A complexity analysis method for EEG signals based on time-varying fuzzy dispersion entropy

Abstract

The present invention belongs to the field of signal processing technology, and specifically relates to a method for analyzing the complexity of electroencephalogram (EEG) signals based on time-varying fuzzy dispersion entropy. The method comprises the following steps: preprocessing EEG data; performing coarse-graining to obtain a coarse-grained time series; considering instantaneous changes within each channel to obtain a change series; mapping the elements of each channel between 0 and 1 based on the normal cumulative distribution function (NCDF), followed by quadratic linear mapping; performing multivariate embedding reconstruction based on multivariate embedding theory; selecting m elements from each multivariate embedding vector at a time, and determining the dispersion pattern of these m elements based on a fuzzy membership function; and calculating multivariate multiscale time-varying fuzzy dispersion entropy based on the definition of Shannon entropy. The present invention comprehensively explores signals at multiple scales, calculates instantaneous changes within channels, and simultaneously considers information within channels when measuring inter-channel relationships. The introduction of fuzzification improves noise resistance and stability.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to an electroencephalogram (EEG) signal complexity analysis method based on time-varying fuzzy dispersion entropy. Background Art

[0002] Electroencephalogram (EEG) is a nonlinear, multivariate, and complex signal that records the brain's electrical activity. With the development of noninvasive sensing technologies, EEG acquisition has become increasingly rapid and convenient. Furthermore, EEG allows for the analysis of signals from multiple perspectives, including frequency bands, inter-channel relationships, and time domain information. Consequently, it has been widely used in various fields.

[0003] Traditional entropy-based complexity analysis methods suffer from common methodological limitations due to their inherent principles. For example, they produce unreliable results when analyzing short signals; they fail to account for transient changes within channels when measuring inter-channel relationships; they have weak noise immunity; and they suffer from large variance and poor stability after repeated analysis. Therefore, it is necessary to develop a new EEG complexity analysis method to address these issues. Summary of the Invention

[0004] In response to the technical problems of the above-mentioned entropy-based complexity analysis method, the present invention provides an EEG signal complexity analysis method based on time-varying fuzzy dispersion entropy, which combines multi-scale information, has strong noise resistance, focuses on the relationship within and between channels, and has high stability.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A method for analyzing the complexity of electroencephalogram (EEG) signals based on time-varying fuzzy dispersion entropy comprises the following steps:

[0007] S1. Preprocess the EEG data; preprocessing operations include: removing useless electrodes, bandpass filtering, removing ICA artifact components, and re-referencing;

[0008] S2, perform coarse-graining processing to obtain the coarse-grained time series;

[0009] S3, considering the instantaneous changes in each channel to obtain the change sequence;

[0010] S4, mapping the elements of each channel between 0 and 1 based on the normal cumulative distribution function NCDF, and then performing a quadratic linear mapping;

[0011] S5. Perform multivariate embedding reconstruction based on multivariate embedding theory; select m elements from each multivariate embedding vector at a time, and determine the dispersion pattern of these m elements based on the fuzzy membership function;

[0012] S6. Calculate the multivariate and multiscale time-varying fuzzy dispersion entropy based on the definition of Shannon entropy.

[0013] The method for performing the coarse-graining process in S2 is:

[0014] For a p-channel time series of length L Split each channel into multi-scale time series

[0015]

[0016] Where s is the scale factor and N is the length of the coarse-grained signal.

[0017] The method for obtaining the change sequence in S3 is:

[0018] Calculate the instantaneous change in each channel to obtain a new change time series

[0019] Where: x k,i =x k,b -x k,b-1 .

[0020] The method of mapping the elements of each channel between 0 and 1 in S4 is to convert the multivariate signal Mapping to Signal First map X to Y using the Normal Cumulative Distribution Function (NCDF), then use Map Y to Z, where Represents the i-th element in the k-th channel.

[0021] The method for performing multivariate embedding reconstruction in S5 is:

[0022] According to the multivariate embedding theory, the multivariate embedding vector is generated. The multivariate embedding reconstruction of Z is defined as:

[0023]

[0024] Where: M=[m1,m2,...,m p ] and τ=[τ1,τ2,...,τ p ] represent the embedding dimension and delay vector respectively; Z m The length of (j) is Assume that τ k =τ and m k =m, that is, all embedding dimension values and delay values are equal.

[0025] The method for determining the dispersion patterns of the m elements according to the fuzzy membership function in S5 is:

[0026] For each Z m(j), we get all possible combinations of m elements at a time from mp elements; these combinations are represented as where q ranges from 1 to and It's Z m The hth element of the qth combination of (j); the number of combinations is equal to The set of dispersion patterns with embedding dimension m and number of categories c where N c ={1,2,...c}; Therefore, for all channels, there are dispersion modes;

[0027] In order to determine the element combination S q (j) For the degree of membership of the class, we introduce M for each class r The fuzzy membership function of Indicates S q (j) the hth element's membership to the rth class, and then each element Assignment to one or two categories uses the following fuzzy functions:

[0028]

[0029] Each combination vector S q (j) is mapped to a dispersion pattern based on its class membership as follows:

[0030] If and only if S q (j) hour, For class v0, for classes v1,..., and For class v m―1 ;

[0031] The algebraic product operator is used in the above fuzzy expression:

[0032]

[0033] S q (J) relative to the dispersion mode The membership degree is equal to each Relative to class v h―1 The product of the membership degrees of , where h = 1, ..., m, j = 1, 2, ..., N―1―(m―1)τ, and For each possible dispersion mode Their relative frequencies are as follows:

[0034]

[0035] The method for calculating the multivariate multiscale time-varying fuzzy dispersion entropy in S6 is: based on the definition of Shannon entropy, the normalized multivariate multiscale time-varying fuzzy dispersion entropy is calculated as follows:

[0036]

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention conducts a comprehensive exploration of signals at multiple scales. By calculating the instantaneous changes within the channel, it simultaneously pays attention to the information within the channel when measuring the relationship between channels, and introduces the idea of fuzzification to improve noise resistance and stability. This method also pays attention to the instantaneous changes within the channel when measuring the relationship between channels, has good noise resistance and stability, and has low dependence on data length. The present invention is suitable for complexity analysis of EEG data. The present invention solves the problem that traditional complexity analysis methods cannot simultaneously consider the instantaneous changes within the channel when measuring the relationship between channels, have weak noise resistance, poor stability, and high data dependence. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can, without inventive effort, derive other implementation drawings based on the provided drawings.

[0040] The structures, proportions, sizes, etc. illustrated in this specification are intended solely to complement the contents disclosed herein and to facilitate understanding and reading by persons skilled in the art. They are not intended to limit the conditions under which the present invention may be implemented and therefore have no substantive technical significance. Any structural modifications, changes in proportions, or adjustments in sizes, without affecting the efficacy and objectives of the present invention, shall remain within the scope of the technical contents disclosed herein.

[0041] Figure 1 This is a flow chart of the algorithm for multivariate multi-scale time-varying fuzzy dispersion entropy of the present invention;

[0042] Figure 2 A multivariate sequence complexity diagram is used to test the multivariate multiscale sample entropy, the multivariate multiscale dispersion entropy, and the proposed multivariate multiscale time-varying fuzzy dispersion entropy in the present invention;

[0043] Figure 3 This is a graph showing the noise resistance of the algorithm of the present invention;

[0044] Figure 4 This is a data length sensitivity diagram of the verification algorithm of the present invention. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of this application, not all the embodiments. These descriptions are only to further illustrate the features and advantages of the present invention, rather than to limit the claims of the present invention. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0046] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following embodiments are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0047] In this embodiment, a method for analyzing EEG signal complexity based on multivariate multiscale time-varying fuzzy dispersion entropy includes the following steps:

[0048] Step 1: Preprocess the EEG data. Preprocessing operations include removing useless electrodes, bandpass filtering, removing ICA artifacts, and re-referencing.

[0049] Step 2: Perform coarse-graining processing to obtain the coarse-grained time series.

[0050] Step 3: Consider the instantaneous changes in each channel to obtain the change sequence.

[0051] Step 4: Map the elements of each channel between 0 and 1 based on the normal cumulative distribution function (NCDF), and then perform a quadratic linear mapping.

[0052] Step 5: Based on the multivariate embedding theory, perform multivariate embedding reconstruction. Select m elements from each multivariate embedding vector at a time and determine the dispersion pattern of these m elements based on the fuzzy membership function.

[0053] Step 6: Calculate the multivariate multiscale time-varying fuzzy dispersion entropy based on the definition of Shannon entropy.

[0054] Furthermore, in step 2, for a p-channel time series of length L

[0055] Split each channel into multi-scale time series

[0056]

[0057] Where s is the scale factor and N is the length of the coarse-grained signal.

[0058] Furthermore, in step 3, the instantaneous change in each channel is calculated to obtain a new change time series

[0059] x k,i =x k,b -x k,b-1

[0060] Furthermore, in step 4, the multivariate signal Mapping to Signal Specifically, we first map X to Y using the normal cumulative distribution function (NCDF), and then use Map Y to Z, where Represents the i-th element in the k-th channel.

[0061] Furthermore, in step 5, in order to take into account both the spatial and temporal domains, a multivariate embedding vector is generated based on the multivariate embedding theory. The multivariate embedding reconstruction of Z is defined as:

[0062]

[0063] Where M=[m1,m2,...,m p ] and τ=[τ1,τ2,...,τ p ] represent the embedding dimension and delay vector respectively. m The length of (j) is For simplicity, we assume that τ k =τ and m k =m, that is, all embedding dimension values and delay values are equal.

[0064] For each Z m (j), we get all possible combinations of taking m elements at a time from mp elements. These combinations are represented as where q ranges from 1 to and It's Z m (j) The hth element of the qth combination. The number of combinations is equal to The set of dispersion patterns with embedding dimension m and number of categories c where N c ={1,2,...c}. Therefore, for all channels, there are dispersion modes.

[0065] In order to determine the element combination S q (j) For the degree of membership of the class, we introduce M for each class r The fuzzy membership function of Indicates S q(j) The hth element of the membership of the rth class. Then each element Assigned to one or two categories. The fuzzy functions used are detailed below:

[0066]

[0067] Each combination vector S q (j) The roots are mapped to a dispersion pattern based on their class membership as follows:

[0068] If and only if S q (j) hour, For class v0, for classes v1,..., and For class v m―1 .

[0069] The algebraic product operator is used in the above fuzzy expression:

[0070]

[0071] S q (j) Relative to dispersion mode The membership degree is equal to each Relative to class v h―1 The product of the membership degrees of , where h = 1, ..., m, j = 1, 2, ..., N―1―(m―1)τ, and For each possible dispersion mode Their relative frequencies are as follows:

[0072]

[0073] Furthermore, in step 6, based on the definition of Shannon entropy, the normalized multivariate multiscale time-varying fuzzy dispersion entropy is calculated as follows:

[0074]

[0075] In order to evaluate the ability of Multivariate Multiscale Sample Entropy (mvMSE), Multivariate Multiscale Dispersion Entropy (mvMDE) and Multivariate Multiscale Variations FuzzyDispersion Entropy (mvMVFDE) proposed in this invention to analyze the complexity of multivariate time series, the present invention generates an uncorrelated three-channel time series consisting of 1 / f and Gaussian white noise. Gaussian white noise is characterized by a mean of 0 and a standard deviation of 1. The number of channels of the generated sequence is always equal to 3. As the number of 1 / f noise channels decreases, the corresponding number of Gaussian white noise channels increases. The data length is set to 5000 and the generation is repeated 20 times. As Figure 2 As shown in the figure, as the number of 1 / f noise channels increases, the entropy of the multivariate multiscale time-varying fuzzy dispersion entropy gradually increases, and reaches its maximum when all three channels are 1 / f noise signals. This is consistent with the fact that the complexity of 1 / f noise is higher than that of Gaussian white noise.

[0076] In order to analyze the noise resistance of these algorithms, a coupled MIX model is used to generate a simulation signal, and Gaussian white noise is superimposed to change the signal-to-noise ratio of the signal. The data length is set to 2000 and repeated 20 times. Before the noise is introduced, the entropy value of the original signal is calculated, and a total of 20 entropy values can be obtained. After superimposing the noise of the corresponding signal-to-noise ratio on the original data, the same method can be used to obtain 20 entropy values. The entropy value calculated after the noise is introduced is subtracted from the entropy value calculated before the noise is introduced, and a single-sample t-test is performed on the 20 differences to test whether there is a significant difference between the signal after the noise of the corresponding signal-to-noise ratio is added and the original signal. Figure 3 As shown in FIG, the signal-to-noise ratio threshold of the multivariate multiscale time-varying fuzzy dispersion entropy proposed in the present invention is 30 dB, which is lower than that of other existing algorithms. Therefore, the multivariate multiscale time-varying fuzzy dispersion entropy proposed in the present invention has good noise resistance.

[0077] In order to evaluate the sensitivity of these algorithms to data length, the present invention uses a coupled MIX model to generate simulation signals with data lengths ranging from 100 to 2000 with an interval of 100. Figure 4 As shown in the figure, the multivariate multiscale sample entropy and the multivariate multiscale dispersion entropy fluctuate greatly with the change of signal length. The multivariate multiscale time-varying fuzzy dispersion entropy is basically stable when the length is 400. Therefore, the multivariate multiscale time-varying fuzzy dispersion entropy has low sensitivity to length.

[0078] Using the public emotion dataset FACED, EEG data were collected from 20 subjects expressing four emotions: happiness, sadness, fear, and neutrality. Multivariate multiscale sample entropy, multivariate multiscale dispersion entropy, and multivariate multiscale time-varying fuzzy dispersion entropy were used to extract the characteristics of these emotions. A support vector machine (SVM) was used to classify the four emotions within the subjects. As shown in Table 1, the proposed mvMVFDE method achieved higher average classification accuracy using SVM than two classic entropy methods (mvMSE and mvMDE) at different scales.

[0079] Table 1 Average accuracy of different scales using the entropy algorithm of the present invention and the existing entropy algorithm using SVM classification

[0080]

[0081] The above only describes in detail the preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the purpose of the present invention, and various changes should be included in the scope of protection of the present invention.

Claims

1. A method for analyzing EEG signal complexity based on time-varying fuzzy dispersion entropy, characterized in that: The following steps are involved: S1. Preprocess the EEG data; preprocessing operations include: removing useless electrodes, bandpass filtering, removing ICA artifact components, and re-referencing; S2. Perform coarse-graining processing to obtain a coarse-grained time series. The method for performing coarse-graining processing in S2 is: For a p-channel time series of length L Split each channel into multi-scale time series Where s is the scale factor, N is the length of the coarse-grained signal; S3, considering the instantaneous changes in each channel to obtain the change sequence; Calculate the instantaneous change in each channel to obtain a new change time series Where: x k,i =x k,b -x k,b-1 ; S4, based on the normal cumulative distribution function NCDF, the elements of each channel are mapped between 0 and 1, and then a quadratic linear mapping is performed; the method of mapping the elements of each channel between 0 and 1 in S4 is to convert the multivariate signal Mapping to Signal First map X to Y using the Normal Cumulative Distribution Function (NCDF), then use Map Y to Z, where represents the i-th element in the k-th channel; S5. Perform multivariate embedding reconstruction based on multivariate embedding theory; select m elements from each multivariate embedding vector at a time, and determine the dispersion pattern of these m elements based on the fuzzy membership function; According to the multivariate embedding theory, the multivariate embedding vector is generated. The multivariate embedding reconstruction of Z is defined as: Where: M=[m1,m2,...,m p ] and τ=[τ1,τ2,...,τ p ] represent the embedding dimension and delay vector respectively; Z m The length of (j) is Assume that τ k =τ and m k =m, that is, all embedding dimension values and delay values are equal; For each Z m (j), we get all possible combinations of m elements at a time from mp elements; these combinations are represented as where q ranges from 1 to and It's Z m The hth element of the qth combination of (j); the number of combinations is equal to The set of dispersion patterns with embedding dimension m and number of categories c where N c ={1,2,...c}; Therefore, for all channels, there are dispersion modes; In order to determine the element combination S q (j) For the degree of membership of the class, we introduce M for each class r The fuzzy membership function of Indicates S q (j) the hth element's membership to the rth class, and then each element Assignment to one or two categories uses the following fuzzy functions: Each combination vector S q (j) is mapped to a dispersion pattern based on its class membership as follows: If and only if S q (j) hour, For class v0, for classes v1,..., and For class v m-1 ; The algebraic product operator is used in the above fuzzy function: S q (j) Relative to dispersion mode The membership degree is equal to each Relative to class v h-1 The product of the membership degrees of , where h = 1, ..., m, j = 1, 2, ..., N-1-(m-1)τ, and For each possible dispersion mode Their relative frequencies are as follows: S6. Calculate the multivariate multiscale time-varying fuzzy dispersion entropy based on the definition of Shannon entropy. Based on the definition of Shannon entropy, the normalized multivariate multiscale time-varying fuzzy dispersion entropy is calculated as follows:

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