MIMO SVMs for classification and regression using the geometric algebra framework

Abstract

This paper introduces the Clifford support vector machines (CSVM) as a generalization of the real- and complex-valued support vector machines using the Clifford geometric algebra. In this framework we handle the design of kernels involving the Clifford or geometric product for linear and nonlinear classification and regression. The major advantage of our approach is that one requires only one CSVM with one kernel (involving the Clifford product) which can admit multiple multivector inputs and it can carry out multi-class classification and regression. In contrast one would need many real valued SVMs for a multi-class problem which is time consuming.