagawa Japan

We introduce a novel method to interpolate a set of data points as well as unit tangent vectors or unit normal vectors at the data points by means of a B-spline curve interpolation technique using geometric algorithms. The advantages of our algorithm are that it has a compact representation, it does not require the magnitudes of the tangent vectors or normal vectors, and it has C-2 continuity. We compare our method with the conventional curve interpolation methods, namely, the standard point interpolation method, the method introduced by Piegl and Tiller, which interpolates points as well as the first derivatives at every point, and the piecewise cubic Hermite interpolation method. Examples are provided to demonstrate the effectiveness of the proposed algorithms. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Interpolation Point-normal interpolation Point-tangent interpolation geometric algorithm B-spline curve

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Optimal geometric algorithms for digitized images on arrays with reconfigurable optical buses

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MICROPROCESSORS AND MICROSYSTEMS 2006年第7期30卷 425-434页

作者： Wu, Chin-Hsiung Horng, Shi-Jinn Wang, Yuh-Rau Tsai, Horng-Ren Shih Chien Univ Dept Informat Technol & Commun Kaohsiung Taiwan Natl Taiwan Univ Sci & Technol Dept Comp Sci & Informat Engn Taipei Taiwan St Johns Univ Dept Comp Sci & Informat Engn Taipei Taiwan Ling Tung Univ Dept Informat Technol Taichung Taiwan

geometric algorithms play an important role in computer graphics and digital image analysis. This paper makes an improvement of computing geometric properties of labelled images using arrays with reconfigurable optical buses (AROB). For an N x N image, we first design two constant time algorithms for computing the leftmost one problem and for the component reallocation problem. Then, several geometric algorithms for the labelled images are derived. These include finding the border pixels, computing the perimeter and area, computing the convex hull, determining whether two figures are linearly separable, computing the smallest enclosing box, solving the nearest neighbor problems, and computing the width and diameter. The major contribution of this work is to design both time and cost optimal algorithms for these problems. To the best of our knowledge, the proposed algorithms are the first constant time algorithms for these problems on the labelled images. (C) 2006 Elsevier B.V. All rights reserved.

关键词： geometric algorithm reconfigurable optical buses pattern recognition digital geometry image labelling

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Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics

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COMPUTER PHYSICS COMMUNICATIONS 2021年 265卷 107981-107981页

作者： Xiao, Jianyuan Qin, Hong Univ Sci & Technol China Dept Plasma Phys & Fus Engn Hefei 230026 Peoples R China Princeton Univ Plasma Phys Lab POB 451 Princeton NJ 08543 USA

Since variational symplectic integrators for the guiding center was proposed [1,2], structure-preserving geometric algorithms have become an active research field in plasma physics. We found that the slow manifolds of the classical Pauli particle enable a family of structure-preserving geometric algorithms for guiding center dynamics with long-term stability and accuracy. This discovery overcomes the difficulty associated with the unstable parasitic modes for variational symplectic integrators when applied to the degenerate guiding center Lagrangian. It is a pleasant surprise that Pauli's Hamiltonian for electrons, which predated the Dirac equation and marks the beginning of particle physics, reappears in classical physics as an effective algorithm for solving an important plasma physics problem. This technique is applicable to other degenerate Lagrangians reduced from regular Lagrangians. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Guiding center motion geometric algorithm Volume preserving algorithm Discrete variation Classical Pauli particle

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geometric Properties of Ribs and Fans of a Bézier Curve

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Journal of Computer Science & Technology 2006年第2期21卷 279-283页

作者： Joo-Haeng Lee Hyungjun Park Electronics and Telecommunications Research Institute Daejeon 305-350 Korea Chosun University Gwangju 501-759 Korea

Ribs and fans are interesting geometric entities that are derived from a given Bézier curve or surface based on the recent theory of rib and fan decomposition. In this paper, we present some of new geometric properties of ribs and fans for a Bézier curve including composite fans, rib-invariant deformation, and fan-continuity in subdivision. We also give some examples for the presented properties.

关键词： geometric algorithm Bézier curve composite fan rib-invariance fan-continuity

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Digital Differential Geometry Processing

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Journal of Computer Science & Technology 2006年第5期21卷 847-860页

作者：刘新国鲍虎军彭群生 State Key Lab of CAD& CG Zhejiang University Hangzhou 310027 P.R. China

The theory and methods of digital geometry processing has been research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient, Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.

关键词： digital geometry geometric algorithm mesh editing Laplacian parameterization

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An efficient algorithm to generate random sphere packs in arbitrary domains

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2016年第8期71卷 1586-1601页

作者： Lozano, Elias Roehl, Deane Celes, Waldemar Gattass, Marcelo Pontificia Univ Catolica Rio de Janeiro Inst Tecgraf Rio de Janeiro Brazil Pontificia Univ Catolica Rio de Janeiro Dept Engn Civil Rio de Janeiro Brazil

Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. For generic domains, the generation of a sphere pack may be complex and time-consuming, especially if the pack must comply with a prescribed sphere size distribution and the stability requirements of the simulation. The primary goal of this paper is to present an efficient algorithm that is capable of producing packs with millions of spheres following a statistical sphere size distribution inside complex arbitrary domains. This algorithm uses a new strategy to ensure that the sphere size distribution is preserved even when large particles are rejected in the growing process. The paper also presents numerical results that enable an evaluation of the proposed algorithm. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Sphere packing Advancing-front approach geometric algorithm Distance field applications

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The irregular cutting-stock problem - a new procedure for deriving the no-fit polygon

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COMPUTERS & OPERATIONS RESEARCH 2001年第3期28卷 271-287页

作者： Bennell, JA Dowsland, KA Dowsland, WB Univ Wales Swansea European Business Management Sch OR Grp Swansea SA2 8PP W Glam Wales Univ Southampton Dept Management Southampton SO9 5NH Hants England

The nofit polygon is a powerful and effective tool for handling the geometry required for a range of solution approaches to two-dimensional irregular cutting-stock problems. However, unless all the pieces are convex, it is widely perceived as being difficult to implement, and its use has therefore been somewhat limited, The primary purpose of this paper is to correct this misconception by introducing a new method of calculating the nofit polygon. Although it is based on previous approaches which use the mathematical concept of Minkowski sums, this new method can be stated as a set of simple rules that can be implemented without an indepth understanding of the underlying mathematics. The result is an approach that is both very general and easy to use. Scope and purpose Cutting and packing problems involving irregular shapes are common in industries ranging from clothing and footware to engineering and shipbuilding. An important feature of any automated solution technique for such problems is the way in which the geometric calculations are handled. One of the most efficient approaches is to pre-process many of the calculations using a concept known as the nofit polygon (NFP). However, use of the NFP has been limited due to the difficulty in its calculation for arbitrary irregular pieces, This paper outlines the concept of the NFP in the context of the irregular cutting-stock problem and introduces a new simplified approach to its calculation. The aim is to make this powerful concept more easily accessible to those involved in the cutting and packing of irregular shapes, (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： irregular cutting stock problem nesting geometric algorithm

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Comparative Study on the Vertical Column Concentration Inversion algorithm of Tropospheric Trace Gas Based on the MAX-DOAS Measurement Spectrum

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REMOTE SENSING 2024年第18期16卷 3359页

作者： Wang, Haoyue Lu, Yuehua Yu, Ke Xiao, Feihong Guo, Rongzhi Yan, Naicong Wang, Weiguo Yunnan Univ Dept Atmospher Sci Kunming 650500 Peoples R China Yunnan Meteorol Observ Kunming 650032 Peoples R China

The tropospheric vertical column concentration (VCDtrop) of NO2, SO2, and HCHO was retrieved, respectively, by employing the geometric method (Geomtry), simplified model method (Model), and look-up table method (Table) with the observation spectra of the multi-axis differential absorption spectroscopy instrument (MAX-DOAS). The correlation and relative differences of the inversion results obtained by these three algorithms, as well as the changes in quantiles, were explored. The comparative analysis reveals that the more concentrated the vertical distribution height of gas components is in the near-surface layer, the better the conformity of the VCDtrop retrieved by different algorithms. However, the increase in relative differences is also related to the diurnal variation of gas components. The influence of aerosols on the inversion of the VCDtrop is greater than the change in the vertical distribution height of the gas component itself. The near-surface concentration and distribution height of gas components are the internal factors that give rise to relative differences in the inversion of the VCDtrop by different algorithms, while aerosols are one of the extremely important external reasons. The VCDtrop inverted by Geomtry without considering the influence of aerosols is generally larger except for NO2. Model sets up aerosols in accordance with the height and meteorological conditions of the atmospheric environment. Table can invert the aerosol profile in real time. Compared with Model, it shows a significant improvement in the refined setting of aerosols. Moreover, while obtaining the vertical distribution of aerosols, it can invert the diurnal variation of the VCDtrop. The VCDtrop inverted by Table is the smallest, and the relative difference with Model is on average about 10% smaller. The relative difference of the VCDtrop for the same height (aerosol optical thickness) quantile is 7-15% (about 25% lower on average). When comparing the inversion results of Ta

关键词： multi-axis differential absorption spectroscopy geometric algorithm mode simplification method look-up table method tropospheric vertical column concentration the relative differences

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