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Twin support vector regression (TSVR) is a useful extension of traditional support vector regression (SVR). As a new regression model, the basic idea of TSVR is generating a pair of nonparallel functions on both sides of the training data points, such that the ε -insensitive upper and lower bounds of the regression function can be determined. Owing to its excellent learning ability, TSVR has become a research hotspot in the field of machine learning. With the deepening of such research, scholars have found that TSVR also has certain limitations, and thus various improved models have been proposed. This review aims to report the recent developments in twin support vector regression. First, the basic concepts and basic models of TSVR are introduced. Second, the improved algorithms and applications of TSVR in recent years are summarized, and the advantages and disadvantages of its representative algorithms are analyzed and compared with the experiments. Finally, we discuss the research conducted on TSVR. [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]