Oriented spatial ordinal patterns
Ten years after the introduction of ordinal patterns for time series analysis by Bandt and Pompe, Ribeiro et al. generalized them to deal with images and textures. In their approach, named Spatial Permutation Entropy (SPE), two-dimensional patterns are constructed, usually square- shaped, which capture spatial correlations in the data. This approach has been used to characterize many spatially extended physical systems, such as excitable cardiac tissue, vegetation fields, laser beam speckle patterns, and the human brain. However, it makes sense to consider that these spatial correlations may have some preferred direction that reflects the intrinsic anisotropy of the underlying system, which the square-shaped symbols, due to their rotational symmetry, lack the ability to detect. In this work, we address this matter by proposing an alternative 2D symbol shape that is able to detect the anisotropy of the system. We apply this technique to two real world systems: the human brain and the global climate. For the former, we show how it can improve the feature extraction and the discrimination of different brain resting states. For the latter, we show how it improves the characterization of a clearly anisotropic region as El Niño in the tropical Pacific, and track its evolution across multiple decades, which we link to global warming. Overall, we show the ability of SPE to capture anisotropies in real world complex spatio-temporal data.
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