Training an Improved TSVR Based on Wavelet Transform Weight Via Unconstrained Convex Minimization

摘要

An improved wavelet transform based weighted ε-twin support vector regression (WW-ε-TSVR) is proposed in this paper. In our WW-ε-TSVR, to reduce the impact of outliers, the wavelet weight matrix is introduced to give different penalties for the samples located in different places. Further, by using the 'plus' function, a pair of unconstrained minimization problems is solved in primal space rather than dual space, in which three smooth functions are introduced to replace the non-differentiable non-smooth 'plus' function. To speed up the training procedure, the generalized derivative iterative approach and Newton iterative approach are used to obtain the approximate solution, and five more detailed iterative algorithms are given. At last, the experimental results on several artificial and UCI datasets indicate that the proposed method is of effectiveness and applicability, it not only gives similar or better generalization performance with other popular methods such as TSVR and ε-TSVR, but also requires less computational time.