Robust twin support vector regression with correntropy-based metric

Machine learning methods have been widely used control and information systems. Robust learning is an important issue in machine learning field. In this work, we propose a novel robust regression framework. Specifically, we propose a robust similarity measure induced by correntropy, and its important properties are demonstrated theoretically such as symmetry, boundedness, nonnegativity, consistency, smoothness and approximation behaviors. Moreover, the proposed robust metric extends the traditional metrics such as the l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{2}$$\end{document}-norm and l0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{0}$$\end{document}-norm as the kernel parameter approaches different values. Then with the proposed similarity metric and ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-insensitive pinball loss, a new robust twin support vector regression framework (RTSVR) is proposed to handle robust regression problems. The linear RTSVR model is first built, and a kernelled RTSVR version is developed to deal with nonlinear regressions. To handle the nonconvexity of the proposed RTSVR, we use DC (different of convex function) programming algorithm to iteratively solve the problem, and the resulting algorithm converges linearly. To test the proposed RTSVR, numerical experiments are implemented on two databases including a public benchmark database and a practical application database. Experiments on benchmark data with different types of noise illustrate that the proposed methods achieve better performance than the traditional methods in most cases. Experiments on the application database, the proposed RTSVR is combined with near-infrared (NIR) spectral technique to analyze the hardness of licorice seeds in low frequency,intermediate frequency and high frequency spectral regions respectively. Experiments on different spectral regions show that the performance of the RTSVR is better than that of the traditional methods in all spectral regions.