Expert systems often rely heavily on the performance of binary classification methods. The need for accurate predictions in artificial intelligence has led to a plethora of novel approaches that aim at correctly predi...
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Expert systems often rely heavily on the performance of binary classification methods. The need for accurate predictions in artificial intelligence has led to a plethora of novel approaches that aim at correctly predicting new instances based on nonlinear classifiers. In this context, Support Vector Machine (SVM) formulations via two nonparallel hyperplanes have received increasing attention due to their superior performance. In this work, we propose a novel formulation for the method, Nonparallel Hyperplane SVM. Its main contribution is the use of robust optimization techniques in order to construct nonlinear models with superior performance and appealing geometrical properties. Experiments on benchmark datasets demonstrate the virtues in terms of predictive performance compared with various other SVM formulations. Managerial insights and the relevance for intelligent systems are discussed based on the experimental outcomes. (C) 2016 Elsevier Ltd. All rights reserved.
This paper presents novel second-order cone programming (SOCP) formulations that determine a linear multi-class predictor using support vector machines (SVMs). We first extend the ideas of OvO (One-versus-One) and OvA...
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This paper presents novel second-order cone programming (SOCP) formulations that determine a linear multi-class predictor using support vector machines (SVMs). We first extend the ideas of OvO (One-versus-One) and OvA (One-versus-All) SVM formulations to SOCP-SVM, providing two interesting alternatives to the standard SVM formulations. Additionally, we propose a novel approach (MC-SOCP) that simultaneously constructs all required hyperplanes for multi-class classification, based on the multi-class SVM formulation (MC-SVM). The use of conic constraints for each pair of training patterns in a single optimization problem provides an adequate framework for a balanced and effective prediction. (C) 2015 Elsevier Inc. All rights reserved.
Although second-order cone programming (SOCP) has been applied to optimise camera parameters in computer vision, it is occasionally been used to refine fisheye camera external parameters as well. This study presents a...
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Although second-order cone programming (SOCP) has been applied to optimise camera parameters in computer vision, it is occasionally been used to refine fisheye camera external parameters as well. This study presents a fisheye camera external parameter estimation based on SOCP in convex optimisation. The homography constraint between two spherical images are first exploited to derive an equation with respect to a given error threshold. Then, the fisheye camera external estimation is transformed into an SOCP optimisation problem through reformulating the parameter estimation equation. The SOCP method has been implemented in Matlab and the optimisation toolbox has been made publicly available. The fisheye camera external parameter optimisation method has been validated by some experiments with synthetic and real data. Comparison experiments between the proposed method and other methods in the literature are also carried out, and the results show that the SOCP method is better for the corrected images.
Frame structures are extensively used in mechanical, civil, and aerospace engineering. Besides generating reasonable designs of frame structures themselves, frame topology optimization may serve as a tool providing us...
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Frame structures are extensively used in mechanical, civil, and aerospace engineering. Besides generating reasonable designs of frame structures themselves, frame topology optimization may serve as a tool providing us with conceptual designs of diverse engineering structures. Due to its nonconvexity, however, most of existing approaches to frame topology optimization are local optimization methods based on nonlinear programming with continuous design variables or (meta)heuristics allowing some discrete design variables. Presented in this paper is a new global optimization approach to the frame topology optimization with discrete design variables. It is shown that the compliance minimization problem with predetermined candidate cross-sections can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution is then computed with an existing solver based on a branch-and-cut algorithm. Numerical experiments are performed to examine computational efficiency of the proposed approach.
In design practice it is often that the structural components are selected from among easily available discrete candidates and a number of different candidates used in a structure is restricted to be small. Presented ...
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In design practice it is often that the structural components are selected from among easily available discrete candidates and a number of different candidates used in a structure is restricted to be small. Presented in this paper is a new modeling of the design constraints for obtaining the minimum compliance truss design in which only a limited number of different cross-section sizes are employed. The member cross-sectional areas are considered either discrete design variables that can take only predetermined values or continuous design variables. In both cases it is shown that the compliance minimization problem can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution of this optimization problem is then computed by using an existing solver based on a branch-and-cut algorithm. Numerical experiments are performed to show that the proposed approach is applicable to moderately large-scale problems.
second-order cone programming (SOCP) formulations have received increasing attention as robust optimization schemes for Support Vector Machine (SVM) classification. These formulations study the worst-case setting for ...
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second-order cone programming (SOCP) formulations have received increasing attention as robust optimization schemes for Support Vector Machine (SVM) classification. These formulations study the worst-case setting for class-conditional densities, leading to potentially more effective classifiers in terms of performance compared to the standard SVM formulation. In this work we propose an SOCP extension for Twin SVM, a recently developed classification approach that constructs two nonparallel classifiers. The linear and kernel-based SOCP formulations for Twin SVM are derived, while the duality analysis provides interesting geometrical properties of the proposed method. Experiments on benchmark datasets demonstrate the virtues of our approach in terms of classification performance compared to alternative SVM methods.
To discretize reinforced soil structures in plane strain and predict their collapse load, a simple three-node triangular finite element is formulated based on the static theorem of the limit analysis. The element sati...
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This letter proposes a flat-top beampattern synthesis method in range and angle domains for frequency diverse array (FDA) based on second-order cone programming (SOCP). By dividing the array into subarrays and applyin...
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This letter proposes a flat-top beampattern synthesis method in range and angle domains for frequency diverse array (FDA) based on second-order cone programming (SOCP). By dividing the array into subarrays and applying each subarray with a distinguishable frequency shift, this approach explores the separated degrees of freedom in range domain and is capable of generating a two-dimensional flat-top beampattern in range and angle domains. Basically, the flat-top beampattern synthesis in range and angle domains is formulated as an SOCP problem that can be exactly and efficiently solved with inner point method. Numerical examples are carried out to demonstrate the effectiveness of the proposed method.
Reliable power system operation requires maintaining sufficient voltage stability margins. Traditional techniques based on continuation and optimization calculate lower bounds for these margins and generally require a...
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ISBN:
(纸本)9780769556703
Reliable power system operation requires maintaining sufficient voltage stability margins. Traditional techniques based on continuation and optimization calculate lower bounds for these margins and generally require appropriate initialization. Building on a previous semidefinite programming (SDP) formulation, this paper proposes a new second-order cone programming (SOCP) formulation which directly yields upper bounds for the voltage stability margin without needing to specify an initialization. Augmentation with integer-constrained variables enables consideration of reactive-power-limited generators. Further, leveraging the ability to globally solve these problems, this paper describes a sufficient condition for insolvability of the power flow equations. Trade-offs between tightness and computational speed of the SDP and SOCP relaxations are studied using large test cases representing portions of European power systems.
We present a global and convex formulation for template-less 3D reconstruction of a deforming object with the perspective camera. We show for the first time how to construct a second-order cone programming (SOCP) prob...
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ISBN:
(纸本)9781467388511
We present a global and convex formulation for template-less 3D reconstruction of a deforming object with the perspective camera. We show for the first time how to construct a second-order cone programming (SOCP) problem for Non-Rigid Shape-from-Motion (NRSfM) using the Maximum-Depth Heuristic (MDH). In this regard, we deviate strongly from the general trend of using affine cameras and factorization-based methods to solve NRSfM. In MDH, the points' depths are maximized so that the distance between neighbouring points in camera space are upper bounded by the geodesic distance. In NRSfM both geodesic and camera space distances are unknown. We show that, nonetheless, given point correspondences and the camera's intrinsics the whole problem is convex and solvable with SOCP. We show with extensive experiments that our method accurately reconstructs quasi-isometric surfaces from partial views under articulated and strong deformations. It naturally handles missing correspondences, non-smooth objects and is very simple to implement compared to previous methods, with only one free parameter (the neighbourhood size).
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