scholarly journals A New Conic Approach to Semisupervised Support Vector Machines

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Ye Tian ◽  
Jian Luo ◽  
Xin Yan
Keyword(s):  
Quadratic Forms ◽  
Optimal Solution ◽  
Positive Cone ◽  
Support Vector ◽  
Completely Positive ◽  
Adaptive Scheme ◽  
Completely Positive Cone ◽  
Vector Machines ◽  
Programming Techniques ◽  
Completely Positive Programming

We propose a completely positive programming reformulation of the 2-norm soft marginS3VMmodel. Then, we construct a sequence of computable cones of nonnegative quadratic forms over a union of second-order cones to approximate the underlying completely positive cone. Anϵ-optimal solution can be found in finite iterations using semidefinite programming techniques by our method. Moreover, in order to obtain a good lower bound efficiently, an adaptive scheme is adopted in our approximation algorithm. The numerical results show that the proposed algorithm can achieve more accurate classifications than other well-known conic relaxations of semisupervised support vector machine models in the literature.

scholarly journals The cone of Z-transformations on Lorentz cone

2019 ◽  
Vol 35 ◽  
pp. 387-393 ◽  
Author(s):  
Sandor Nemeth ◽  
Muddappa Gowda
Keyword(s):  
Structural Properties ◽  
Positive Cone ◽  
Linear Program ◽  
Completely Positive ◽  
Completely Positive Cone ◽  
Lorentz Cone ◽  
Semidefinite Cone

In this paper, the structural properties of the cone of $\calz$-transformations on the Lorentz cone are described in terms of the semidefinite cone and copositive/completely positive cones induced by the Lorentz cone and its boundary. In particular, its dual is described as a slice of the semidefinite cone as well as a slice of the completely positive cone of the Lorentz cone. This provides an example of an instance where a conic linear program on a completely positive cone is reduced to a problem on the semidefinite cone.

Optimal Reliability-Based Design Using Support Vector Machines and Artificial Life Algorithms

2007 ◽  
pp. 59-79
Author(s):  
Jorge Hurtado
Keyword(s):  
Support Vector Machines ◽  
Earthquake Engineering ◽  
Artificial Life ◽  
Numerical Models ◽  
Optimal Solution ◽  
Support Vector ◽  
Practical Application ◽  
Reliability Based Design ◽  
Vector Machines ◽  
Reliability Based Optimization

Reliability-based optimization is considered by many authors as the most rigorous approach to structural design, because the search for the optimal solution is performed with consideration of the uncertainties present in the structural and load variables. The practical application of this idea, however, is hindered by the computational difficulties associated to the minimisation of cost functions with probabilistic constraints involving the computation of very small probabilities computed over implicit threshold functions, that is, those given by numerical models such as finite elements. In this chapter, a procedure intended to perform this task with a minimal amount of calls of the finite element code is proposed. It is based on the combination of a computational learning method (the support vector machines) and an artificial life technique (particle swarm optimisation). The former is selected because of its information encoding properties as well as for its elitist procedures that complement hose of the a-life optimisation method. The later has been chosen du to its advantages over classical genetic algorithms. The practical application of the procedure is demonstrated with earthquake engineering examples.

Prediction of Networks Security Situation Based on Wavelet Kernel Function Network

2011 ◽  
Vol 127 ◽  
pp. 53-58
Author(s):  
Jian Qiong Xiao
Keyword(s):  
Kernel Function ◽  
Optimal Solution ◽  
Support Vector ◽  
Situation Models ◽  
Convex Programming Problem ◽  
Value Prediction ◽  
The Neural Network ◽  
Vector Machines ◽  
Wavelet Kernel Function ◽  
Function Network

Based on the foundation of prediction of networks security situation models, this article proposed a method about applying wavelet kernel function network to prediction of networks security situation. Wavelet kernel function network combined with the neural network and the support vector machines merits, which avoid support vector machine (SVM) solving binding second convex programming problem, network scale doesn't happen dimension disasters problem because kernel function is introduced, and its solution is the global optimal solution, so the situation prediction is more accurate. The experiment tests indicated that this method can accurately acquire the situation value prediction results, it has the good situation prediction potency, which provided one new key for prediction of networks security situation.

Improved Learning Algorithm Based on Semi-Supervised Support Vector

2011 ◽  
Vol 474-476 ◽  
pp. 1-6
Author(s):  
Guo Xing Peng ◽  
Bei Li
Keyword(s):  
Support Vector Machines ◽  
Lower Bound ◽  
Simulation Analysis ◽  
Learning Algorithm ◽  
Optimal Solution ◽  
Support Vector ◽  
Dual Function ◽  
Data Set ◽  
Vector Machines ◽  
Improved Learning

Improved learning algorithm for branch and bound for semi-supervised support vector machines is proposed, according to the greater difference in the optimal solution in different semi-supervised support vector machines for the same data set caused by the local optimization. The lower bound of node in IBBS3VM algorithm is re-defined, which will be pseudo-dual function value as the lower bound of node to avoid the large amount of calculation of 0-1 quadratic programming, reducing the lower bound of each node calculate the time complexity; at the same time, in determining the branch nodes, only based on the credibility of the unlabeled samples without the need to repeatedly carry out the training of support vector machines to enhance the training speed of the algorithm. Simulation analysis shows that IBBS3VM presented in this paper has faster training speed than BBS3VM algorithms, higher precision and stronger robustness than the other semi-supervised support vector machines.

scholarly journals The automorphism group of a completely positive cone and its Lie algebra

2013 ◽  
Vol 438 (10) ◽  
pp. 3862-3871 ◽  
Author(s):  
M. Seetharama Gowda ◽  
Roman Sznajder ◽  
Jiyuan Tao
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Positive Cone ◽  
Completely Positive ◽  
Completely Positive Cone
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