Stochastic gradient descent for minimal enclosing ball

In this paper, we apply Stochastic Gradient Descent framework to the problem of finding minimal enclosing ball for anomaly detection purpose. The main difficulty lies in the fact that the primal form of the optimization problem behind minimal enclosing ball is not convex and hence a convergence to a global minima with a good convergence rate is not guaranteed in theory. We address this issue by transforming the problem of finding a minimal enclosing ball to that of finding a largest margin hyperplane in the extended space. We validate the proposed method on several benchmark datasets. The experimental results point out that our proposed method gains higher testing accuracy while simultaneously achieving a significantly computational speedup.