| Summary: | As a measure of complexity, information entropy is frequently used to categorize time series, such as machinery failure diagnostics, biological signal identification, etc., and is thought of as a characteristic of dynamic systems. Many entropies, however, are ineffective for multivariate scenarios due to correlations. In this paper, we propose a local structure entropy (LSE) based on the idea of a recurrence network. Given certain tolerance and scales, LSE values can distinguish multivariate chaotic sequences between stochastic signals. Three financial market indices are used to evaluate the proposed LSE. The results show that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi><msup><mi>E</mi><mrow><mi>F</mi><mi>S</mi><mi>T</mi><mi>E</mi><mn>100</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi><msup><mi>E</mi><mrow><mi>S</mi><mo>&</mo><mi>P</mi><mn>500</mn></mrow></msup></mrow></semantics></math></inline-formula> are higher than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi><msup><mi>E</mi><mrow><mi>S</mi><mi>Z</mi><mi>I</mi></mrow></msup></mrow></semantics></math></inline-formula>, which indicates that the European and American stock markets are more sophisticated than the Chinese stock market. Additionally, using decision trees as the classifiers, LSE is employed to detect bearing faults. LSE performs higher on recognition accuracy when compared to permutation entropy.
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