Least squares twin support vector machine with Universum data for classification

KNN weighted reduced universum twin SVM for class imbalance learning

A novel ?-twin support vector machine with Universum data (U?$\mathfrak {U}_{\nu }$-TSVM) is proposed in this paper. U?$\mathfrak {U}_{\nu }$-TSVM allows to incorporate the prior knowledge embedded in the unlabeled samples into the supervised learning. It aims to utilize these prior knowledge to improve the generalization performance. Different from the conventional U$\mathfrak {U}$-SVM, U?$\mathfrak {U}_{\nu }$-TSVM employs two Hinge loss functions to make the Universum data lie in a nonparallel insensitive loss tube, which makes it exploit these prior knowledge more flexibly. In addition, the newly introduced parameters ?1, ?2 in the U?$\mathfrak {U}_{\nu }$-TSVM have better theoretical interpretation than the penalty factor c in the U$\mathfrak {U}$-TSVM. Numerical experiments on seventeen benchmark datasets, handwritten digit recognition, and gender classification indicate that the Universum indeed contributes to improving the prediction accuracy. Moreover, our U?$\mathfrak {U}_{\nu }$-TSVM is far superior to the other three algorithms (U$\mathfrak {U}$-SVM, ?-TSVM and U$\mathfrak {U}$-TSVM) from the prediction accuracy.

EEG signal classification using universum support vector machine

In this paper, for an improved twin support vector machine (TWSVM), we give it a theoretical explanation based on the concept of Universum and then name it Self-Universum support vector machine (SUSVM). For the binary classification problem, SUSVM takes the positive class and negative class as Universum separately to construct two classification problems with Universum; therefore, two nonparallel hyperplanes are derived. SUSVM has several improved advantages compared with TWSVMs. Furthermore, we improve SUSVM by formulating it as a pair of linear programming problems instead of quadratic programming problems (QPPs), which leads to the better generalization performance and less computational time. The effectiveness of the enhanced method is demonstrated by experimental results on several benchmark datasets.

Weighted Twin Support Vector Machines with Local Information and its application

Twin support vector machine (TWSVM) is a new machine learning method, as opposed to solving a single quadratic programming problem in support vector machine (SVM), which generates two nonparallel hyperplanes by solving two smaller size quadratic programming problems. However, the TWSVM obtains the final classifier by giving the same importance to all training samples which may be important for classification performance. In order to address this problem, in this paper, we propose a novel entropy-based fuzzy twin bounded support vector machine (EFTBSVM) for binary classification problems. By considering the fuzzy membership value for each sample and assigning it based on the entropy value, the samples with higher class certainty are assigned to relatively larger fuzzy membership. In addition, the proposed EFTBSVM not only maintains the superior characteristics of the TWSVM but also exploits the structural risk minimization principle by introducing a regularization term. The experimental results achieved on synthetic datasets and benchmark datasets illustrate the effectiveness of the proposed method.

Twin support vector machine (TWSVM) and twin support vector regression (TSVR) are newly emerging efficient machine learning techniques which offer promising solutions for classification and regression challenges respectively. TWSVM is based upon the idea to identify two nonparallel hyperplanes which classify the data points to their respective classes. It requires to solve two small sized quadratic programming problems (QPPs) in lieu of solving single large size QPP in support vector machine (SVM) while TSVR is formulated on the lines of TWSVM and requires to solve two SVM kind problems. Although there has been good research progress on these techniques; there is limited literature on the comparison of different variants of TSVR. Thus, this review presents a rigorous analysis of recent research in TWSVM and TSVR simultaneously mentioning their limitations and advantages. To begin with, we first introduce the basic theory of support vector machine, TWSVM and then focus on the various improvements and applications of TWSVM, and then we introduce TSVR and its various enhancements. Finally, we suggest future research and development prospects.

In this paper, a novel unconstrained convex minimization problem formulation for the Lagrangian dual of the recently introduced twin support vector machine (TWSVM) in simpler form is proposed for constructing binary classifiers. Since the objective functions of the modified minimization problems contain non-smooth `plus' function, we solve them by Newton iterative method either by considering their generalized Hessian matrices or replacing the `plus' function by a smooth approximation function. Numerical experiments were performed on a number of interesting real-world benchmark data sets. Computational results clearly illustrates the effectiveness and the applicability of the proposed approach as comparable or better generalization performance with faster learning speed is obtained in comparison with SVM, least squares TWSVM (LS-TWSVM) and TWSVM.

Over the past decades, 1-norm techniques based on algorithms are widely used to suppress input features. Quite different from traditional 1-norm support vector machine (SVM), direct 1-norm optimization based on the primal problem of nonparallel plane classifiers like generalized proximal support vector machine, twin support vector machine (TWSVM) and least squares twin support vector machine (LSTSVM) are not capable of generating very sparse solutions that are vital for classification and can make them easier to store and faster to compute. To address the issue, in this paper, we develop a feature selection method for LSTSVM, called a feature selection method for nonparallel plane support vector machine classification (FLSTSVM), which is specially designed for strong feature suppression. We incorporate a Tikhonov regularization term to the objective of LSTSVM, and then minimize its 1-norm measure. Solution of FLSTSVM can follow directly from solving two smaller quadratic programming problems (QPPs) arising from two primal QPPs as opposed to two dual ones in TWSVM. FLSTSVM is capable of generating very sparse solutions. This means that FLSTSVM can reduce input features, for the linear case. When a nonlinear classifier is used, few kernel functions determine the classifier. In addition to having strong feature suppression, the edge of our method still lies in its faster computing time compared to that of TWSVM, Newton Method for Linear Programming SVM (NLPSVM) and LPNewton. Lastly, this algorithm is compared on public data sets, as well as an Exclusive Or (XOR) example.

Sparse pinball twin support vector machines

Classical support vector machine (SVM) and its twin variant twin support vector machine (TWSVM) utilize the Hinge loss that shows linear behaviour, whereas the least squares version of SVM (LSSVM) and twin least squares support vector machine (LSTSVM) uses L2-norm of error which shows quadratic growth. The robust Huber loss function is considered as the generalization of Hinge loss and L2-norm loss that behaves like the quadratic L2-norm loss for closer error points and the linear Hinge loss after a specified distance. Three functional iterative approaches based on generalized Huber loss function are proposed in this paper to solve support vector classification problems of which one is based on SVM, i.e. generalized Huber support vector machine and the other two are in the spirit of TWSVM, namely generalized Huber twin support vector machine and regularization on generalized Huber twin support vector machine. The proposed approaches iteratively find the solutions and eliminate the requirements to solve any quadratic programming problem (QPP) as for SVM and TWSVM. The main advantages of the proposed approach are: firstly, utilize the robust Huber loss function for better generalization and for lesser sensitivity towards noise and outliers as compared to quadratic loss; secondly, it uses functional iterative scheme to find the solution that eliminates the need to solving QPP and also makes the proposed approaches faster. The efficacy of the proposed approach is established by performing numerical experiments on several real-world datasets and comparing the result with related methods, viz. SVM, TWSVM, LSSVM and LSTSVM. The classification results are convincing.

Twin support vector machine (TWSVM) is a classical distance metric learning method for classification problems. The formulation of TWSVM criterion is based on L2-norm distance, which makes TWSVM prone to being influenced by the presence of outliers. In this paper, to develop a robust distance metric learning method, we propose a new objective for TWSVM classifier using L1-norm distance metric, termed as L1-TWSVM. The optimization strategy is to maximize the ratio of the inter-class distance dispersion to the intra-class distance dispersion by using L1-norm distance rather than L2-norm distance. Besides, we design a simple and valid iterative algorithm to solve L1-norm optimal problems, which is easy to actualize and its convergence to an optimum is theoretically ensured. The efficiency and robustness of L1-TWSVM have been validated by experiments on UCI datasets and artificial datasets. The promising experimental results indicate that our proposals outperform relevant state-of-the-art methods in all kinds of experimental settings.

The condition monitoring and fault diagnosis of power transformers plays a significant role in the safe, stable and reliable operation of the whole power system. Dissolved gas analysis (DGA) methods are widely used for fault diagnosis, however, their accuracy is limited by the selection of DGA features and the performance of fault diagnosis models, for example, the classical support vector machine (SVM), is easily affected by unbalanced training samples. This paper presents a transformer fault diagnosis model based on chemical reaction optimization and a twin support vector machine. Twin support vector machines (TWSVMs) are used as classifiers for solving problems involving unbalanced and insufficient samples. Restricted Boltzmann machines (RBMs) are used for data preprocessing to ensure the effective identification of feature parameters and improve the efficiency and accuracy of fault diagnosis. The chemical reaction optimization (CRO) algorithm is used to optimize TWSVM parameters to select the optimal training parameters. The cross-validation (CV) method is used to ensure the reliability and generalization ability of the diagnostic model. Finally, the validity of the model is verified using real fault samples and random testing.

The traditional vector-based algorithms, such as Support Vector Machine (SVM) and Twin Support Vector Machine (TSVM), have many limitations especially when tensor is considered as input matrix. In this paper, we proposed a novel algorithm with a tensor-based classification paradigm to utilize the structural information. The new proposed algorithm is called  -Twin Support Tensor Machine ( -TSTM), which is an extension of  -Twin Support Vector Machine ( -TSVM). Similarly,  -TSTM solves a pair of smaller-sized Quadratic Programming Problems (QPPs). It reduces the computational complexity substantially. Besides, we formulate  -TSTM, which separates samples in the tensor space with two non-parallel hyperplanes, and the pair of parameters ( ) have theoretical interpretation which are used to control the bounds of the fractions of support tensors and the error margins. What’s more, the structure information of data is retained by the direct use of tensor representation. The proposed  -TSTM can preferably overcome overfitting problem and deal with big data while most vector-based algorithms could hardly compare. In addition, it has better performances on high dimensional and small-sample-size (S3) problem. The efficiency and superiority of the proposed method are demonstrated by experiments on various datasets.

Color image classification and retrieval through ternary decision structure based multi-category TWSVM