An overview on nonparallel hyperplane support vector machine algorithms

Using information technology such as search engine for collecting and monitoring of network public opinion is a practical and effective method. This paper puts forward an improved algorithm of SVM classifier based on incremental learning online, and then implements a topic crawler system for network public opinion and to grab the public opinion.

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.

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) 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.

To solve the problem that traditional multi-label support vector machine (SVM) classification algorithm adopting nonlinear kernel has been severely restricted from being used on large-scale data sets, we propose fast multi-label low-rank-linearized SVM classification algorithm based on approximate extreme points (AEML-LLSVM). First, it adopts the approximate extreme points' method to obtain representative sets from the training data set. Then, the approximate extreme points' low-rank-linearized SVM (AELLSVM) is trained on the representative sets. The AELLSVM integrates the advantages of approximate extreme points' method and LLSVM. Experimental results on three large-scale multi-label data sets have proven that the training and the testing speed of AEML-LLSVM classification algorithm are greatly improved under the premise that its classification performance is similar to that of ML-LIBSVM classification algorithm and superior to that of other fast multi-label SVM classification algorithms.

abstractUniversum, a third class not belonging to either class of the classification problem, allows to incorporate the prior knowledge into the learning process. A lot of previous work have demonstrated that the Universum is helpful to the supervised and semi-supervised classification. Moreover, Universum has already been introduced into the support vector machine (SVM) and twin support vector machine (TSVM) to enhance the generalisation performance. To further increase the generalisation performance, we propose a least squares TSVM with Universum data (-TSVM) in this paper. Our -TSVM possesses the following advantages: first, it exploits Universum data to improve generalisation performance. Besides, it implements the structural risk minimisation principle by adding a regularisation to the objective function. Finally, it costs less computing time by solving two small-sized systems of linear equations instead of a single larger-sized quadratic programming problem. To verify the validity of our proposed algorithm, we conduct various experiments around the size of labelled samples and the number of Universum data on data-sets including seven benchmark data-sets, Toy data, MNIST and Face images. Empirical experiments indicate that Universum contributes to making prediction accuracy improved even stable. Especially when fewer labelled samples given, -TSVM is far superior to the improved LS-TSVM (ILS-TSVM), and slightly superior to the -TSVM.

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.

Distributed Denial of Service (DDoS) attacks represent a significant danger in network security because they can lead to extensive service interruptions. With these attacks increasingly mirroring regular traffic, smart and effective detection systems are essential. This research seeks to assess the efficacy of the Support Vector Machine (SVM) classification algorithm in identifying DDoS attacks in network traffic. The data utilized is CICIDS2017, focusing on the subset Friday-WorkingHours-Afternoon-DDos.pcap_ISCX.csv, which contains both legitimate traffic and DDoS attacks like DoS-Hulk, DoS-GoldenEye, and DDoS. The preprocessing stage included eliminating duplicates and null entries, label binary encoding, normalization through Min-Max Scaler, and feature selection applying the Chi-Square technique. The data was divided into 80% for training and 20% for testing purposes. The Radial Basis Function (RBF) kernel was utilized to train the SVM model, and hyperparameter optimization was performed with GridSearchCV. The evaluation of the model's performance was conducted through accuracy, precision, recall, F1-score, confusion matrix, and visual representations including ROC and Precision-Recall Curves. The findings indicate that prior to tuning, the model reached an accuracy of 97%, which increased to 99% post-tuning, accompanied by an F1-score of 0.99. This shows that the SVM algorithm, when paired with appropriate preprocessing and optimization, is very efficient in identifying DDoS attacks within network traffic.

Weighted least squares projection twin support vector machines with local information

Recursive projection twin support vector machine (PTSVM) and Locality preserving projection twin support vector machine (LPPTSVM) are two extensions of traditional support vector machine (SVM). However, they may lead to a weak classifier in the application where some data points may not be fully assigned to one class. In this paper, we introduce the basic idea of fuzzy membership into LPPTSVM and propose a fuzzy LPPTSVM (FLPPTSVM) algorithm. Through fuzzy weighting technique, input points with different confidence degrees can make different contributions to the learning of decision surface. In this way, FLPPTSVM not only maintains the advantages of LPPTSVM which considers the local geometrical structure of the data and enhances the generalization ability of the algorithm, but also decreases the influence of outliers and noises. We construct experiments on artificial and UCI benchmark datasets and the results show the effectiveness and robustness of the proposed FLPPTSVM method.

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.

In the field of machine learning, support vector machine is a supervised learning model which can analyze the data and identify patterns, and this theory is used for classification and regression analysis which is related to the learning algorithm.Support vector machine is a new machine learning method based on statistical learning theory, and has become a hot research topic in the machine learning field because of its excellent learning performance.Support vector machine is also a learning machine based on kernel function, and its generalization ability depends on the chosen kernel function to a great extent.Nevertheless, traditional support vector machine cannot achieve the desired results when training large-scale data set.Therefore, in order to improve training efficiency and generalization performance of support vector machine, we have to improve this algorithm.Although support vector machine has great advantages in theory, the research on its application is comparatively delayed.In this paper, we focus on novel support vector machine generated from multi-subjects amalgamation, such as fuzzy support vector machine, granular support vector machine, twin support vector machine.We analyze a large number of literature review about development trend of support vector machine and its applications in computer field, laying foundation for the systematic research on the correlation algorithm based on support vector machine.

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.

The current classification algorithms have weak fault-tolerance. In order to solve problem, a multiple support vector machines method, called Upper preferred Multiple Directed Acyclic Graph Support Vector Machines (UMDAG-SVMs), is proposed. Firstly, we present least squares projection twin support vector machine (LSPTSVM) with confidence-degree for generating binary classifiers. It uses idea that when confidence-degree outputted from node in directed graph, is below threshold, decision-making process will go on along with two branches of node at same time., which strengthens algorithm's fault-tolerance. In order to select parameters of algorithm, we use genetic algorithm to select these parameters. Secondly, according to minimal hypersphere distance, and known principle the upper-level classifiers bring up better performance of classification in DAG-SVMs , we present a new classification algorithm, called UMDAG-SVMs. This algorithm has two advantages of strong fault-tolerance and high classification accuracy. Finally, we make experiments to test performance of algorithm. Experimental results in public datasets show that our UMDAG-SVMs has comparable classification accuracy to that other algorithms but with remarkable less computation.

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.