This paper proposes a novel hypersphere support vector machines (HSVMs) based on generalized multiplicativeupdates. This algorithm can obtain the boundary of hypersphere containing one class of samples by the description of thetraining samples from one class and use this boundary to classify the test samples. The generalized multiplicative updatesare applied to solving boundary optimization programming. Multiplicative updates available are suited for nonnegativequadratic convex programming. The generalized multiplicative updates are derived to box and sum constrained quadraticprogramming in this paper. They provide an extremely straightforward way to implement support vector machines (SVMs)where all variables are updated in parallel. The generalized multiplicative updates converge monotonically to the solution ofthe maximum margin hyperplane. The experiments showthe superiority of our new algorithm.