LOCAL LEGENDRE POLYNOMIAL FITTING-BASED PREPROCESSING fOR IMPROVING THE INTERPRETATION OF PERMUTATION ENTROPY IN STATIONARY TIME SERIES
Abstract
Permutation entropy (PE) and its variants are ordinal
pattern-based techniques that have become widely used
as complexity measures to quantify the degree of disorder or
randomness in a time series. Despite their popularity, these
techniques have several limitations, such as sensitivity to the
embedding dimension, the sampling frequency, and their specific
preprocessing strategies. The information captured by these
techniques is difficult to interpret and may not fully reflect the
complexity of time series.
We propose an alternative PE variant to overcome these
limitations. We first divide the signal into short segments of a
fixed length sufficient enough to allow for a local polynomial
modelling of this signal. We use a discrete orthonormal polynomial
basis of a limited degree to ensure that for each segment,
the model parameters obtained are uncoupled and have similar
value ranges. By ranking these parameters, we construct an
ordinal pattern (OP) for each segment. The proposed PE variant
is then defined as the Shannon entropy applied to the probability
distribution of these OPs.
The proposed local polynomial fitting-based preprocessing
helps improve the PE interpretation. The advantages of the
proposed PE method over some existing PE variants are demonstrated
using simulated signals and real data.