Time series classification via divergence measures between probability density functions

Abstract

In this work, we describe a new method for time series classification (TSC) that consists of modeling time series as probability density functions (PDFs) and applies the divergence (the Integrated Squared Error) between two PDFs as a similarity measure for classification via k-Nearest Neighbours (kNN). The proposed method starts by projecting the original time series data into the reconstructed phase space (RPS) via time delay embedding. From these data points in RPS, the corresponding underlying PDF is estimated by Kernel Density Estimation (KDE). Then, a similarity matrix is built by using the Integrated Squared Error (ISE) as a distance measure between two PDFs, from which kNN algorithms can be eventually applied for classification. Two experiments were conducted in order to evaluate this proposal. The first one investigated the impact of the time delay embedding parameters on classification accuracy. We concluded that the embedding dimension is the most influential parameter, for which the results have shown to be highly sensitive. The second experiment provides a comparative analysis of the proposed method against the main state-of-the-art methods for TSC on several well-known benchmark datasets. The results were quite encouraging, and our proposal was able to outperform the compared TSC methods in the majority of the datasets.