Characterizing unstructured data with the nearest neighbor permutation entropy
arxiv(2024)
摘要
Permutation entropy and its associated frameworks are remarkable examples of
physics-inspired techniques adept at processing complex and extensive datasets.
Despite substantial progress in developing and applying these tools, their use
has been predominantly limited to structured datasets such as time series or
images. Here, we introduce the k-nearest neighbor permutation entropy, an
innovative extension of the permutation entropy tailored for unstructured data,
irrespective of their spatial or temporal configuration and dimensionality. Our
approach builds upon nearest neighbor graphs to establish neighborhood
relations and uses random walks to extract ordinal patterns and their
distribution, thereby defining the k-nearest neighbor permutation entropy. This
tool not only adeptly identifies variations in patterns of unstructured data,
but also does so with a precision that significantly surpasses conventional
measures such as spatial autocorrelation. Additionally, it provides a natural
approach for incorporating amplitude information and time gaps when analyzing
time series or images, thus significantly enhancing its noise resilience and
predictive capabilities compared to the usual permutation entropy. Our research
substantially expands the applicability of ordinal methods to more general data
types, opening promising research avenues for extending the permutation entropy
toolkit for unstructured data.
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