Recurrent Clifford Support Machines

This paper introduces the recurrent Clifford support vector machines (RCSVM). First we explain the 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 and one redefines the optimization variables as multivectors. This allows us to have a multivector as output therefore we can represent multiple classes according to the dimension of the geometric algebra in which we work. We show that one can apply CSVM to build a recurrent CSVM.We study the performance of the recurrent CSVM with experiments using time series and tasks of visually guided robotics.