A Novel Time Series Kernel for Sequences Generated by LTI Systems

Abstract

The recent introduction of Hankelets to describe time series relies on the assumption that the time series has been generated by a vector autoregressive model (VAR) of order p. The success of Hankelet-based time series representations prevalently in nearest neighbor classifiers poses questions about if and how this representation can be used in kernel machines without the usual adoption of mid-level representations (such as codebook-based representations). It is also of interest to investigate how this representation relates to probabilistic approaches for time series modeling, and which characteristics of the VAR model a Hankelet can capture. This paper aims at filling these gaps by: deriving a time series kernel function for Hankelets (TSK4H), demonstrating the relations between the derived TSK4H and former dissimilarity/similarity scores, highlighting an alternative probabilistic interpretation of Hankelets. Experiments with an off-the-shelf SVM implementation and extensive validation in action classification and emotion recognition on several feature representations, show that the proposed TSK4H allows achieving state-of-the-art or even superior accuracy values in classification with respect to past work. In contrast to state-of-the-art time series kernel functions that suffer of numerical issues and tend to provide diagonally dominant kernel matrices, empirical results suggest that the TSK4H has limited numerical issues in high-dimensional spaces. On three widely used public benchmarks, TSK4H consistently outperforms other time series kernel functions despite its simplicity and limited time complexity.