Nonparallel Support Vector Machine Research Articles

Multi-class nonparallel support vector machine

Multi-class nonparallel support vector machine

Fused robust geometric nonparallel hyperplane support vector machine for pattern classification

Recently, introducing nonconvex loss functions in support vector machine (SVM) to improve the robustness against varies noises has been drawing much attention. In this paper, we first construct a new robust capped asymmetric elastic net (CaEN) loss function. Second, we describe a novel robust Huberized kernel-based (HK) loss function and theoretically demonstrate several important properties, such as smoothness, boundness and the trade-off between the standard least squares and the truncated least squares. Finally, we apply the CaEN loss and the HK loss into elastic net nonparallel hyperplane SVM (ENNHSVM) to develop a fused robust geometric nonparallel SVM (FRGNHSVM). The proposed FRGNHSVM not only inherits the advantages of ENNHSVM but also improves the robustness of classification problems. An efficient Pegasos-based DC (difference of convex functions) algorithm is implemented to solve the FRGNHSVM optimization problem. In comparison with four famous SVMs, including Lagrangian SVM, twin SVM, pinball SVM and C-loss twin SVM, experimental results on simulations and twelve UCI datasets show that the proposed FRGNHSVM can often improve more than 5% average prediction accuracy. Moreover, the performance of the high prediction accuracy of FRGHNSVM is more significant along with the ratio of label noise increasing, indicating its superiority in dealing with label-contaminated datasets.

Robust Twin Bounded Support Vector Classifier With Manifold Regularization.

Support vector machine (SVM), as a supervised learning method, has different kinds of varieties with significant performance. In recent years, more research focused on nonparallel SVM, where twin SVM (TWSVM) is the typical one. In order to reduce the influence of outliers, more robust distance measurements are considered in these methods, but the discriminability of the models is neglected. In this article, we propose robust manifold twin bounded SVM (RMTBSVM), which considers both robustness and discriminability. Specifically, a novel norm, that is, capped L₁-norm, is used as the distance metric for robustness, and a robust manifold regularization is added to further improve the robustness and classification performance. In addition, we also use the kernel method to extend the proposed RMTBSVM for nonlinear classification. We introduce the optimization problems of the proposed model. Subsequently, effective algorithms for both linear and nonlinear cases are proposed and proved to be convergent. Moreover, the experiments are conducted to verify the effectiveness of our model. Compared with other methods under the SVM framework, the proposed RMTBSVM shows better classification accuracy and robustness.

Laplacian generalized elastic net Lp-norm nonparallel support vector machine for semi-supervised classification

Laplacian generalized elastic net Lp-norm nonparallel support vector machine for semi-supervised classification

Union nonparallel support vector machines framework with consistency

Though there are several dozens of nonparallel support vector machines (NSVMs), little studies on general forms and characteristics of NSVMs are investigated. To fill in this gap, this paper categorizes the existing NSVMs into two types and reveals the advantages and defects of different types of them. In particular, inconsistency problems for these models are pointed out and discussed. Based on this observation, this paper further proposes and investigates a novel max–min distance-based nonparallel support vector machine (NSVM) with desired consistency. Compared with the existing methods, the proposed NSVM has the consistency of training and test and the consistency of metric. In addition, NSVM also assigns each sample an ascertained loss, which not only is able to identify if a data sample being classified correctly, but also makes NSVM completely in line with its decision rule. NSVM can be easily extended to its nonlinear version, and both of them are effectively solved through a modified proximal difference-of-convex algorithm with extrapolation algorithm. Experimental results on the artificial dataset, benchmark datasets and a real-world dataset support the advantages of the proposed model.

Robust nonparallel support vector machine with privileged information for pattern recognition

Robust nonparallel support vector machine with privileged information for pattern recognition

Nonparallel Support Vector Machine with L2-norm Loss and its DCD-type Solver

Nonparallel Support Vector Machine with L2-norm Loss and its DCD-type Solver

Nu -Improved nonparallel support vector machine

In this paper, a nu -improved nonparallel support vector machine (nu -IMNPSVM) is proposed to solve binary classification problems. In this model, we use related ideas of nu -support vector machine(nu -SVM), the parameter nu is introduced to control the limits of the support vectors percentage. In the objective function, the parameter varepsilon is increased to ensure that varepsilon -band is kept as small as possible. It has played a great role in the classification of unbalanced data sets. On the basis of maximizing the interval between two classes, nu -IMNPSVM can fully fit the distribution of data points in the class by minimizing the varepsilon -band, which enhances the generalization ability of the model. The results on the benchmark datasets testify that the proposed model has a good effect on the classification accuracy.

Parametric non-parallel support vector machines for pattern classification

Parametric non-parallel support vector machines for pattern classification

Hyperspectral Image Classification Based on a Least Square Bias Constraint Additional Empirical Risk Minimization Nonparallel Support Vector Machine

Hyperspectral image classification technology is important for the application of hyperspectral technology. Support vector machines (SVMs) work well in supervised classifications of hyperspectral images; however, they still have some shortcomings, and their use of a parallel decision plane makes it difficult to conform to real hyperspectral data distribution. The improved nonparallel support vector machine based on SVMs, i.e., the bias constraint additional empirical risk minimization nonparallel support vector machine (BC-AERM-NSVM), has improved classification accuracy compared its predecessor. However, BC-AERM-NSVMs have a more complicated solution problem than SVMs, and if the dataset is too large, the training speed is significantly reduced. To solve this problem, this paper proposes a least squares algorithm, i.e., the least square bias constraint additional empirical risk minimization nonparallel support vector machine (LS-BC-AERM-NSVM). The dual problem of the LS-BC-AERM-NSVM is an unconstrained convex quadratic programming problem, so its solution speed is greatly improved. Experiments on hyperspectral image data demonstrate that the LS-BC-AERM-NSVM displays a vast improvement in terms of solution speed compared with the BC-AERM-NSVM and achieves good classification accuracy.

Improved robust nonparallel support vector machines

Improved robust nonparallel support vector machines

L2-Loss nonparallel bounded support vector machine for robust classification and its DCD-type solver

In this paper, we study a new classification methodology to enhance the robustness and convergence of the nonparallel support vector machine (NPSVM), namely L2-Loss nonparallel bounded SVM (L2-NPBSVM). We first define a L2-Loss and an adjustable hinge loss for NPSVM. Then, using the two loss functions, we propose the L2-NPBSVM algorithm. Both the L2-loss and the adjustable hinge loss are insensitive to the feature noise around the decision boundary. In addition, the L2-Loss can make full use of the margin distribution information in the training samples. The margin distribution is more important than margin maximization for generalization performance. Furthermore, an additional regularization term is added into the objective functions of L2-NPBSVM. It can ensure the global solution and stability of optimization problems. Thus, the classification performance of L2-NPBSVM can be further improved. In addition, in order to shorten the training time, the dual coordinate descent (DCD) algorithm is described and analyzed to optimize L2-NPBSVM. Numerical experiments on different datasets demonstrate that our L2-NPBSVM has the advantages of strong robustness, strong generalization ability and fast convergence.

Multi-task nonparallel support vector machine for classification

Direct multi-task twin support vector machine (DMTSVM) explores the shared information between multiple correlated tasks, then it produces better generalization performance. However, it contains matrix inversion operation when solving the dual problems, so it costs much running time. Moreover, kernel trick cannot be directly utilized in the nonlinear case. To effectively avoid above problems, a novel multi-task nonparallel support vector machine (MTNPSVM) including linear and nonlinear cases is proposed in this paper. By introducing ε-insensitive loss instead of square loss in DMTSVM, MTNPSVM effectively avoids matrix inversion operation and takes full advantage of the kernel trick. Theoretical implication of the model is further discussed. To further improve the computational efficiency, the alternating direction method of multipliers (ADMM) is employed when solving the dual problem. The computational complexity and convergence of the algorithm are provided. In addition, the property and sensitivity of the parameter in model are further explored. The experimental results on fifteen benchmark datasets and twelve image datasets demonstrate the validity of MTNPSVM in comparison with the state-of-the-art algorithms. Finally, it is applied to real Chinese Wine dataset, and also verifies its effectiveness.

Hyperspectral Image Classification Based on Non-Parallel Support Vector Machine

Support vector machine (SVM) has a good effect in the supervised classification of hyperspectral images. In view of the shortcomings of the existing parallel structure SVM, this article proposes a non-parallel SVM model. Based on the traditional parallel boundary structure vector machine, this model adds an additional empirical risk minimization term to the original optimization problem by adding the least square term of the sample and obtains two non-parallel hyperplanes, respectively, forming a new non-parallel SVM algorithm to minimize the additional empirical risk of non-parallel SVM (Additional Empirical Risk Minimization Non-parallel Support Vector Machine, AERM-NPSVM). On the basis of AERM-NPSVM, the bias constraint is added to it, and AERM-NPSVM (BC-AERM-NPSVM) is further obtained. The experimental results show that, compared with the traditional parallel SVM model and the classical non-parallel SVM model, Twin Support Vector Machine (TWSVM), the new model, has a better effect in hyperspectral image classification and better generalization performance.

Path planning of patrol robot based on improved discrete electrostatic discharge algorithm

Safety is the premise of the stable and sustainable development of the chemical industry, safety accidents will not only cause casualties and economic losses, but also cause panic among workers and nearby residents. Robot safety inspection based on the fire risk level in a chemical industrial park can effectively reduce process accident losses and can even prevent accidents. The optimal inspection path is an important support for patrol efficiency, therefore, in this study, the fire risk level of each location to be inspected, which is obtained by the electrostatic discharge algorithm (ESDA)–nonparallel support vector machine evaluation model, is combined with the optimisation of the inspection path; that is, the fire risk level is used to guide the inspection path planning. The inspection path planning problem is a typical travelling salesman problem (TSP). The discrete ESDA (DESDA), based on the ESDA, is proposed. In view of the shortcomings of the long convergence time and ease of falling into the local optimum of the DESDA, further improvements are proposed in the form of the IDESDA, in which the greedy algorithm is used for the initial population, the 2-opt algorithm is applied to generate new solutions, and the elite set is joined to provide the best segment for jumping out of the local optimum. In the experiments, 11 public calculation examples were used to verify the algorithm performance. The IDESDA exhibited higher accuracy and better stability when solving the TSP. Its application to chemical industrial parks can effectively solve the path optimisation problem of patrol robots.

Joint rescaled asymmetric least squared nonparallel support vector machine with a stochastic quasi-Newton based algorithm

Joint rescaled asymmetric least squared nonparallel support vector machine with a stochastic quasi-Newton based algorithm

Single and Union Non-Parallel Support Vector Machine Frameworks

Single and Union Non-Parallel Support Vector Machine Frameworks

A Multiclass Nonparallel Parametric-Margin Support Vector Machine

The twin parametric-margin support vector machine (TPMSVM) is an excellent kernel-based nonparallel classifier. However, TPMSVM was originally designed for binary classification, which is unsuitable for real-world multiclass applications. Therefore, this paper extends TPMSVM for multiclass classification and proposes a novel K multiclass nonparallel parametric-margin support vector machine (MNP-KSVC). Specifically, our MNP-KSVC enjoys the following characteristics. (1) Under the “one-versus-one-versus-rest” multiclass framework, MNP-KSVC encodes the complicated multiclass learning task into a series of subproblems with the ternary output {−1,0,+1}. In contrast to the “one-versus-one” or “one-versus-rest” strategy, each subproblem not only focuses on separating the two selected class instances but also considers the side information of the remaining class instances. (2) MNP-KSVC aims to find a pair of nonparallel parametric-margin hyperplanes for each subproblem. As a result, these hyperplanes are closer to their corresponding class and at least one distance away from the other class. At the same time, they attempt to bound the remaining class instances into an insensitive region. (3) MNP-KSVC utilizes a hybrid classification and regression loss joined with the regularization to formulate its optimization model. Then, the optimal solutions are derived from the corresponding dual problems. Finally, we conduct numerical experiments to compare the proposed method with four state-of-the-art multiclass models: Multi-SVM, MBSVM, MTPMSVM, and Twin-KSVC. Experimental results demonstrate the feasibility and effectiveness of MNP-KSVC in terms of multiclass accuracy and learning time.

Reductive and effective discriminative information-based nonparallel support vector machine

Reductive and effective discriminative information-based nonparallel support vector machine

Sampling Active Learning Based on Non-parallel Support Vector Machines

Labeled examples are scarce while there are numerous unlabeled examples in real-world. Manual labeling these unlabeled examples is often expensive and inefficient. Active learning paradigm seeks to handle this problem by identifying the most informative examples from the unlabeled examples to label. In this paper, we present two novel active learning approaches based on non-parallel support vector machines and twin support vector machines which adopt the margin sampling method and the manifold-preserving graph reduction algorithm to select the most informative examples. The manifold-preserving graph reduction is a sparse subset selecting algorithm which exploits the structural space connectivity and spatial diversity among examples. In each iteration, an active learner draws the informative and representative candidates from the subset instead of the whole unlabeled data. This strategy can keep the manifold structure and reduce noisy points and outliers in the whole unlabeled data. Experimental results on multiple datasets validate the effective performance of the proposed methods.