6533b86cfe1ef96bd12c8c9c

RESEARCH PRODUCT

A Novel Time Series Kernel for Sequences Generated by LTI Systems

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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.