EEG signal complexity analysis method based on time-varying fuzzy dispersion entropy

Abstract

The invention belongs to the technical field of signal processing, and particularly relates to an electroencephalogram signal complexity analysis method based on time-varying fuzzy dispersion entropy, which comprises the following steps of: preprocessing electroencephalogram EEG data; carrying out coarse graining treatment to obtain a time sequence after coarse graining; considering the instantaneous change in each channel to obtain a change sequence; performing 0-1 mapping on the elements of each channel based on a normal cumulative distribution function NCDF, and then performing quadratic linear mapping; performing multi-element embedding reconstruction according to a multi-element embedding theory; m elements are selected from each multi-element embedded vector each time, and dispersion modes of the m elements are determined according to a fuzzy membership function; and calculating the multivariate multi-scale time-varying fuzzy dispersion entropy based on the definition of the Shannon entropy. According to the method, the signals are comprehensively explored under multiple scales, the information in the channels is concerned while the relationship between the channels is measured by calculating the instantaneous change in the channels, and the anti-noise capability and the stability are improved by introducing the fuzzification thought.

Description

Technical Field

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

[0002] Electroencephalogram (EEG) is a nonlinear multivariate complex signal that records the electrical activity of the brain. With the development of non-invasive sensing technology, the acquisition of EEG has become faster and more convenient. In addition, EEG can explore signals from multiple angles such as frequency bands, inter-channel relationships, and time domain information, so it has been widely used in many fields.

[0003] Traditional entropy-based complexity analysis methods are generally limited by methodology due to their own principles. For example, unreliable results will appear when analyzing short signals; when measuring the relationship between channels, the instantaneous changes within the channel are not taken into account; the anti-noise ability is weak; the variance of repeated analysis is large and the stability is poor. Based on this, it is necessary to invent a new EEG complexity analysis method to solve the above problems. 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, pays attention to 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; the preprocessing operations include: removing useless electrodes, bandpass filtering, removing ICA artifact components, and re-referencing;

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

[0009] S3, considering the instantaneous changes in each channel, and obtaining 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 each time, and determine the dispersion mode of the 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 coarse-graining processing in S2 is:

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

[0015]

[0016] Among them, 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 changes 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), and 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, and 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 modes 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 taking m elements at a time from mp elements; these combinations are represented by 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) The degree of membership of the class is introduced for each category and represented as M r The fuzzy membership function of Indicates S q (j) the membership of the hth element with respect to the rth class, and then 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, is of class 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 the signal at multiple scales, calculates the instantaneous changes within the channel, pays attention to the information within the channel while measuring the relationship between channels, and introduces the idea of ​​fuzzification to improve the 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 the traditional complexity analysis method cannot simultaneously consider the instantaneous changes within the channel when measuring the relationship between channels, has weak noise resistance, poor stability, and high data dependence. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0040] The structures, proportions, sizes, etc. illustrated in this specification are only used to match the contents disclosed in the specification so as to facilitate understanding and reading by persons familiar with the technology. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantial technical significance. Any structural modification, change in proportion or adjustment of size shall still fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

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

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

[0043] Figure 3 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 the present application, rather than 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 the present 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 specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

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

[0048] Step 1: Preprocess the EEG data. The preprocessing operations include: removing useless electrodes, bandpass filtering, removing ICA artifact components, 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: Perform multivariate embedding reconstruction based on multivariate embedding theory. Select m elements from each multivariate embedding vector each 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] Among them, 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] Further, 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 consider both the spatial domain and the temporal domain, 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 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 mode.

[0065] In order to determine the element combination S q (j) The degree of membership of the class is introduced for each category and represented as M r The fuzzy membership function of Indicates S q(j) is the membership degree of the hth element of the rth class. Then each element Assigned to one or two categories. The fuzzy functions used are detailed as follows:

[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, is of class 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 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:

[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 the present 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. Figure 2 As shown in the figure, as the number of 1 / f noise channels increases, the entropy value of multivariate multiscale time-varying fuzzy dispersion entropy gradually increases, and when all three channels are 1 / f noise signals, the entropy value reaches the maximum. 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 analog signals, 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 introduction of noise, the entropy value of the original signal is calculated, and a total of 20 entropy values ​​are 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 introduction of noise is subtracted from the entropy value calculated before the introduction of noise, 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 addition of the noise of the corresponding signal-to-noise ratio and the original signal. Figure 3 As shown, the signal-to-noise ratio threshold of the multivariate multiscale time-varying fuzzy dispersion entropy proposed by the present invention is 30 dB, which is lower than other existing algorithms. Therefore, the multivariate multiscale time-varying fuzzy dispersion entropy proposed by 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 simulated 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 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] By using the public emotion dataset FACED, the EEG data of 20 subjects with four emotions of happiness, sadness, fear and neutrality were obtained, and the characteristics of different emotions were extracted using multivariate multiscale sample entropy, multivariate multiscale dispersion entropy and multivariate multiscale time-varying fuzzy dispersion entropy respectively. The four emotions in the subjects were classified using support vector machine (SVM). As shown in Table 1, at different scales, the mvMVFDE method proposed in the present invention has a higher average accuracy rate using SVM for classification than the two classic entropy methods (mvMSE and mvMDE).

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

[0080]

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

Claims

1. A method for analyzing the complexity of EEG signals based on time-varying fuzzy dispersion entropy, characterized in that: The following steps are involved: S1. Preprocess the EEG data; the 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; S3, considering the instantaneous changes in each channel, and obtaining the change sequence; 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; S5. Perform multivariate embedding reconstruction based on multivariate embedding theory; select m elements from each multivariate embedding vector each time, and determine the dispersion mode of the m elements based on the fuzzy membership function; S6. Calculate the multivariate and multiscale time-varying fuzzy dispersion entropy based on the definition of Shannon entropy.

2. According to claim 1, a method for analyzing the complexity of electroencephalogram signals based on time-varying fuzzy dispersion entropy is characterized in that: 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 Among them, s is the scale factor and N is the length of the coarse-grained signal.

3. The electrical signal complexity analysis method based on time-varying fuzzy dispersion entropy brain according to claim 1 is characterized in that: The method for obtaining the change sequence in S3 is: Calculate the instantaneous changes in each channel to obtain a new change time series Where: x k,i =x k,b -x k,b-1 .

4. The method for analyzing the complexity of electroencephalogram signals based on time-varying fuzzy dispersion entropy according to claim 1, characterized in that: 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), and then use Map Y to Z, where Represents the i-th element in the k-th channel.

5. The method for analyzing electrical signal complexity based on time-varying fuzzy dispersion entropy brain according to claim 1, characterized in that: The method for performing multivariate embedding reconstruction in S5 is: According to the multivariate embedding theory, the multivariate embedding vector is generated, and 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.

6. The method for analyzing electrical signal complexity based on time-varying fuzzy dispersion entropy brain according to claim 5, characterized in that: The method for determining the dispersion modes of the m elements according to the fuzzy membership function in S5 is: For each Z m (j), we get all possible combinations of taking m elements at a time from mp elements; these combinations are represented by 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 a total of (N―1―(m―1)τ) Dispersion modes; In order to determine the element combination S q (j) The degree of membership of the class is introduced for each category and represented as M r The fuzzy membership function of Indicates S q (j) the membership of the hth element with respect to the rth class, and then 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, is of class ν1,..., and For class ν m―1 ; The algebraic product operator is used in the above fuzzy expression: 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:

7. The method for analyzing the complexity of electroencephalogram signals based on time-varying fuzzy dispersion entropy according to claim 1, characterized in that: 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:

Images