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geometric algorithms to Large Margin Classifier Based on Affine Hulls

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2012年第2期23卷 236-246页

作者： Peng, Xinjun Wang, Yifei Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China Shanghai Univ Dept Math Shanghai 200444 Peoples R China

The geometric framework for binary data classification problems provides an intuitive foundation for the comprehension and application of geometric optimization algorithms, leading to practical solutions of real-world classification problems. In this paper, some theoretical results on the candidate extreme points of the notion of reduced affine hull (RAH) are introduced. These results allow the existing nearest point algorithms to be directly applied to solve both separable and inseparable classification problems based on RAHs successfully and efficiently. As the practical applications of the new theoretical results, the popular Gilbert-Schlesinger-Kozinec and Mitchell-Dem'yanov-Malozemov algorithms are presented to solve binary classification problems in the context of the RAH framework. The theoretical analysis and some experiments show that the proposed methods successfully achieve significant performance.

关键词： Candidate extreme point geometric algorithms nearest point problem reduced affine hull (RAH) support vector machine

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geometric algorithms for kinematic calibration of robots containing closed loops

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JOURNAL OF MECHANICAL DESIGN 2003年第1期125卷 23-32页

作者： Iurascu, CC Park, FC Seoul Natl Univ Sch Mech & Aerosp Engn Seoul 151742 South Korea

We present a coordinate-invariant, differential geometric formulation of the kinematic calibration problem for a general class of mechanisms. The mechanisms considered may have multiple closed loops, be redundantly actuated, and include an arbitrary number of passive joints that may or may not be equipped with joint encoders. Some form of measurement information on the position and orientation of the tool frame may also be available. Our approach rests on viewing the joint configuration space of the mechanism as an embedded submanifold of an ambient manifold, and formulating error measures in terms of the Riemannian metric specified in the ambient manifold. Based on this geometric framework, we pose the kinematic calibration problem as one of determining a parametrized multidimensional surface that is a best fit (in the sense of the chosen metric) to a given set of measured points in both the ambient and task space manifolds. Several optimization algorithms that address the various possibilities with respect to available measurement data and choice of error measures are given. Experimental and simulation results are given for the Eclipse, a six degree-of-freedom redundantly actuated parallel mechanism. The geometric framework and algorithms presented in this article have the desirable feature of being invariant with respect to the local coordinate representation of the forward and inverse kinematics and of the loop closure equations, and also provide a high-level framework in which to classify existing approaches to kinematic calibration.

关键词： measurement data Task space Manifolds configuration space CLOSED LOOP Joints inverse kinematics geometric algorithms kinematic calibration Robot Optimization algorithms

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geometric algorithms for sensor networks

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PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2012年第1958期370卷 27-51页

作者： Gao, Jie Guibas, Leonidas SUNY Stony Brook Dept Comp Sci Stony Brook NY 11794 USA Stanford Univ Dept Comp Sci Stanford CA 94305 USA

This paper surveys the use of geometric methods for wireless sensor networks. The close relationship of sensor nodes with their embedded physical space imposes a unique geometric character on such systems. The physical locations of the sensor nodes greatly impact on system design in all aspects, from low-level networking and organization to high-level information processing and applications. This paper reviews work in the past 10 years on topics such as network localization, geometric routing, information discovery, data-centric routing and topology discovery.

关键词： geometric algorithms wireless sensor networks localization routing topology discovery

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geometric algorithms for least squares estimation of 3-D information from monocular image

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 2005年第2期15卷 269-282页

作者： Han, YM Ewha Womans Univ Dept Informat Elect Seoul 120750 South Korea

Estimating the three-dimensional (3-D) information of an object from a sequence of projections is of paramount importance in diverse domains such. as autonomous navigation, robot vision, object recognition, world modeling,, and human-computer interaction. In this paper, we present geometric optimization-based algorithms for simultaneous 3-D shape (depth) and motion (linear and angular velocities) recovery that minimizes the squared distance between the observed and predicted optical flow measurements. A principal advantage of our approach is that, using a separable nonlinear least-squares approach in, various Ways, the search space dimension in the numerical optimization is reduced. For improvement of performance in the numerical optimization, we also develop various methods to take advantage of the separable nonlinear least-squares approach effectively. A second advantage is that, by explicitly accounting for the existence of an one-parameter family of solutions, a geometric optimization algorithms on the Cartesian product manifold can be applied. The Hessian is straightforwardly evaluated as a by-product of the algorithm, making sensitivity analysis straight forward.

关键词： geometric algorithms Newton's method separable nonlinear least squares shape and motion recovery steepest descent method

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geometric algorithms for density-based data clustering

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INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS 2005年第3期15卷 239-260页

作者： Chen, DZ Smid, M Xu, B Univ Notre Dame Dept Comp Sci & Engn Notre Dame IN 46556 USA Carleton Univ Sch Comp Sci Ottawa ON K1S 5B6 Canada

Data clustering is a fundamental problem arising in many practical applications. In this paper, we present new geometric approximation and exact algorithms for the density-based data clustering problem in d-dimensional space R-d (for any constant integer d >= 2). Previously known algorithms for this problem are efficient only when the specified range around each input point, called the delta-neighborhood, contains on average a constant number of input points. Different distributions of the input data points have significant impact on the efficiency of these algorithms. In the worst case when the data points are highly clustered, these algorithms run in quadratic time, although such situations might not occur very frequently on real data. By using computational geometry techniques, we develop faster approximation and exact algorithms for the density-based data clustering problem in R-d. In particulax, our approximation algorithm based on the C-fuzzy distance function takes O(n log n) time for any given fixed value epsilon > 0, and our exact algorithms take sub-quadratic time. The running times and output quality of our algorithms do not depend on any particular data distribution. We believe that our fast approximation algorithm is of considerable practical importance, while our sub-quadratic exact algorithms are more of theoretical interest. We implemented our approximation algorithm and the experimental results show that our approximation algorithm is efficient on arbitrary input point sets.

关键词： density-based clustering geometric algorithms approximation algorithms range search nearest neighbor search BBD trees graph traversal

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Canonical symplectic structure and structure-preserving geometric algorithms for Schrodinger-Maxwell systems

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JOURNAL OF COMPUTATIONAL PHYSICS 2017年 349卷 441-452页

作者： Chen, Qiang Qin, Hong Liu, Jian Xiao, Jianyuan Zhang, Ruili He, Yang Wang, Yulei Univ Sci & Technol China Sch Nucl Sci & Technol Hefei 230026 Anhui Peoples R China Univ Sci & Technol China Dept Modern Phys Hefei 230026 Anhui Peoples R China Luoyang Elect Equipment Testing Ctr Luoyang 471000 Peoples R China Princeton Univ Plasma Phys Lab POB 451 Princeton NJ 08543 USA Univ Sci & Technol Beijing Sch Math & Phys Beijing 100083 Peoples R China

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon-matter interactions described by the Schrodinger-Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. This new numerical capability enables us to carry out first-principle based simulation study of important photon-matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Schrodinger-Maxwell equations Symplectic structure Discrete Poisson bracket geometric algorithms First-principle simulation

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New geometric algorithms for fully connected staged self-assembly

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THEORETICAL COMPUTER SCIENCE 2017年 671卷 4-18页

作者： Demaine, Erik D. Fekete, Sandor P. Scheffer, Christian Schmidt, Arne MIT Cambridge MA 02139 USA TU Braunschweig Dept Comp Sci Braunschweig Germany

We consider staged self-assembly systems, in which square-shaped tiles can be added to bins in several stages. Within these bins, the tiles may connect to each other, depending on the glue types of their edges. Previous work by Demaine et al. showed that a relatively small number of tile types suffices to produce arbitrary shapes in this model. However, these constructions were only based on a spanning tree of the geometric shape, so they did not produce full connectivity of the underlying grid graph in the case of shapes with holes;self-assembly of fully connected assemblies with a polylogarithmic number of stages was left as a major open problem. We resolve this challenge by presenting new systems for staged assembly that produce fully connected polyominoes in (sic)(log(2) n) stages, for various scale factors and temperature tau = 2 as well as tau = 1. Our constructions work even for shapes with holes and use only a constant number of glues and tiles. Moreover, the underlying approach is more geometric in nature, implying that it promises to be more feasible for shapes with compact geometric description. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Self-assembly Staged assembly Fully connected assemblies geometric algorithms

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Synchronizing Parallel geometric algorithms on Multi-Core Machines 5

Synchronizing Parallel Geometric Algorithms on Multi-Core Ma...

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5th International Symposium on Computing and Networking (CANDAR)

作者： Fuentes, Joel Luo, Fei Scherson, Isaac D. Univ Bio Bio Dept Comp Sci & Informat Technol Chillan Chile East China Univ Sci & Technol Sch Informat & Engn Shanghai Peoples R China Univ Calif Irvine Donald Bren Sch Informat & Comp Sci Irvine CA USA

ISBN: (纸本)9781538620878

A thread synchronization mechanism called Spatial Locks for parallel geometric algorithms is presented. We demonstrate that Spatial Locks can ensure thread synchronization on geometric algorithms that perform concurrent operations over geometric surfaces and shapes in two-dimensional or three-dimensional space, considering also that these operations follow a certain order of processing. A parallel algorithm for mesh simplification was implemented using Spatial Locks to show its usefulness when parallelizing geometric algorithms with ease on multi-core machines. Experimental results illustrate the advantage of using this synchronization mechanism, where significant computational improvement can be achieved.

关键词： Three-dimensional displays Synchronization Two dimensional displays Shape Yarn Computational modeling Electronic mail three-dimensional displays electronic mail geometric algorithms Yarns Computational modeling Locks concurrency operation Shape

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Visualization of geometric algorithms in an electronic classroom

Visualization of geometric algorithms in an electronic class...

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8th Annual IEEE Conference on Visualization

作者： Shneerson, M Tal, A Weizmann Inst Sci Dept Appl Math IL-76100 Rehovot Israel

ISBN: (纸本)1581130112

This paper investigates the visualization and animation of geometric computing in a distributed electronic classroom. We show how focusing in a well-defined domain makes it possible to develop a compact system that is accessible to even naive users. We present a conceptual model and a system, GASP-II, that realizes this model in the geometric domain. The system allows the presentation and interactive exploration of 3-dimensional geometric algorithms over the network.

关键词： algorithm animation visualization in education geometric algorithms

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Blending weight BSP Tree for mesh Boolean operations

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COMPUTER-AIDED DESIGN 2025年 182卷

作者： Zhang, Hangcheng Song, Tianqi Zhang, Ganxuan Dai, Kai Wang, Le Liu, Yi Yang, Yi-Jun Zeng, Wei Xi An Jiao Tong Univ Sch Comp Sci & Technol Xian Peoples R China Xi An Jiao Tong Univ Sch Math & Stat Xian Peoples R China

Boolean operations play an important role in geometry processing and CAD/ CAM. To accelerate it, spatial searching trees such as Binary Space Partitioning (BSP) Trees and KD-trees are utilized. In this paper, an approach is presented to construct the BSP Trees for the Boolean operation, where each model is efficiently located in a separate subspace. Unlike conventional methods to calculate the splitting plane, our method utilizes a size-distribution blending weighted squared distance in the BSP Tree construction, where the intrinsic weight is determined based on the size and distribution of the three-dimensional (3D) model and largely reflects the model shape. After determining the intrinsic size-distribution blending weighted squared distance, the effective splitting plane is calculated using the Weighted Squared Distance Minimization (WSDM) method. By utilizing the size-distribution blending weighted squared distance, the generated BSP Tree can divide the two models efficiently, even when dealing with 3D models that exhibit substantial geometric variations. In our experiments, the BSP Tree generated by our method reaches higher Intersecting Triangle Report Accuracy (ITRA) and Non- intersecting Triangles Removal Rate (NTRR), which means more efficient hierarchies than other techniques on two mesh models. The results of intersection tests time consumption and the Boolean operations demonstrate the effectiveness and efficiency of the BSP Tree generated by our method.

关键词： Boolean operation Binary Space Partitioning Squared Distance Minimization geometric algorithms

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