A Robust Regularization Path Algorithm for $\nu $ -Support Vector Classification
TL;DR: A robust regularization path algorithm is proposed for LaTeX vector classification, based on lower upper decomposition with partial pivoting, that can avoid the exceptions completely, handle the singularities in the key matrix, and fit the entire solution path in a finite number of steps.
Abstract: The $
u $ -support vector classification has the advantage of using a regularization parameter $
u $ to control the number of support vectors and margin errors. Recently, a regularization path algorithm for $
u $ -support vector classification ( $
u $ -SvcPath) suffers exceptions and singularities in some special cases. In this brief, we first present a new equivalent dual formulation for $
u $ -SVC and, then, propose a robust $
u $ -SvcPath, based on lower upper decomposition with partial pivoting. Theoretical analysis and experimental results verify that our proposed robust regularization path algorithm can avoid the exceptions completely, handle the singularities in the key matrix, and fit the entire solution path in a finite number of steps. Experimental results also show that our proposed algorithm fits the entire solution path with fewer steps and less running time than original one does.
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2,140 citations
TL;DR: An optimization problem is formulated to minimize the energy consumption of the offloading system, where the energy cost of both task computing and file transmission are taken into consideration, and an EECO scheme is designed, which jointly optimizes offloading and radio resource allocation to obtain the minimal energy consumption under the latency constraints.
Abstract: Mobile edge computing (MEC) is a promising paradigm to provide cloud-computing capabilities in close proximity to mobile devices in fifth-generation (5G) networks. In this paper, we study energy-efficient computation offloading (EECO) mechanisms for MEC in 5G heterogeneous networks. We formulate an optimization problem to minimize the energy consumption of the offloading system, where the energy cost of both task computing and file transmission are taken into consideration. Incorporating the multi-access characteristics of the 5G heterogeneous network, we then design an EECO scheme, which jointly optimizes offloading and radio resource allocation to obtain the minimal energy consumption under the latency constraints. Numerical results demonstrate energy efficiency improvement of our proposed EECO scheme.
730 citations
Additional excerpts
...org) extra transmission energy cost [7]....
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01 Apr 2019
TL;DR: The fuzzy information entropy can accurately and more completely extract the characteristics of the vibration signal, the improved PSO algorithm can effectively improve the classification accuracy of LS-SVM, and the proposed fault diagnosis method outperforms the other mentioned methods.
Abstract: Aiming at the problem that the most existing fault diagnosis methods could not effectively recognize the early faults in the rotating machinery, the empirical mode decomposition, fuzzy information entropy, improved particle swarm optimization algorithm and least squares support vector machines are introduced into the fault diagnosis to propose a novel intelligent diagnosis method, which is applied to diagnose the faults of the motor bearing in this paper. In the proposed method, the vibration signal is decomposed into a set of intrinsic mode functions (IMFs) by using empirical mode decomposition method. The fuzzy information entropy values of IMFs are calculated to reveal the intrinsic characteristics of the vibration signal and considered as feature vectors. Then the diversity mutation strategy, neighborhood mutation strategy, learning factor strategy and inertia weight strategy for basic particle swarm optimization (PSO) algorithm are used to propose an improved PSO algorithm. The improved PSO algorithm is used to optimize the parameters of least squares support vector machines (LS-SVM) in order to construct an optimal LS-SVM classifier, which is used to classify the fault. Finally, the proposed fault diagnosis method is fully evaluated by experiments and comparative studies for motor bearing. The experiment results indicate that the fuzzy information entropy can accurately and more completely extract the characteristics of the vibration signal. The improved PSO algorithm can effectively improve the classification accuracy of LS-SVM, and the proposed fault diagnosis method outperforms the other mentioned methods in this paper and published in the literature. It provides a new method for fault diagnosis of rotating machinery.
365 citations
01 Oct 2017
TL;DR: The experiment results show that the DOADAPO algorithm can improve the convergence speed and enhance the local search ability and global search ability, and the multi-objective optimization model of gate assignment can improved the comprehensive service of gate assignments.
Abstract: Display Omitted An improved adaptive PSO based on Alpha-stable distribution and dynamic fractional calculus is studied.A new multi-objective optimization model of gate assignment problem is proposed.The actual data are used to demonstrate the effectiveness of the proposed method. Gate is a key resource in the airport, which can realize rapid and safe docking, ensure the effective connection between flights and improve the capacity and service efficiency of airport. The minimum walking distances of passengers, the minimum idle time variance of each gate, the minimum number of flights at parking apron and the most reasonable utilization of large gates are selected as the optimization objectives, then an efficient multi-objective optimization model of gate assignment problem is proposed in this paper. Then an improved adaptive particle swarm optimization(DOADAPO) algorithm based on making full use of the advantages of Alpha-stable distribution and dynamic fractional calculus is deeply studied. The dynamic fractional calculus with memory characteristic is used to reflect the trajectory information of particle updating in order to improve the convergence speed. The Alpha-stable distribution theory is used to replace the uniform distribution in order to escape from the local minima in a certain probability and improve the global search ability. Next, the DOADAPO algorithm is used to solve the constructed multi-objective optimization model of gate assignment in order to fast and effectively assign the gates to different flights in different time. Finally, the actual flight data in one domestic airport is used to verify the effectiveness of the proposed method. The experiment results show that the DOADAPO algorithm can improve the convergence speed and enhance the local search ability and global search ability, and the multi-objective optimization model of gate assignment can improve the comprehensive service of gate assignment. It can effectively provide a valuable reference for assigning the gates in hub airport.
324 citations
TL;DR: Experimental results show that the proposing MIMAGA-Selection method significantly reduces the dimension of gene expression data and removes the redundancies for classification and the reduced gene expression dataset provides highest classification accuracy compared to conventional feature selection algorithms.
253 citations
Cites methods from "A Robust Regularization Path Algori..."
...To demonstrate the effectiveness of the MIMAGA-Selection algorithm, we apply three existing feature selection algorithms: ReliefF [39,40] , sequential forward selection (SFS) [41,42] and MIM on the same datasets with the same target gene numbers....
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References
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01 Jan 1998
TL;DR: Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.
Abstract: A comprehensive look at learning and generalization theory. The statistical theory of learning and generalization concerns the problem of choosing desired functions on the basis of empirical data. Highly applicable to a variety of computer science and robotics fields, this book offers lucid coverage of the theory as a whole. Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.
26,531 citations
"A Robust Regularization Path Algori..." refers methods in this paper
...…first give the linear relationship between α, g, and ν (see line 4 in Algorithm 1 and Section III-A1), then compute the maximal adjustment quantity νmax (see line 5 in Algorithm 1 and Section III-A2), and finally update α, g̃, d1, d2, SS , SR , and SE (see line 6 in Algorithm 1 and Section III-A3)....
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TL;DR: A new class of support vector algorithms for regression and classification that eliminates one of the other free parameters of the algorithm: the accuracy parameter in the regression case, and the regularization constant C in the classification case.
Abstract: We propose a new class of support vector algorithms for regression and classification. In these algorithms, a parameter ν lets one effectively control the number of support vectors. While this can be useful in its own right, the parameterization has the additional benefit of enabling us to eliminate one of the other free parameters of the algorithm: the accuracy parameter epsilon in the regression case, and the regularization constant C in the classification case. We describe the algorithms, give some theoretical results concerning the meaning and the choice of ν, and report experimental results.
2,737 citations
"A Robust Regularization Path Algori..." refers methods in this paper
...According to convex optimization theory [13, p. 229], the solution of the dual problem with two equality constraints can be obtained by minimizing the following convex function: min 0≤αi≤1/ l Wν = 1 2 αT Qα + b′ ⎛ ⎝ l ∑ i=1 yiαi ⎞ ⎠+ ρ′ ⎛ ⎝ l ∑ i=1 αi − ν ⎞ ⎠ (3) where both b′ and ρ′ are Lagrangian multipliers....
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...In order to propose the ν-SvcRPath, i.e., Algorithm 1, we first give the linear relationship between α, g, and ν (see line 4 in Algorithm 1 and Section III-A1), then compute the maximal adjustment quantity νmax (see line 5 in Algorithm 1 and Section III-A2), and finally update α, g̃, d1, d2, SS ,…...
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...For each adjustment of ν (i.e., ∑ i∈S αi ), in order to keep all the samples satisfying the KKT conditions, the weights of the samples in SS , and the Lagrange multipliers (b ′ and ρ′) should also be adjusted accordingly....
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...(13) According to the convex optimization theory [13], the solution of (13) can also be obtained by minimizing the following convex function: min 0≤αi≤1/ l W ′ν = 1 2 αT Qα + d1 ⎛ ⎝ ∑ i∈S+ αi − ν2 ⎞ ⎠ + d2 ⎛ ⎝ ∑ i∈S− αi − ν2 ⎞ ⎠ (14) where both d1 and d2 are Lagrangian multipliers....
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...8: end while 1) Compute Linear Relationship Between α, g, and ν: For each adjustment of ν (i.e., ∑ i∈S αi ), in order to keep all the samples satisfying the KKT conditions, the weights of the samples in SS , and the Lagrange multipliers (d1 and d2) should also be adjusted accordingly....
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2,140 citations
TL;DR: In this paper, the authors present a method to analyze the powers of a given trilinear form (a special kind of algebraic constructions also called a tensor) and obtain upper bounds on the asymptotic complexity of matrix multiplication.
Abstract: This paper presents a method to analyze the powers of a given trilinear form (a special kind of algebraic constructions also called a tensor) and obtain upper bounds on the asymptotic complexity of matrix multiplication. Compared with existing approaches, this method is based on convex optimization, and thus has polynomial-time complexity. As an application, we use this method to study powers of the construction given by Coppersmith and Winograd [Journal of Symbolic Computation, 1990] and obtain the upper bound $\omega<2.3728639$ on the exponent of square matrix multiplication, which slightly improves the best known upper bound.
940 citations