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geometric projection twin support vector machine for pattern classification

MULTIMEDIA TOOLS AND APPLICATIONS 2021年第15期80卷 23073-23089页

作者： Chen, Xiaobo Xiao, Yan Jiangsu Univ Automot Engn Res Inst Zhenjiang 212013 Jiangsu Peoples R China Jiangsu Univ Sch Automot & Traff Engn Zhenjiang 212013 Jiangsu Peoples R China

In this paper, a novel binary classifier termed as GPTSVM (projection twin support vector machine via geometric Interpretation) is presented. In the spirit of original PTSVM, GPTSVM tries to seek two projection axes, one for each class, such that the projected samples of one class are well separated from that of the other class along its own projection axis. A pair of parameters (nu) are introduced in GPTSVM to control the bounds of the fractions of the support vectors and the error margins. Moreover, GPTSVM can be interpreted as a pair of minimum Mahalanobis norm problems on two reduced convex hulls (RCHs). Then, an efficient geometric algorithm for GPTSVM is presented based on the well-known Gilbert's algorithm. By doing so, the dual problem of GPTSVM can be solved very fast without resorting to any specialized optimization toolbox. The experimental results on several UCI benchmark data sets, traffic accident prediction data, and large scale NDCC database show the feasibility and effectiveness of the proposed algorithm.

关键词： Support vector machine Quadratic programming Reduced convex hull geometric algorithm Multiple plane classifier

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Photogrammetry-based computational fluid dynamics

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2023年第PartB期417卷

作者： Wang, Xuguang Jaiswal, Monu Corpuz, Ashton M. Paudel, Shashwot Balu, Aditya Krishnamurthy, Adarsh Yan, Jinhui Hsu, Ming -Chen Univ Illinois Urbana & Champaign Dept Civil & Environm Engn 205 N Mathews Ave Urbana IL 61801 USA Iowa State Univ Dept Mech Engn 2043 Black Engn Ames IA 50011 USA

Computational fluid dynamics (CFD) is the cornerstone of the design and analysis process in many engineering applications. Not only has it been applied in the design phase, but it has also been employed for analyzing the fluid flow phenomena during the operation phase for many in-use structures, such as vehicles, buildings, and landscapes. However, creating a 3D mesh-based model of in-use structures that can be used by conventional boundary-fitted CFD methods is labor-intensive, time-consuming, and sometimes impossible. Due to the challenges introduced by geometry complexity and lack of design information, it is often difficult to perform an accurate and efficient CFD analysis of these objects. This paper aims to overcome such challenges by proposing a novel photogrammetry-based CFD framework for simulating in-use structures whose design models and analysis meshes are hard to obtain. The proposed framework integrates machine learning-based 3D point cloud reconstruction of structures from 2D images obtained from portable devices (e.g., cell phones and drones) and an immersogeometric approach that can carry out flow analysis directly on reconstructed point clouds. We first present the technical details of point cloud reconstruction techniques and the immersogeometric analysis method. We then simulate the flow past a standard 12 oz soda can reconstructed using photogrammetry and compare the results with reference solutions to assess the accuracy of the approach. Finally, the proposed photogrammetry-based CFD is applied to simulations of a bell tower and the Kavita and Lalit Bahl Smart Bridge on the University of Illinois Urbana-Champaign (UIUC) campus to demonstrate the robustness of the framework and its applicability to real-world in-use civil structures.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Photogrammetry Point cloud reconstruction geometric algorithm Deep learning Computational fluid dynamics Immersed method

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Parallel Sphere Packing for Arbitrary Domains 16th

Parallel Sphere Packing for Arbitrary Domains

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16th International Symposium on Visual Computing (ISVC)

作者： Cuba Lajo, Ruben Adrian Loaiza Fernandez, Manuel Eduardo Univ Catolica San Pablo Dept Comp Sci Arequipa Peru

ISBN: (纸本)9783030904364;9783030904357

Particle packings are methods used to fill a container with particles. These are used to simulate granular matter, which has various uses. Particle packings seek to be dense, however, particle packings are slow, they don't become completely dense, and most only work in simple containers. Currently, several techniques have been proposed to achieve a dense packing, significantly reducing packing construction time, but little progress has been seen in increasing the density of the packing. Particle packings reach an average maximum density of approximately 70% in rectangular and cylindrical containers, and 60% in arbitrary containers. The density of the packings is also known as compaction or solid fraction. The objective of this work is to make a compact packing that in arbitrary containers reaches between 60% and 70% of compaction. For this, a compact periodic packing of spheres is taken as a basis, which from the use of spheres of the same size achieves the highest compaction, that is, it is the most dense. Searched packing is made following a periodic hexagonal pattern, to this are added three sizes of spheres, which are smaller than the initial size, these spheres go in the empty spaces left by the hexagonal packing. The proposed method, reaches densities in arbitrary containers between 60% and 70% in times less than 5 min using a parallel optimization on GPU resource.

关键词： Sphere packing geometric algorithm Parallel

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Fast and efficient particle packing algorithms based on triangular mesh

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POWDER TECHNOLOGY 2020年 366卷 448-459页

作者： Zhang, Kaiyu Liu, Feng Zhao, Gaofeng Xia, Kaiwen Tianjin Univ Sch Civil Engn State Key Lab Hydraul Engn Simulat & Safety Tianjin 300072 Peoples R China Monash Univ Dept Civil Engn Clayton Vic 3800 Australia

The point of departure for the particle-based discrete element simulations is the generation of disk or sphere packing of interest domain. In this paper, based on a triangular mesh, two geometric packing algorithms are proposed for 2D problems. New disk(s) are obtained element-wise by solving system of equations, which can be easily derived according to the local topological relationships. In this way, the adjacent disks are guaranteed to be in contact with each other exactly. Related issues are discussed in detail, such as boundary treatment for good definition of the boundaries, elimination of incorrect overlaps, random perturbation for avoiding over-homogeneous packing. The main advantages of these two algorithms are the high efficiency and applicability for arbitrary domains. Furthermore, with a refined mesh, a refined packing can be easily obtained, which is a potential alternative for multiscale simulations. The proposed methods are verified by several examples. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Specimen generation Random packing Disk packing geometric algorithm Distinct element method

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Islamic geometric Patterns in Higher Dimensions

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NEXUS NETWORK JOURNAL 2020年第3期22卷 777-798页

作者： Moradzadeh, Sam Ebrahimi, Ahad Nejad Tabriz Islamic Art Univ Dept Architecture & Urbanism Azadi BlvdHak Nizami Ganjavi Sq Tabriz Iran

The purpose of this paper is to develop the Islamic geometric patterns from planar coordinates to three or higher dimensions through their repeat units. We use historical plane methods, polygons in contact (PIC) and point-joined, in our deductive approaches. The mentioned approach makes use of a novel method of tessellation that generates 3D Islamic patterns called "interior polyhedral stellations". The outputs showed that both the PIC and point-joined methods have strengths and weaknesses. Point-joined stellations are more efficient for regular repeat units and PIC is suitable for complex designs. These two methods can produce a large range of patterns and can be employed simultaneously. This study effectively answers the question regarding the gap between planar design from Muslim achievements and contemporary demands in modern art and architecture. We also propose techniques for constructing aperiodic three-dimension Islamic geometric patterns tessellation and two-point family.

关键词： Islamic ornaments geometric algorithm Space tessellation Dimensions Symmetry

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Norm-mixed twin support vector machine classifier and its geometric algorithm

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NEUROCOMPUTING 2013年 99卷 486-495页

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

In this paper, a novel classifier named norm-mixed twin support vector machine (NMTWSVM) is presented. The main idea in each primal problem of this NMTWSVM is to replace the hinge loss of the other class with the L-1-norm-based loss, which are obtained from equality constraints, such that each hyperplane is closest to the corresponding class and is as possible as far from the other class. The geometric analysis shows that the dual problems of NMTWSVM can be interpreted as a pair of minimum generalized Mahalanobis-norm problems (MGMNPs) on the two reduced affine hulls (RAHs) composed of two classes of points. As the practical application of the geometric analysis for NMTWSVM, a novel geometric algorithm is suggested based on the geometric properties of RAHs. The experimental results on several artificial and benchmark datasets indicate that the proposed algorithm not only obtains comparable accuracy, but also needs less kernel operations compared with the geometric algorithm of classical support vector machine (SVM). (C) 2012 Elsevier B.V. All rights reserved.

关键词： Support vector machine Nonparallel hyperplanes Minimum norm problem Reduced affine hull geometric algorithm

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Computing melodic templates in oral music traditions

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APPLIED MATHEMATICS AND COMPUTATION 2019年 344卷 219-229页

作者： Bereg, Sergey Diaz-Banez, Jose-Miguel Kroher, Nadine Ventura, Inmaculada Univ Texas Dallas Dept Comp Sci 800 West Campbell Rd Richardson TX 75080 USA Univ Seville Dept Appl Math 2 Camino Descubrimientos S-N Seville 41092 Spain

The term melodic template or skeleton refers to a basic melody which is subject to variation during a music performance. In many oral music traditions, these templates are implicitly passed throughout generations without ever being formalized in a score. In this work, we introduce a new geometric optimization problem, the spanning tube problem, to approximate a melodic template for a set of labeled performance transcriptions corresponding to a specific style in oral music traditions. Given a set of n piecewise linear functions, we solve the problem of finding a continuous function, f*, and a minimum value, epsilon*, such that, the vertical segment of length 2 epsilon* centered at (x, f*(x)) intersects at least p functions (p <= n). The method explored here also provide a novel tool for quantitatively assess the amount of melodic variation which occurs across performances. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Melodic skeleton geometric algorithm Oral music tradition

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Mixed-radix Naccache-Stern encryption

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JOURNAL OF CRYPTOGRAPHIC ENGINEERING 2019年第3期9卷 277-282页

作者： Geraud, Remi Naccache, David PSL Res Univ ENS CNRS Dept InformatInformat Secur Grp Paris France

In this work, we explore a combinatorial optimization problem stemming from the Naccache-Stern cryptosystem. We show that solving this problem results in bandwidth improvements, and suggest a polynomial-time approximation algorithm to find an optimal solution. Our work suggests that using optimal radix encoding results in an asymptotic 50% increase in bandwidth.

关键词： Non-linear optimization Public-key encryption geometric algorithm Naccache-Stern cryptosystem Numeration systems

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Computing optimal shortcuts for networks

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期279卷 26-37页

作者： Garijo, Delia Marquez, Alberto Rodriguez, Natalia Silveira, Rodrigo, I Univ Seville Dept Matemat Aplicada 1 Avda Reina Mercedes S-N E-41012 Seville Spain Univ Buenos Aires Dept Computat Pabellon 1Ciudad UnivC1428EGA Buenos Aires DF Argentina Univ Politecn Cataluna Dept Matemat Jordi Girona 1-3 ES-08034 Barcelona Spain

We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention recently, mostly for discrete variants of the problem. We consider a fully continuous setting, where the problem of computing distances and placing a shortcut is much harder as all points on the network, instead of only the vertices, must be taken into account. We present the first results on the computation of optimal shortcuts for general networks in this model: a polynomial time algorithm and a discretization of the problem that leads to an approximation algorithm. We also improve the general method for networks that are paths, restricted to two types of shortcuts: those with a fixed orientation and simple shortcuts. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Networks geometric algorithm Complexity Discrete optimization Graph augmentation

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Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers 27

Universal Reconfiguration of Facet-Connected Modular Robots ...

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27th Annual European Symposium on algorithms (ESA)

作者： Akitaya, Hugo A. Damian, Mirela Dujmovic, Vida Korman, Matias Parada, Irene Sacristan, Vera Arkin, Esther M. Demaine, Erik D. Flatland, Robin Palop, Belen van Renssen, Andre Tufts Univ Medford MA 02155 USA Villanova Univ Villanova PA 19085 USA Univ Ottawa Ottawa ON Canada Graz Univ Technol Graz Austria Univ Politecn Cataluna Barcelona Spain SUNY Stony Brook Stony Brook NY 11794 USA MIT 77 Massachusetts Ave Cambridge MA 02139 USA Siena Coll Loudonville NY USA Univ Valladolid Valladolid Spain Univ Sydney Sydney NSW Australia

ISBN: (纸本)9783959771245

We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precisely, we show that five extra "helper" modules ("musketeers") suffice to reconfigure the remaining n modules between any two given configurations. Our algorithm uses O(n(2)) pivot moves, which is worst-case optimal. Previous reconfiguration algorithms either require less restrictive "sliding" moves, do not preserve facet-connectivity, or for the setting we consider, could only handle a small subset of configurations defined by a local forbidden pattern. Configurations with the forbidden pattern do have disconnected reconfiguration graphs (discrete configuration spaces), and indeed we show that they can have an exponential number of connected components. But forbidding the local pattern throughout the configuration is far from necessary, as we show that just a constant number of added modules (placed to be freely reconfigurable) suffice for universal reconfigurability. We also classify three different models of natural pivot moves that preserve facet-connectivity, and show separations between these models.

关键词： Reconfiguration geometric algorithm pivoting squares modular robots

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