{'fraction_non_alphanumeric': 0.025910931174089068, 'fraction_numerical': 0.0032388663967611335, 'mean_word_length': 4.971014492753623, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Empirical mode decomposition revisited using ordinal pattern concepts

The empirical mode decomposition (EMD) is a well-known data-driven signal decomposition. It produces a finite number of intrinsic mode functions (IMF) well adapted to Hilbert spectral analysis. Since the EMD is not a theoretical approach but rather an iterative algorithm, the question of how the EMD can achieve spectral band separation remains open. Several attempts to experimentally and theoretically explore this issue were addressed. However, to the best of our knowledge, none of them has investigated the EMD from an ordinal pattern point of view. The purpose of this paper is threefold. First, the EMD limitations are reexamined using the concept of ordinal patterns (OP) of length 3. Second, we propose to incorporate the OP probability distribution into the definition of the mean envelop and the stopping criterion during the sifting process. This turns out to be helpful in reducing mode mixing and thus improves the EMD robustness. Finally, we propose to extend the EMD to different pattern lengths (2, 4, 5, etc). Academic and real-life time series are processed and the results show that the ordinal pattern-based EMD outperforms the classical EMD.