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Twin support vector machines (TWSVM) is a new machine learning method based on the theory of Support Vector Machine (SVM). Unlike SVM, TWSVM would generate two non-parallel planes, such that each plane is closer to one of the two classes and is as far as possible from the other. In TWSVM, a pair of smaller sized quadratic programming problems (QPPs) is solved, instead of solving a single large one in SVM, making the computational speed of TWSVM approximately 4 times faster than the standard SVM. At present, TWSVM has become one of the popular methods because of its excellent learning performance. In this paper, the research progress of TWSVM is reviewed. Firstly, it analyzes the basic theory of TWSVM, then tracking describes the research progress of TWSVM including the learning model and specific applications in recent years, finally points out the research and development prospects. This helps researchers to effectively use TWSVM as an emerging research approach, encouraging them to work further on performance improvement. [ABSTRACT FROM AUTHOR]

Recently, some nonparallel plane regressors, such as twin support vector regression (TSVR), and least squares TSVR (LSTSVR), have been proposed and have attracted much attention. However, these algorithms are not sparse, which would make their learning speed low. In this paper, we propose a novel nonparallel plane regressor, which can automatically select the relevant features. Firstly, we introduce a regularization term to the objective function of LSTSVR, which can guarantee two quadratic programming problems (QPPs) are strong convex, implying that the proposed algorithm can obtain the global but unique solution. Secondly, the primal formulation is converted to a linear programming (LP) problem. Then, we solve the dual of the LP formulation by minimizing its exterior penalty problem, which would make our method yield very sparse solutions. In other words, this method can suppress input features so that it can obtain comparable regression performance when using fewer computational time. Numerical experiments on artificial dataset and benchmark datasets demonstrate the feasibility and validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract Functional networks (FNs) are extensions of neural networks (NNs). Unlike NNs, FNs considers general functional models instead of sigmoid-like models. Additionally, in FNs, there are no weights associated with the links that connect neurons. In this paper, we review the research progress and applications of FNs models in recent years. First, we introduce FNs architecture, three typical functional models and the learning process, and we explain the differences between NNs and FNs. Second, we discuss recent applications of FNs that have been introduced in many fields, such as time series prediction, differential and functional equations, pattern classification, detection and prediction, approximation computation, complex system modeling, computer-aided design (CAD), and linear and nonlinear regression. Finally, we present some remarks on future research directions for FNs. [ABSTRACT FROM AUTHOR]