Model-based kernel for efficient time series analysis

We present novel, efficient, model based kernels for time series data rooted in the reservoir computation framework. The kernels are implemented by fitting reservoir models sharing the same fixed deterministically constructed state transition part to individual time series. The proposed kernels can naturally handle time series of different length without the need to specify a parametric model class for the time series. Compared with most time series kernels, our kernels are computationally efficient. We show how the model distances used in the kernel can be calculated analytically or efficiently estimated. The experimental results on synthetic and benchmark time series classification tasks confirm the efficiency of the proposed kernel in terms of both generalization accuracy and computational speed. This paper also investigates on-line reservoir kernel construction for extremely long time series.