Dynamic system reconstruction from multivariate time series via multilinear map and time delay emmbedding
Keywords: dimensionality reduction, dynamical system, multilinear algebra
TL;DR: A tensor as a multilinear map is used from dynamic reconstruction system in low-dimensional space for multivariate time series.
Abstract: This paper examines the properties of dynamic system reconstruction using time delay embedding and multilinear (tensor) algebra.
The tensor dynamical system model for time series prevents the loss of higher-order information.
The key idea is to use the tensor as a multilinear map from set phase spaces to one subspace.
Due to the simplicity of the linear approach and linear dependencies between components, the results show that the method in several cases allows for a better reconstruction of the original attractor from an incomplete set of variables.
A computational experiment was carried out on Lorenz attractor and measurements of the accelerometer of a mobile device with three classes of human movements.
Submission Number: 31
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