Due to the fast evolution of the information on the Internet, update summarization has received much attention in recent years. It is to summarize an evolutionary document collection at current time supposing the user...
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Due to the fast evolution of the information on the Internet, update summarization has received much attention in recent years. It is to summarize an evolutionary document collection at current time supposing the users have read some related previous documents. In this paper, we propose a graph-ranking-based method. It performs constrained reinforcements on a sentence graph, which unifies previous and current documents, to determine the salience of the sentences. The constraints ensure that the most salient sentences in current documents are updates to previous documents. Since this method is NP-hard, we then propose its approximate method, which is polynomial time solvable. Experiments on the TAC 2008 and 2009 benchmark data sets show the effectiveness and efficiency of our method.
We introduce a new and very simple algorithm for a class of smooth convex constrained minimization problems which is an iterative scheme related to sequential quadratically constrained quadratic programming methods, c...
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We introduce a new and very simple algorithm for a class of smooth convex constrained minimization problems which is an iterative scheme related to sequential quadratically constrained quadratic programming methods, called sequential simple quadratic method (SSQM). The computational simplicity of SSQM, which uses first-order information, makes it suitable for large scale problems. Theoretical results under standard assumptions are given proving that the whole sequence built by the algorithm converges to a solution and becomes feasible after a finite number of iterations. When in addition the objective function is strongly convex then asymptotic linear rate of convergence is established.
A new approach to the design of robust adaptive beamforming is introduced. In the proposed approach, the mismatch vector of the desired steering vector is estimated by solving a quadraticallyconstrainedquadratic pro...
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A new approach to the design of robust adaptive beamforming is introduced. In the proposed approach, the mismatch vector of the desired steering vector is estimated by solving a quadratically constrained quadratic programming problem using an interference-plus-noise subspace projection matrix. The presumed look direction of desired signal is the only prior information of the proposed approach, and the parameters of uncertainty set or the angular sectors of the desired signal are not needed. In the presence of large DOA mismatch, the proposed beamformer performs well. Moreover, the proposed approach can deal with arbitrary steering vector mismatch in theory while many existing advanced robust beamformers cannot. Hence, it is very suitable for many practical applications. Crown Copyright (c) 2013 Published by Elsevier B.V. All rights reserved.
Time-of-use (ToU) electricity tariffs are currently employed or considered for implementation in many jurisdictions around the world. In ToU modalities, a set of different tariffs for different hours of the day and/or...
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Time-of-use (ToU) electricity tariffs are currently employed or considered for implementation in many jurisdictions around the world. In ToU modalities, a set of different tariffs for different hours of the day and/or seasons of the year is defined at the beginning of a given horizon, and then kept constant until its end. While designing ToU tariffs, one of the most significant sources of uncertainty to be considered relates to price-elasticities of demand. We propose an approach for ToU tariff design based in quadratically constrained quadratic programming and stochastic optimization techniques, addressing these uncertainties and dealing with various aspects of tariff design from the point of view of the regulator/regulated utility.
In this paper, we consider the automated learning of the kernel matrix over a convex combination of pre-specified kernel matrices in Regularized Kernel Discriminant Analysis (RKDA), which performs linear discriminant ...
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ISBN:
(纸本)9781595936097
In this paper, we consider the automated learning of the kernel matrix over a convex combination of pre-specified kernel matrices in Regularized Kernel Discriminant Analysis (RKDA), which performs linear discriminant analysis in the feature space via the kernel trick. Previous studies have shown that this kernel learning problem can be formulated as a semidefinite program (SDP), which is however computationally expensive, even with the recent advances in interior point methods. Based on the equivalence relationship between RKDA and least square problems in the binary-class case, we propose a quadratically constrained quadratic programming (QCQP) formulation for the kernel learning problem, which can be solved more efficiently than SDP. While most existing work on kernel learning deal with binary-class problems only, we show that our QCQP formulation can be extended naturally to the multi-class case. Experimental results on both binary-class and multi-class benchmark data sets show the efficacy of the proposed QCQP formulations.
This paper constructs the framework of the reproducing kernel Hilbert space for multiple kernel learning, which provides clear insights into the reason that multiple kernel support vector machines (SVM) outperform sin...
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This paper constructs the framework of the reproducing kernel Hilbert space for multiple kernel learning, which provides clear insights into the reason that multiple kernel support vector machines (SVM) outperform single kernel SVM. These results can serve as a fundamental guide to account for the superiority of multiple kernel to single kernel learning. Subsequently, the constructed multiple kernel learning algorithms are applied to model a nonlinear blast furnace system only based on its input-output signals. The experimental results not only confirm the superiority of multiple kernel learning algorithms, but also indicate that multiple kernel SVM is a kind of highly competitive data-driven modeling method for the blast furnace system and can provide reliable indication for blast furnace operators to take control actions. Note to Practitioners-This paper is motivated by the problem of predicting the silicon content in blast furnace hot metal, which is an open problem for realizing blast furnace automation. Here, based on the single kernel and multiple kernel SVM, we pay special attention to the silicon trend prediction since it can provide more direct guideline for taking control action in the blast furnace operation. Theoretically, we have given the detailed reasons that multiple kernel SVM is superior to single kernel SVM, which can improve the transparency of multiple kernel learning algorithm. The experimental results, not only confirm the superiority of multiple kernel learning algorithms, but also indicate that multiple kernel SVM is a kind of highly competitive data-driven modeling method for the blast furnace system and can provide reliable indication for blast furnace operators to take control actions.
As a kernel based method, the performance of least squares support vector machine (LS-SVM) depends on the selection of the kernel as well as the regularization parameter (Duan, Keerthi, & Poo, 2003). Cross-validat...
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As a kernel based method, the performance of least squares support vector machine (LS-SVM) depends on the selection of the kernel as well as the regularization parameter (Duan, Keerthi, & Poo, 2003). Cross-validation is efficient in selecting a single kernel and the regularization parameter: however, it suffers from heavy computational cost and is not flexible to deal with multiple kernels. In this paper, we address the issue of multiple kernel learning for LS-SVM by formulating it as semidefinite programming (SDP). Furthermore, we show that the regularization parameter can be optimized in a unified framework with the kernel, which leads to an automatic process for model selection. Extensive experimental validations are performed and analyzed. (C) 2011 Elsevier Ltd. All rights reserved.
In this paper, we present a new sequential quadratically constrained quadratic programming (SQCQP) algorithm, in which a simple updating strategy of the penalty parameter is adopted. This strategy generates nonmonoton...
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In this paper, we present a new sequential quadratically constrained quadratic programming (SQCQP) algorithm, in which a simple updating strategy of the penalty parameter is adopted. This strategy generates nonmonotone penalty parameters at early iterations and only uses the multiplier corresponding to the bound constraint of the quadratically constrained quadratic programming (QCQP) subproblem instead of the multipliers of the quadratic constraints, which will bring some numerical advantages. Furthermore, by using the working set technique, we remove the constraints of the QCQP subproblem that are locally irrelevant, and thus the computational cost could be reduced. Without assuming the convexity of the objective function or the constraints, the algorithm is proved to be globally, superlinearly and quadratically convergent. Preliminary numerical results show that the proposed algorithm is very promising when compared with the tested SQP algorithms. (C) 2011 Elsevier B.V. All rights reserved.
In this article, we study the convex hull presentation of a quadraticallyconstrained set. Applying the new result, we solve a kind of quadratically constrained quadratic programming problems, which generalizes many w...
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In this article, we study the convex hull presentation of a quadraticallyconstrained set. Applying the new result, we solve a kind of quadratically constrained quadratic programming problems, which generalizes many well-studied problems.
In this paper, we consider the problem of minimizing a nonconvex quadratic function, subject to two quadratic inequality constraints. As an application, such a quadratic program plays an important role in the trust re...
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In this paper, we consider the problem of minimizing a nonconvex quadratic function, subject to two quadratic inequality constraints. As an application, such a quadratic program plays an important role in the trust region method for nonlinear optimization;such a problem is known as the Celis, Dennis, and Tapia (CDT) subproblem in the literature. The Lagrangian dual of the CDT subproblem is a semidefinite program (SDP), hence convex and solvable. However, a positive duality gap may exist between the CDT subproblem and its Lagrangian dual because the CDT subproblem itself is nonconvex. In this paper, we present a necessary and sufficient condition to characterize when the CDT subproblem and its Lagrangian dual admits no duality gap (i.e., the strong duality holds). This necessary and sufficient condition is easy verifiable and involves only one (any) optimal solution of the SDP relaxation for the CDT subproblem. Moreover, the condition reveals that it is actually rare to render a positive duality gap for the CDT subproblems in general. Moreover, if the strong duality holds, then an optimal solution for the CDT problem can be retrieved from an optimal solution of the SDP relaxation, by means of a matrix rank-one decomposition procedure. The same analysis is extended to the framework where the necessary and sufficient condition is presented in terms of the Lagrangian multipliers at a KKT point. Furthermore, we show that the condition is numerically easy to work with approximatively.
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