scholarly journals Smooth augmented lagrangian method for twin bounded support vector machine

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fatemeh Bazikar ◽  
Saeed Ketabchi ◽  
Hossein Moosaei
Keyword(s):  
Support Vector Machine ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Binary Classification ◽  
Unconstrained Minimization ◽  
Lagrangian Method ◽  
Superior Performance ◽  
Support Vector ◽  
Minimization Problems ◽  
Bounded Support

<p style='text-indent:20px;'>In this paper, we propose a method for solving the twin bounded support vector machine (TBSVM) for the binary classification. To do so, we use the augmented Lagrangian (AL) optimization method and smoothing technique, to obtain new unconstrained smooth minimization problems for TBSVM classifiers. At first, the augmented Lagrangian method is recruited to convert TBSVM into unconstrained minimization programming problems called as AL-TBSVM. We attempt to solve the primal programming problems of AL-TBSVM by converting them into smooth unconstrained minimization problems. Then, the smooth reformulations of AL-TBSVM, which we called AL-STBSVM, are solved by the well-known Newton's algorithm. Finally, experimental results on artificial and several University of California Irvine (UCI) benchmark data sets are provided along with the statistical analysis to show the superior performance of our method in terms of classification accuracy and learning speed.</p>

scholarly journals Entropy-Based Fuzzy Twin Bounded Support Vector Machine for Binary Classification

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 86555-86569 ◽  
Author(s):  
Sugen Chen ◽  
Junfeng Cao ◽  
Zhong Huang ◽  
Chuansheng Shen
Keyword(s):  
Support Vector Machine ◽  
Binary Classification ◽  
Support Vector ◽  
Bounded Support

scholarly journals An augmented Lagrangian method for solving total variation (TV)-based image registration model

2020 ◽  
Vol 14 ◽  
pp. 174830262097353
Author(s):  
Noppadol Chumchob ◽  
Ke Chen
Keyword(s):  
Image Registration ◽  
Augmented Lagrangian ◽  
Numerical Solutions ◽  
Augmented Lagrangian Method ◽  
Closed Form Solution ◽  
Numerical Algorithms ◽  
Lagrangian Method ◽  
Form Solution ◽  
The Other ◽  
Other Hand

Variational methods for image registration basically involve a regularizer to ensure that the resulting well-posed problem admits a solution. Different choices of regularizers lead to different deformations. On one hand, the conventional regularizers, such as the elastic, diffusion and curvature regularizers, are able to generate globally smooth deformations and generally useful for many applications. On the other hand, these regularizers become poor in some applications where discontinuities or steep gradients in the deformations are required. As is well-known, the total (TV) variation regularizer is more appropriate to preserve discontinuities of the deformations. However, it is difficult in developing an efficient numerical method to ensure that numerical solutions satisfy this requirement because of the non-differentiability and non-linearity of the TV regularizer. In this work we focus on computational challenges arising in approximately solving TV-based image registration model. Motivated by many efficient numerical algorithms in image restoration, we propose to use augmented Lagrangian method (ALM). At each iteration, the computation of our ALM requires to solve two subproblems. On one hand for the first subproblem, it is impossible to obtain exact solution. On the other hand for the second subproblem, it has a closed-form solution. To this end, we propose an efficient nonlinear multigrid (NMG) method to obtain an approximate solution to the first subproblem. Numerical results on real medical images not only confirm that our proposed ALM is more computationally efficient than some existing methods, but also that the proposed ALM delivers the accurate registration results with the desired property of the constructed deformations in a reasonable number of iterations.

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