An extension of Fisherʹs discriminant analysis for stochastic processes

In this paper we present a general notion of Fisherʹs linear discriminant analysis that extends the classical multivariate concept to situations that allow for function-valued random elements. The development uses a bijective mapping that connects a second order process to the reproducing kernel Hilbert space generated by its within class covariance kernel. This approach provides a seamless transition between Fisherʹs original development and infinite dimensional settings that lends itself well to computation via smoothing and regularization. Simulation results and real data examples are provided to illustrate the methodology.