PSGF (phase space gap filling): um novo método para substituição de valores ausentes em séries temporais caóticas

Abstract

The preprocessing step performed to deal with missing or invalid information in datasets is a relevant task in Machine Learning (ML) applications to avoid producing wrong models and make feasible the usage of specific algorithms that do not work in such a condition. In general, missing values occours for different reasons as, for instance, problems in the device used to monitor a system, network issues between monitoring and storage services, and the authentic absence of data. By collecting data in an i.i.d (independent and identically distributed) manner, traditional ML models are able to replace missing values. However, when there are temporal dependencies between collected observations, e.g., time series, such models are unsuitable for not considering the existing relationship in time instants. The treatment of missing data in time series is performed by several techniques such as interpolation methods (e.g. Lagrange, Newton, and Splines) and Singular Spectrum Analysis (SSA). Experiments during this project highlighted that these methods provided poor results when the time series present a chaotic behavior once their attractors in the phase space are not taken into account. Therefore, this work presents a new method that considers Dynamical System and Chaos Theory tools to unfold series from the temporal domain into phase space, making it possible the adoption of ML models to replace missing values. Our results emphasize the importance of this new paradigm to deal with missing values, outperforming the state-of-the-art.