Tensor time delay embedding extension for multivariate time series analysis

This paper aims to construct a new dimensionality reduction method that uses time series analysis approaches, multilinear algebra, and dynamical system reconstruction theory.The proposed multilinear method combines time delay embedding and tensor as a multilinear map to a low-dimensional space.It prevents the loss of nonlinear higher-order information between various time series and allows the selection of time series components that are recognized as noise in a single case.The results show that the method allows for a better reconstruction of the original attractor from an incomplete set of variables. A computational experiment was carried out on the Lorenz attractor, and the accelerometer of a mobile device was measured using two classes of human movements.The accuracy of the reconstructed attractor is tested to determine the ability to forecast an unused time series from the dynamic system under study.