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Primal least squares twin support vector regression

The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space. However, this solution is affected by time and memory constraints when dealing with large datasets. In this paper, we present a least squares version for TSVR in the primal space, termed primal least squares TSVR (PLSTSVR). By introducing the least squares method, the inequality constraints of TSVR are transformed into equality constraints. Furthermore, we attempt to directly solve the two QPPs with equality constraints in the primal space instead of the dual space; thus, we need only to solve two systems of linear equations instead of two QPPs. Experimental results on artificial and benchmark datasets show that PLSTSVR has comparable accuracy to TSVR but with considerably less computational time. We further investigate its validity in predicting the opening price of stock.