Univariate and Multivariate Time Series Manifold Learning

Abstract

Time series analysis aims to extract meaningful information from data that has been generated in sequence by a dynamic process. The modelling of the non-linear dynamics of a signal is often performed using a linear space with a similarity metric which is either linear or attempts to model the non-linearity of the data in the linear space. In this research, a different approach is taken where the non-linear dynamics of the time series are represented using a phase space. Training data is used to construct the phase space in which the data lies on or close to a lower-dimensional manifold. The basis of the non-linear manifold is derived using the kernel principal components derived using kernel principal component analysis where fewer components are retained in order to identify the lower-dimensional manifold. Data instances are projected onto the manifold, and those with a large distance between the original point and the projection are considered to be derived from a different underlying process. The proposed algorithm is able to perform time series classification on univariate and multivariate data. Evaluations on a large number of real-world data sets demonstrate the accuracy of the new algorithm and how it exceeds state-of-the-art performance.