On the Solution of Bi-level Large Scale Quadratic Programming Problem with Stochastic Parameters in the Constraints

The quadratic programming problem in the standard support vector machine (SVM) algorithm has high time complexity and space complexity in solving the large-scale problems which becomes a bottleneck in the SVM applications. Ball Vector Machine (BVM) converts the quadratic programming problem of the traditional SVM into the minimum enclosed ball problem (MEB). It can indirectly get the solution of quadratic programming through solving the MEB problem which significantly reduces the time complexity and space complexity. The experiments show that when handling five large-scale and high-dimensional data sets, the BVM and standard SVM have a considerable accuracy, but the BVM has higher speed and less requirement space than standard SVM.

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Selection of Support Vector Candidates Using Relative Support Distance for Sustainability in Large-Scale Support Vector Machines

Applied Sciences ◽

10.3390/app10196979 ◽

2020 ◽

Vol 10 (19) ◽

pp. 6979

Author(s):

Minho Ryu ◽

Kichun Lee

Keyword(s):

Support Vector Machines ◽

Quadratic Programming ◽

Decision Trees ◽

Programming Problem ◽

Large Scale ◽

Classification Performance ◽

Quadratic Programming Problem ◽

Support Vector ◽

Training Time ◽

Vector Machines

Support vector machines (SVMs) are a well-known classifier due to their superior classification performance. They are defined by a hyperplane, which separates two classes with the largest margin. In the computation of the hyperplane, however, it is necessary to solve a quadratic programming problem. The storage cost of a quadratic programming problem grows with the square of the number of training sample points, and the time complexity is proportional to the cube of the number in general. Thus, it is worth studying how to reduce the training time of SVMs without compromising the performance to prepare for sustainability in large-scale SVM problems. In this paper, we proposed a novel data reduction method for reducing the training time by combining decision trees and relative support distance. We applied a new concept, relative support distance, to select good support vector candidates in each partition generated by the decision trees. The selected support vector candidates improved the training speed for large-scale SVM problems. In experiments, we demonstrated that our approach significantly reduced the training time while maintaining good classification performance in comparison with existing approaches.

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An Algorithm for the Solution of a Quadratic Programming Problem, with Application to Constrained Matrix and Spatial Price Equilibrium Problems

Environment and Planning A Economy and Space ◽

10.1068/a210099 ◽

1989 ◽

Vol 21 (1) ◽

pp. 99-114 ◽

Cited By ~ 11

Author(s):

A Nagurney ◽

Referee H K Chen

Keyword(s):

Quadratic Programming ◽

Programming Problem ◽

Large Scale ◽

Equilibrium Problems ◽

Quadratic Programming Problem ◽

Price Equilibrium ◽

Spatial Price Equilibrium ◽

Special Cases ◽

Spatial Price ◽

Matrix Problems

In this paper a quadratic programming problem is considered. It contains, as special cases, formulations of constrained matrix problems with unknown row and column totals, and classical spatial price equilibrium problems with congestion. An equilibration algorithm, which is of the relaxation type, is introduced into the problem. It resolves the system into subproblems, which in turn, can be solved exactly, even in the presence of upper bounds. Also provided is computational experience for several large-scale examples. This work identifies the equivalency between constrained matrix problems and spatial price equilibrium problems which had been postulated, but, heretofore, not made.

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