In this paper we propose an innovative learning algorithm - a variation of One-class ? Support Vector Machines (SVMs) learning algorithm to produce sparser solutions with much reduced computational complexities. The proposed technique returns an approximate solution, nearly as good as the solution set obtained by the classical approach, by minimizing the original risk function along with a regularization term. We introduce a bi-criterion optimization that helps guide the search towards the optimal set in much reduced time. The outcome of the proposed learning technique was compared with the benchmark one-class Support Vector machines algorithm which more often leads to solutions with redundant support vectors. Through out the analysis, the problem size for both optimization routines was kept consistent. We have tested the proposed algorithm on a variety of data sources under different conditions to demonstrate the effectiveness. In all cases the proposed algorithm closely preserves the accuracy of standard one-class ? SVMs while reducing both training time and test time by several factors.