CN113349795B - Depression electroencephalogram analysis method based on sparse low-rank tensor decomposition - Google Patents

Depression electroencephalogram analysis method based on sparse low-rank tensor decomposition Download PDF

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CN113349795B
CN113349795B CN202110660709.4A CN202110660709A CN113349795B CN 113349795 B CN113349795 B CN 113349795B CN 202110660709 A CN202110660709 A CN 202110660709A CN 113349795 B CN113349795 B CN 113349795B
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高云园
黄金诚
张卷卷
金可滢
何韦聪
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Abstract

The invention discloses a depression electroencephalogram analysis method based on sparse low-rank tensor decomposition. Firstly, extracting electroencephalogram signal time-frequency characteristics by adopting complex Morlet wavelet transform, and constructing the electroencephalogram signal time-frequency characteristics into a sample tensor according to a channel sequence; secondly, according to the characteristics of low rank and sparseness of the sample tensor, the SLRaTucker is proposed to decompose and extract the multi-domain features of the sample tensor, and classification and identification are carried out on two groups of people, namely depression patients (MDDs) and normal control groups (HCs). In order to further study the similarities and differences of the two groups of people in brain activation areas when the two groups of people are stimulated by different moods, the invention analyzes the differences of the static and dynamic brain activation areas of the two groups of people. The SLRaTucker decomposition method provided by the experiment can effectively extract multi-domain characteristics in the electroencephalogram signals, and can accurately and objectively diagnose and analyze the depression, so that patients or doctors can better understand the illness state and timely treat or prevent the depression.

Description

Depression electroencephalogram analysis method based on sparse low-rank tensor decomposition
Technical Field
The invention relates to an analysis method for depression electroencephalogram signals by using low-rank sparse tensor decomposition, in particular to an analysis method for static and dynamic active brain areas under different emotional stimuli based on electroencephalogram signals of depression patients, and belongs to the technical field of intelligent mode recognition.
Background
Major Depressive Disorder (MDD) is a serious psychoemotional Disorder mental disease, and the incidence of depression reported in recent two years tends to rise year by year, and the age of onset also tends to be low. The electroencephalogram signals contain important information of brain activities, and MDD patients based on the electroencephalogram signals have been formally effective and feasible in active brain area research and objective depression diagnosis.
Electroencephalography (EEG) is a neurophysiological signal collected in a non-invasive manner, and an event-related potential (ERP), which is an evoked potential generated by stimulation of external objects, exists in brain-spontaneous Electroencephalogram signals. The existing research shows that the MDD patients have the phenomenon of attention deviation to negative emotion, and the ERP component of the MDD patients shows the phenomena of latent period increase, active brain area asymmetry and the like.
The brain is a rather complex system, and in recent years, time-frequency analysis, nonlinear analysis, entropy transmission and other methods are used for analyzing ERP, for example, time-frequency analysis shows that the latent period of a depression patient is increased under negative emotional stimulation. The depression patients often generate abnormal ERP components under negative emotional stimulation, and the active brain area shows an asymmetric phenomenon, so that abnormal information is doped in the ERP. Currently, there is less literature for ERP analysis studies of tensor-based depression patients, and further study analysis is needed. The ERP signals of the depression patients are effectively analyzed, and the difference and the connection between the patients and the active brain area of a normal control group under different emotional stimuli are researched, so that the method has important significance for diagnosing, treating and researching the depression.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a depression EEG analysis method based on sparse low-rank tensor decomposition by utilizing electroencephalogram signals of depression patients under different emotional stimuli. The method can effectively extract the EEG spatial features which cannot be extracted by the traditional algorithm, and provides a new idea for the active brain area analysis of the following mental disease patients based on the EEG signals.
The technical scheme adopted by the invention is as follows.
Collecting multichannel scalp electroencephalogram (EEG) signals of a depression patient under different emotional stimuli;
preprocessing the EEG signal: removing baseline offset and ocular artifacts by using eeglab, and filtering by using a 50Hz notch filter and a 0.3-30Hz band-pass filter; re-referencing;
and (3) segment averaging: the appearance of the stimulus is taken as an indication of the start of the stimulus, 800ms after the stimulus is intercepted as a trial (trial), the sampling frequency being 250 Hz. For each individual, 10 samples under the same stimulus were subjected to a superposition average to extract relatively pure ERP components.
Step (3), generating ERP tensor:
1) and mapping the superposed samples to a time-frequency domain through complex Morlet wavelet transform according to a channel:
Figure BDA0003115130290000021
where σ represents a bandwidth parameter, for a single ERP signal sample of second order (channels × sample points)
Figure BDA0003115130290000022
(where c represents the lead and t represents the sampling time point) by computing the wavelet function, a single sample ERP third-order tensor (channels × sample points × frequency) can be obtained to obtain
Figure BDA0003115130290000023
And (4) showing. Obtaining a 201 × 40 two-dimensional matrix (time × frequency) for each channel;
2) arranging the transformed data in the first dimension of the tensor according to the sequence of the channels to obtain a three-dimensional tensor with one dimension of channels multiplied by time multiplied by frequency, wherein the three-dimensional tensor naturally contains space, time and frequency information of each ERP sample; 3) and arranging the obtained three-dimensional tensors in a fourth dimension to generate a four-dimensional tensor with the dimensions of channels, time, frequency and samples, wherein the four-dimensional tensor is a sample tensor.
And (4) performing feature extraction by using SLARaTucker decomposition:
and simultaneously carrying out tensor decomposition on the first three dimensions of the sample tensor by using the SLRaTucker decomposition. On the basis of the traditional Tucker decomposition (2):
Figure BDA0003115130290000024
whereinYThe representation of the original tensor is,Grepresenting the core tensor, AnAnd n is 1,2 and 3 to represent a factor matrix.
Rewriting the traditional Tucker decomposition by using the low-rank and sparse characteristics shown by the ERP sample tensor by a low-rank approximation method:
Figure BDA0003115130290000031
wherein
Figure BDA0003115130290000032
IkIndicating the other dimension of n ≠ k,
Figure BDA0003115130290000033
the core tensor representing the tensor decomposition is,
Figure BDA00031151302900000314
representing the transpose of the matrix, Y(n)The original tensor after n-mode expansion is expressed, and the tensor n-mode is expanded, so that the low-rank approximation matrix decomposition objective function is
Figure BDA0003115130290000034
Wherein
Figure BDA0003115130290000035
And
Figure BDA0003115130290000036
for the low-rank approximate representation of Y, after obtaining the low-rank approximate representation of the matrix Y, fixing
Figure BDA0003115130290000037
And
Figure BDA0003115130290000038
will be provided with
Figure BDA0003115130290000039
The carry-in (3) obtains an objective function of LraTucker decomposition (Low rank apuach Tucker decomposition).
Figure BDA00031151302900000310
In order to improve the generalization capability of LraTucker decomposition in an ERP tensor and improve the obvious degree of extracted features, a sparse regular term lambda S (A) is added to the LraTucker decomposition, and an SLraTucker decomposition algorithm is provided
Figure BDA00031151302900000311
Wherein S (-) is a sparse representation, such as L0 norm | A0And L1 norm | A +1There are some problems in practical applications (solving the L0 norm is an NP hard problem, and the L1 norm is not derivable at 0), and here we use the following formula as the sparse representation function
Figure BDA00031151302900000312
Finally, the updating formula of the factor matrix of the SLARaTucker decomposition is obtained as follows:
Figure BDA00031151302900000313
and extracting a former three-dimensional factor matrix of the ERP tensor according to the updating formula, updating, and finally obtaining the Tucker expression of the ERP tensor, wherein the core matrix is the specific multi-domain feature of each sample, and the factor matrix is a high-dimensional space base matrix shared by all samples and is also the shared feature of all samples.
Compared with the existing methods for classifying the EEG/ERP signals of the depression, the method has the following characteristics:
firstly, the invention starts from multi-domain feature extraction, stores ERP signals in a tensor form, directly and simultaneously extracts multi-domain features (time domain, space domain and frequency domain) containing spatial features through tensor decomposition, and can ensure the objectivity of the space domain features and the comprehensiveness of the extracted features.
Secondly, an SLARaTucker decomposition algorithm is proposed to perform tensor decomposition by using low-rank and sparse characteristics shown by the ERP tensor, so that the generalization capability of the tensor decomposition algorithm in the EEG/ERP field is ensured while the decomposition efficiency is greatly improved.
Thirdly, in order to objectively diagnose the depression, the machine learning classical classification algorithm is introduced, and the core tensor obtained by tensor decomposition is used as the sample characteristic to identify the depression ERP sample.
Fourthly, in order to analyze the active brain areas of the depression patients under different emotional stimuli, the factor matrix representing the spatial characteristics obtained by tensor decomposition is presented in the form of a brain topographic map, and the difference of the static active brain areas of the two groups of people is observed.
And fifthly, in order to visually observe the dynamic response of the two groups of people in the active brain areas after different emotional stimuli, the invention adopts a sliding time window to extract dynamic ERP components, adopts SLRaTucker to decompose and extract the dynamic spatial characteristics of the dynamic ERP components, and observes the difference of the dynamic active brain areas after the two groups of people are stimulated by different emotions.
Drawings
Fig. 1 is a flow chart of EEG analysis for low rank sparse tensor decomposition.
FIG. 2 is an experimental paradigm for mood-stimulating EEG acquisition.
Fig. 3 is a single sample ERP three-dimensional tensor.
Fig. 4 is an ERP sample tensor.
FIG. 5 is a comparison of the static brain topography of two classes of population.
Fig. 6 is a comparison of dynamic brain topography of two groups of people.
Detailed Description
In order to more objectively and comprehensively analyze the ERP components of the depression patients, the invention mainly improves the ERP analysis method. The present invention stores ERP data using tensors as the basic data structure. Fully utilizing the low-rank and sparse characteristics of the ERP tensor, providing an SLRaTucker decomposition to decompose the ERP tensor so as to extract the multi-domain characteristics of the ERP tensor, identifying a depression ERP sample by using a Support Vector Machine (SVM), and observing the comparison of static active brain areas of two groups of people under different emotional stimuli; as shown in fig. 2; and finally, extracting dynamic ERP components by adding a sliding time window, and dynamically analyzing the difference of the two groups of people in active brain areas after emotional stimulation.
The specific tensor decomposition-based depression electroencephalogram analysis method flow chart is shown in fig. 1, the experiment provides a low-rank sparse tensor decomposition algorithm-based multi-domain feature analysis for ERP components, and the method comprises the following specific steps:
step 1, EEG Collection of Depression patients, 53 subjects of this example including 24 MDD patients (13 men, 11 women, age 16-56 years) and 29 healthy controls (20 men, 9 women; age 18-55 years) were not significantly different in age and sex, among which the MDD patients were screened according to the American psychiatric Association, 1994 clinical diagnostic and statistics Scale for mental disorders (DSM-IV), and were first-onset depression-drug-free patients in good health before the trial. On the basis of a classical point measurement paradigm, different emotion human face faces are added to serve as stimulation clues, round points serve as target detection points, and EEG signals under attention tasks are induced through external emotion picture stimulation. Wherein, the emotional face data is 80 pictures with different titers (positive, negative and neutral) selected from Chinese emotional face picture system (CFAPS). When the stimulus clues are displayed, one of three different emotions (fear, sadness and happiness) is randomly selected to be combined with the neutral emotion face to form an emotion-neutral face stimulus pair.
The experimental paradigm was written using E-prime (Version: 1.2) and presented on a 17 inch display with a resolution of 1280X 1024 and a screen refresh rate of 60Hz, and before the experiment began, the subject was asked to complete 10 trials of the same trial runs as the official experiment to become familiar with the experiment. In the official experiment, the entire experiment included three blocks, each block including 160 dials. During the experiment, the subject needs to keep focus on the emotional face stimulus pairs. At the beginning of each trial, a fixed white cross appears in the center of the screen for 300ms and will always be displayed in the center of the screen. Next, the emotional face stimulus pairs presented in random order are displayed on the screen for 500 ms; after the interval of 100-; followed by a 600ms black screen rest. The experimental paradigm is shown in figure two. When EEG signals are collected, a GSN128 brain conduction helmet under an international standard lead 10-20 system established by the International electroencephalogram society is used for collecting scalp brain electrical signals, the sampling frequency is 250Hz, and the impedance value of a whole brain electrode is kept below 50k omega.
And 2, filtering out signals of about 50Hz with power line interference in the EEG data. And then carrying out noise elimination processing on the EEG data, filtering by using a 0.3-30Hz band-pass filter, intercepting 800ms after stimulation as a test time, and carrying out superposition averaging on 10 samples under the same stimulation for each individual to extract a pure ERP component.
Step 3, mapping the superposed samples to a time-frequency domain sequentially through complex Morlet wavelet transformation according to channels, and obtaining a 201 x 40 two-dimensional matrix (time x frequency) for each channel; arranging the transformed data in the first dimension of the tensor according to the sequence of the channels to obtain a three-dimensional tensor (channels × time × frequency) with one dimension of 128 × 201 × 40, as shown in fig. 3, which naturally contains the space, time and frequency information of each ERP sample; the obtained three-dimensional tensors are arranged in the fourth dimension, and a four-dimensional tensor (channels × time × frequency × samples) with the dimension of 128 × 201 × 40 × 848 is generated, and this four-dimensional tensor is a sample tensor, as shown in fig. 4.
And 4, decomposing the ERP sample tensor through the SLRaTucker decomposition, wherein the core tensor is the specific multi-domain characteristic of each sample, and the factor matrix is a high-dimensional space basis matrix which is common to all samples, namely the common characteristic of all samples.
And 5, inputting the extracted multi-domain features of the MDD and HC groups, namely the core tensor, into the SVM after vectorization, and obtaining recognition rates of 91.5%, 90.6% and 84.3% under the emotional stimulation of pleasure, sadness and fear.
And 6, extracting multi-domain features within 800ms after stimulation of the two groups of people by using an SLARaTucker decomposition algorithm, wherein the algorithm is a process of estimating all sample tensors in the first three dimensions, and the obtained factor matrix is the features shared by all samples. And respectively decomposing the two sample tensors by using an SLA Tucker algorithm by generating the respective sample tensors of the MDD and the HC to obtain the Tucker decomposition of the sample tensors of the MDD patient and the HC control group. In order to observe the similarities and differences of the two groups of people in the active brain areas under different emotional stimuli, a mode-1 factor matrix representing the spatial characteristics is presented in the form of a brain topographic map, and the positions of the brain areas are shown in fig. 5.
And 6, selecting a sliding time window with the length of 200ms and the overlapping rate of 50% in order to dynamically analyze the change condition of the ERP. In combination with the difference between the 800ms brain atlas HC control group and the MDD patients, 20 electrodes including frontal lobe, central region, parietal lobe and occipital lobe were selected from 128 channels, as shown in table 1, data tensors were generated for each group of people, the sample tensors in each time period were decomposed using the slatucker algorithm, and the mode-1 factor matrix was presented in the form of a brain atlas, as shown in fig. 6.
TABLE 1 channel selection
Figure BDA0003115130290000061

Claims (3)

1. The depression electroencephalogram analysis method based on sparse low-rank tensor decomposition is characterized by comprising the following steps of:
collecting multichannel scalp electroencephalogram (EEG) signals of depression patients under different emotional stimuli;
step (2) preprocessing, re-referencing and piecewise averaging the EEG signal; for each individual, performing superposition averaging on N samples under the same stimulus to extract ERP components;
step (3), generating ERP tensor:
1) and mapping the superposed samples to a time-frequency domain through complex Morlet wavelet transform according to a channel:
Figure FDA0003115130280000011
where σ represents the bandwidth parameter, for a single ERP signal sample of second order, i.e., channels × sample points
Figure FDA0003115130280000012
Obtaining a single sample ERP third-order tensor, namely channels x sample points x frequency, by calculating a wavelet function, wherein c represents a lead, and t represents a sampling time point, so as to obtain a single sample ERP third-order tensor
Figure FDA0003115130280000013
Denotes, f denotes frequency; obtaining a 201 × 40 two-dimensional matrix for each channel, namely time × frequency;
2) arranging the transformed data in the first dimension of the tensor according to the sequence of the channels to obtain a three-dimensional tensor with one dimension of channels multiplied by time multiplied by frequency, wherein the three-dimensional tensor comprises space, time and frequency information of each ERP sample;
3) arranging the obtained three-dimensional tensors in a fourth dimension to generate a four-dimensional tensor with the dimensions of channels, time, frequency and samples, wherein the four-dimensional tensor is a sample tensor;
and (4) providing sparse regular low-rank approximation Tucker decomposition, and extracting the features of the electroencephalogram tensor:
carrying out tensor decomposition on the first three dimensions of the sample tensor by adopting low-rank approximation Tucker decomposition; on the basis of the traditional Tucker decomposition:
Figure FDA0003115130280000014
wherein
Figure FDA0003115130280000015
The representation of the original tensor is,
Figure FDA0003115130280000016
representing the core tensor, AnN-1, 2,3 represents a factor matrix;
rewriting the traditional Tucker decomposition by using the low-rank and sparse characteristics shown by the ERP sample tensor by a low-rank approximation method:
Figure FDA0003115130280000021
wherein
Figure FDA0003115130280000022
IkIndicating the other dimension of n ≠ k,
Figure FDA0003115130280000023
the core tensor representing the tensor decomposition is,
Figure FDA00031151302800000214
representing the transpose of the matrix, Y(n)The original tensor after n-mode expansion is expressed, and the tensor n-mode is expanded, so that the low-rank approximation matrix decomposition objective function is
Figure FDA0003115130280000024
Wherein
Figure FDA0003115130280000025
And
Figure FDA0003115130280000026
for the low-rank approximate representation of Y, after obtaining the low-rank approximate representation of the matrix Y, fixing
Figure FDA0003115130280000027
And
Figure FDA0003115130280000028
will be provided with
Figure FDA0003115130280000029
Carrying in formula (3) to obtain a target function of Low rank approach Tucker decomposition;
Figure FDA00031151302800000210
in order to improve the generalization capability of the Low rank approach Tucker decomposition in the ERP tensor and improve the obvious degree of characteristic extraction, a sparse regularization term lambda S (A) is added to the Low rank approach Tucker decomposition, and a Low rank approximation Tucker decomposition algorithm is provided
Figure FDA00031151302800000211
Where λ represents the regular term sparsity, S (-) is the sparse representation, using the following equation as the sparse representation function
Figure FDA00031151302800000212
Wherein A isiRow vector representing A
Finally, the updating formula of the factor matrix of the SLARaTucker decomposition is obtained as follows:
Figure FDA00031151302800000213
and extracting a former three-dimensional factor matrix of the ERP tensor according to the updating formula, updating, and finally obtaining the Tucker expression of the ERP tensor, wherein the core matrix is the specific multi-domain feature of each sample, and the factor matrix is a high-dimensional space base matrix shared by all samples and is also the shared feature of all samples.
2. The depression electroencephalogram analysis method based on sparse low rank tensor decomposition according to claim 1, characterized in that: preprocessing the EEG signal, specifically: and removing baseline offset and ocular artifacts by using eeglab, and filtering by using a 50Hz notch filter and a 0.3-30Hz band-pass filter.
3. The depression electroencephalogram analysis method based on sparse low rank tensor decomposition according to claim 1, characterized in that: the segment averaging specifically includes: the appearance of the stimulus is taken as the sign of the beginning of the stimulus, 800ms after the stimulus is intercepted as a trial, and the sampling frequency is 250 Hz.
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