Average Volatility Dimensioning (AVD): dimension reduction technique for multivariate time series

Abstract Reducing the features while preserving a dataset’s inner dynamics is a challenging task. This is particularly evident for nonlinear and time-dependent processes. We propose a novel dimension reduction technique, Average Volatility Dimensioning (AVD), which captures the behavior between features and reduces the multiple dimensions to a univariate signal. This article describes the developed mechanisms and compares this dimension reduction technique against nine state-of-the-art methods. The ability to retain the information of the data is evaluated by using the reduced dimensions for machine learning classification tasks and comparing the phase-space portraits. The validation is performed on eight different datasets featuring nonlinear time series data, covering domains such as movement recognition, fault detection, and environmental monitoring. Overall, the results show that AVD encapsulates the data dynamics best, demonstrating superior performance for the discussed machine learning approach while maintaining an interpretable phase-space trajectory, resisting noise, and remaining computationally efficient.