Theoretical properties and implementation of the one-sided mean kernel for time series

Abstract : In this paper we introduce a new kernel for sequences of structured data, investigate its properties and propose a fast implementation. We demonstrate using the theory of infinitely divisible kernels that this kernel is positive definite, that it is a radial basis kernel and that it reduces to a product kernel when comparing two sequences of the same length. We present an implementation of this kernel using dynamic programming techniques that leads to an algorithm of lower complexity than competing kernels. We illustrate that this kernel presents a consistent behavior in the context of sub-sampling of continuous time series. Finally we compare this kernel with the global alignment kernel in two classification tasks with real world data using support vector machines.