Optimized Fuzzy Slope Entropy: A Complexity Measure for Nonlinear Time Series

Entropy has long been a subject that has attracted researchers from a diverse range of fields, including healthcare, finance, and fault detection. Slope entropy (SE) has recently been proposed as a new approach to address the shortcomings of permutation entropy (PE), which ignores magnitude informat...

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Published in:	IEEE transactions on instrumentation and measurement Vol. 73; pp. 1 - 14
Main Authors:	Li, Yuxing, Tian, Ge, Cao, Yuan, Yi, Yingmin, Zhou, Dingsong
Format:	Journal Article
Language:	English
Published:	New York IEEE 2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Artificial rabbit optimization (ARO) Automation Classification Complexity Complexity theory Datasets Entropy Fault detection fuzzification fuzzy slope entropy (FuSE) Optimization optimized FuSE (OFuSE) Parameter sensitivity Performance evaluation Permutations slope entropy (SE) Symbols Synthetic data Time measurement Time series Time series analysis
ISSN:	0018-9456, 1557-9662
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Abstract	Entropy has long been a subject that has attracted researchers from a diverse range of fields, including healthcare, finance, and fault detection. Slope entropy (SE) has recently been proposed as a new approach to address the shortcomings of permutation entropy (PE), which ignores magnitude information; however, SE is sensitive to parameters <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\gamma } </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\delta } </tex-math></inline-formula>, and some information may be lost when segmenting symbols. The <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\delta } </tex-math></inline-formula>, moreover, has only a limited gain on the time series classification performance of SE and increases the algorithm complexity. Considering the aforementioned limitations, this study introduces the concept of fuzzification to the SE and eliminates the <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\delta } </tex-math></inline-formula> to simplify the parameters, resulting in the proposal of fuzzy SE (FuSE); furthermore, we incorporate the artificial rabbit optimization (ARO) algorithm to optimize the parameter <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\gamma } </tex-math></inline-formula> to enhance the effectiveness of FuSE for time series classification and finally proposed an optimized FuSE (OFuSE). OFuSE can greatly reduce the information loss in the mapping process and adaptively search for the optimal parameter. The study evaluated FuSE and OFuSE on several synthetic datasets and concluded that FuSE is more sensitive to changes in signal amplitude and frequency while confirming the advantage of OFuSE in classification. The application of OFuSE on three different real datasets verifies that its classification performance and generalization ability are better than other entropy methods.
AbstractList	Entropy has long been a subject that has attracted researchers from a diverse range of fields, including healthcare, finance, and fault detection. Slope entropy (SE) has recently been proposed as a new approach to address the shortcomings of permutation entropy (PE), which ignores magnitude information; however, SE is sensitive to parameters <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\gamma } </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\delta } </tex-math></inline-formula>, and some information may be lost when segmenting symbols. The <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\delta } </tex-math></inline-formula>, moreover, has only a limited gain on the time series classification performance of SE and increases the algorithm complexity. Considering the aforementioned limitations, this study introduces the concept of fuzzification to the SE and eliminates the <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\delta } </tex-math></inline-formula> to simplify the parameters, resulting in the proposal of fuzzy SE (FuSE); furthermore, we incorporate the artificial rabbit optimization (ARO) algorithm to optimize the parameter <inline-formula> <tex-math notation="LaTeX">\boldsymbol {\gamma } </tex-math></inline-formula> to enhance the effectiveness of FuSE for time series classification and finally proposed an optimized FuSE (OFuSE). OFuSE can greatly reduce the information loss in the mapping process and adaptively search for the optimal parameter. The study evaluated FuSE and OFuSE on several synthetic datasets and concluded that FuSE is more sensitive to changes in signal amplitude and frequency while confirming the advantage of OFuSE in classification. The application of OFuSE on three different real datasets verifies that its classification performance and generalization ability are better than other entropy methods. Entropy has long been a subject that has attracted researchers from a diverse range of fields, including healthcare, finance, and fault detection. Slope entropy (SE) has recently been proposed as a new approach to address the shortcomings of permutation entropy (PE), which ignores magnitude information; however, SE is sensitive to parameters [Formula Omitted] and [Formula Omitted], and some information may be lost when segmenting symbols. The [Formula Omitted], moreover, has only a limited gain on the time series classification performance of SE and increases the algorithm complexity. Considering the aforementioned limitations, this study introduces the concept of fuzzification to the SE and eliminates the [Formula Omitted] to simplify the parameters, resulting in the proposal of fuzzy SE (FuSE); furthermore, we incorporate the artificial rabbit optimization (ARO) algorithm to optimize the parameter [Formula Omitted] to enhance the effectiveness of FuSE for time series classification and finally proposed an optimized FuSE (OFuSE). OFuSE can greatly reduce the information loss in the mapping process and adaptively search for the optimal parameter. The study evaluated FuSE and OFuSE on several synthetic datasets and concluded that FuSE is more sensitive to changes in signal amplitude and frequency while confirming the advantage of OFuSE in classification. The application of OFuSE on three different real datasets verifies that its classification performance and generalization ability are better than other entropy methods.
Author	Zhou, Dingsong Li, Yuxing Yi, Yingmin Tian, Ge Cao, Yuan
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Snippet	Entropy has long been a subject that has attracted researchers from a diverse range of fields, including healthcare, finance, and fault detection. Slope...
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SubjectTerms	Algorithms Artificial rabbit optimization (ARO) Automation Classification Complexity Complexity theory Datasets Entropy Fault detection fuzzification fuzzy slope entropy (FuSE) Optimization optimized FuSE (OFuSE) Parameter sensitivity Performance evaluation Permutations slope entropy (SE) Symbols Synthetic data Time measurement Time series Time series analysis
Title	Optimized Fuzzy Slope Entropy: A Complexity Measure for Nonlinear Time Series
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