The Experts below are selected from a list of 35367 Experts worldwide ranked by ideXlab platform
Bo Zhang - One of the best experts on this subject based on the ideXlab platform.
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a fast algorithm of Convex Hull vertices selection for online classification
IEEE Transactions on Neural Networks, 2018Co-Authors: Shuguang Ding, Xiangli Nie, Hong Qiao, Bo ZhangAbstract:Reducing samples through Convex Hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the Convex Hull vertices, based on the Convex Hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a Convex Hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, Convex Hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate Convex Hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.
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online support vector machine based on Convex Hull vertices selection
IEEE Transactions on Neural Networks, 2013Co-Authors: Di Wang, Hong Qiao, Bo Zhang, Min WangAbstract:The support vector machine (SVM) method, as a promising classification technique, has been widely used in various fields due to its high efficiency. However, SVM cannot effectively solve online classification problems since, when a new sample is misclassified, the classifier has to be retrained with all training samples plus the new sample, which is time consuming. According to the geometric characteristics of SVM, in this paper we propose an online SVM classifier called VS-OSVM, which is based on Convex Hull vertices selection within each class. The VS-OSVM algorithm has two steps: 1) the samples selection process, in which a small number of skeleton samples constituting an approximate Convex Hull in each class of the current training samples are selected and 2) the online updating process, in which the classifier is updated with newly arriving samples and the selected skeleton samples. From the theoretical point of view, the first d+1 (d is the dimension of the input samples) selected samples are proved to be vertices of the Convex Hull. This guarantees that the selected samples in our approach keep the greatest amount of information of the Convex Hull. From the application point of view, the new algorithm can update the classifier without reducing its classification performance. Experimental results on benchmark data sets have shown the validity and effectiveness of the VS-OSVM algorithm.
Ross Baldick - One of the best experts on this subject based on the ideXlab platform.
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a Convex primal formulation for Convex Hull pricing
IEEE Transactions on Power Systems, 2017Co-Authors: Bowen Hua, Ross BaldickAbstract:In certain electricity markets, because of nonConvexities that arise from their operating characteristics, generators that follow the independent system operator's (ISO's) decisions may fail to recover their cost through sales of energy at locational marginal prices. The ISO makes discriminatory side payments to incentivize the compliance of generators. Convex Hull pricing is a uniform pricing scheme that minimizes these side payments. The Lagrangian dual problem of the unit commitment problem has been solved in the dual space to determine Convex Hull prices. However, this approach is computationally expensive. We propose a polynomially solvable primal formulation for the Lagrangian dual problem. This formulation explicitly describes for each generating unit the Convex Hull of its feasible set and the Convex envelope of its cost function. We cast our formulation as a second-order cone program when the cost functions are quadratic, and a linear program when the cost functions are piecewise linear. A 96-period 76-unit transmission-constrained example is solved in less than 15 s on a personal computer.
Vadim Borokhov - One of the best experts on this subject based on the ideXlab platform.
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Modified Convex Hull pricing for power markets with price-sensitive load
International Journal of Electrical Power & Energy Systems, 2018Co-Authors: Vadim BorokhovAbstract:Abstract We consider a general power market with price-sensitive consumer bids and non-Convexities originating from supply (start-up and no-load costs, nonzero minimum output limits of generating units, etc.) and demand. The Convex Hull (minimum-uplift) pricing method produces the set of power prices that minimizes the total uplift payments to the market players needed to compensate their potential profits lost by accepting the centralized dispatch solution. All opportunities to supply (consume) any other output (consumption) volumes allowed by market player individual operational constraints are considered as foregone in the Convex Hull pricing method. We modify the Convex Hull pricing algorithm by defining for each market player a modified individual feasible set that is utilized in the lost profit calculation. These sets are based on the output (consumption) volumes that are economically and technologically feasible in the centralized dispatch. The new pricing method results in the generally different set of market prices and lower (or equal) total uplift payment compared to the Convex Hull pricing algorithm.
Hugo Reyes - One of the best experts on this subject based on the ideXlab platform.
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IWCIA - Relative Convex Hull Determination from Convex Hulls in the Plane
Lecture Notes in Computer Science, 2015Co-Authors: Petra Wiederhold, Hugo ReyesAbstract:A new algorithm for the determination of the relative Convex Hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative Convex Hull is also known as geodesic Convex Hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and encircling A. Algorithms solving this problem known from Computational Geometry are based on the triangulation or similar decomposition of that difference set. The algorithm presented here does not use such decomposition, but it supposes that A and B are given as ordered sequences of vertices. The algorithm is based on Convex Hull calculations of A and B and of smaller polygons and polylines, it produces the output list of vertices of the relative Convex Hull from the sequence of vertices of the Convex Hull of A.
Hong Qiao - One of the best experts on this subject based on the ideXlab platform.
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a fast algorithm of Convex Hull vertices selection for online classification
IEEE Transactions on Neural Networks, 2018Co-Authors: Shuguang Ding, Xiangli Nie, Hong Qiao, Bo ZhangAbstract:Reducing samples through Convex Hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the Convex Hull vertices, based on the Convex Hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a Convex Hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, Convex Hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate Convex Hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.
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online support vector machine based on Convex Hull vertices selection
IEEE Transactions on Neural Networks, 2013Co-Authors: Di Wang, Hong Qiao, Bo Zhang, Min WangAbstract:The support vector machine (SVM) method, as a promising classification technique, has been widely used in various fields due to its high efficiency. However, SVM cannot effectively solve online classification problems since, when a new sample is misclassified, the classifier has to be retrained with all training samples plus the new sample, which is time consuming. According to the geometric characteristics of SVM, in this paper we propose an online SVM classifier called VS-OSVM, which is based on Convex Hull vertices selection within each class. The VS-OSVM algorithm has two steps: 1) the samples selection process, in which a small number of skeleton samples constituting an approximate Convex Hull in each class of the current training samples are selected and 2) the online updating process, in which the classifier is updated with newly arriving samples and the selected skeleton samples. From the theoretical point of view, the first d+1 (d is the dimension of the input samples) selected samples are proved to be vertices of the Convex Hull. This guarantees that the selected samples in our approach keep the greatest amount of information of the Convex Hull. From the application point of view, the new algorithm can update the classifier without reducing its classification performance. Experimental results on benchmark data sets have shown the validity and effectiveness of the VS-OSVM algorithm.
