Reduced Twin Support Vector Regression For The Simultaneous Learning Of A Function And Its Deriyatiyes

Twin Support Vector Regression（TSVR）is a new regression algorithm based onTwin Support Vector Machine（TSVM） which proposed by Jayadeva. The basic idea isgenerating a pair of nonparallel hyperplanes such that each function determines the-insensitive down or up bounds of the unknown regressor, the end regressor is decidedby the mean of these two functions. Reduced Twin Support Vector Regression（RTSVR）uses the notion of rectangular kernels to reduce the size of QPP in TSVR. The problemof learning a function and its derivatives simultaneously are widely used in many fields.The subject of this article is to study how to uses Reduced Twin Support VectorRegression to learning of a function and its derivatives simultaneously. We haveaccomplished the following work.The paper describes the two algorithms of learning a function and its derivativessimultaneously: Classical SVR, and Regularized least squares support vector regression.We study application of TSVR algorithm on learning a function and its derivativessimultaneously, then present the regressor for a real valued function of a single realvariable and more than one variable. Analyze the estimation accuracy of TSVRalgorithm, and its convergence. We compare the advantages and disadvantages of SVR、RLSVR、TSVR algorithm experimentally.Experimental results show that TSVR in the function of more than one variabledemonstrates its effectiveness over other existing approaches in terms of improvingestimation accuracy, and has an additional feature of admitting to sparseness in case oflarge datasets. But especially in large sized datasets, the huge amount of calculation insolving QPP make the efficiency is low. By introducing the notion of rectangularkernels to improve the TSVR algorithm, we point out the Reduced Twin Support VectorRegression algorithm. Experimental results show that the reduced new algorithmobtains significant improvements in execution time, thus facilitating its application tolarger sized datasets.