Semester of Graduation
Master of Science in Electrical Engineering (MSEE)
The present thesis explores some approaches to classify time series without prior statistical information using the concept of permutation entropy. Motivated by the results from a previous published and relevant work that set similarity relationships between EEG time series, a reproduction of the proposed approach was performed giving negative results. The failure to reproduce those results led to the conclusion that the approach of building statistics from permutation patterns have to be complemented with another metric in order to be used for classification purposes. The concept of Total Variation Distance (TVD) was then used to develop three algorithms to classify time series in a non-parametric way.
At first, the developed algorithms were tested using EEG time series. Even though the results using the developed algorithms were better than previous results, they were not as satisfactory as desired. However, the inherent complexity of brain measurements led to switch to self-generated data to test the algorithms. Using time series coming from different sets of filtered versions of Gaussian white noise the classification was performed. For comparison purposes a parametric classification approach using the Maximum Likelihood Estimation was also used. Results showed that when each set of data came from the same filtering equation the classification using the developed algorithms was optimal reaching 100% success rate in many cases, being as good as the ML approach. On the other hand, when each set of data came from a mixture of different filter equations that generate the time series (reflecting the complex situations we faced when processing EEG data) , results were fairly successful with variations with respect to the ML approach, which was outperformed in some cases but also not surpassed in others.
The results obtained pointed the permutation entropy analysis to be an approach in the right direction to efficiently classify time series, however more research needs to be done to adjust the correct metric to get better results.
Duarte Vera Tudela, Aldo, "Non-Parametric Classification of Time Series Using Permutation Ordinal Statistics" (2018). LSU Master's Theses. 4815.