CN111539472A - Sleep physiological signal feature extraction method and system based on tensor complexity - Google Patents

Sleep physiological signal feature extraction method and system based on tensor complexity Download PDF

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CN111539472A
CN111539472A CN202010320743.2A CN202010320743A CN111539472A CN 111539472 A CN111539472 A CN 111539472A CN 202010320743 A CN202010320743 A CN 202010320743A CN 111539472 A CN111539472 A CN 111539472A
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魏守水
张志民
董孝彤
崔怀杰
谢佳静
王春元
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Abstract

The invention discloses a sleep physiological signal feature extraction method and system based on tensor complexity, which comprises the steps of collecting sleep physiological signals and converting a multi-lead time sequence of the sleep physiological signals into tensor expression; the sleep physiological signal is expressed as an N-order tensor which consists of N-order sub-tensors; the difference between each element in each sub-tensor and each element in the global sub-tensor is judged to determine the approximate entropy of the N-order tensor, the approximate entropy of the tensor is used as the characteristic of the sleep physiological signal extraction, the extracted characteristic can accurately reflect the internal characteristic of the sleep physiological signal data, and therefore the sleep stage is more accurate in the subsequent classification processing.

Description

Sleep physiological signal feature extraction method and system based on tensor complexity
Technical Field
The invention belongs to the technical field of physiological signal feature extraction, and particularly relates to a sleep physiological signal feature extraction method and system based on tensor complexity.
Background
The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
Tensor representation of data and corresponding data processing in a tensor format, such as tensor decomposition and the like, provide a new solution for biomedical signal processing, and have been successfully applied in the field of electroencephalogram.
Processing the signal in the form of a tensor has its own advantages. Firstly, almost all biomedical signals have multi-dimensionality, such as 32-lead sleep electroencephalogram signals or 12-lead sleep electrocardiosignals, which are physiological expressions of the same signal source at different positions on the body surface, the physiological signals of all leads do not exist independently and have certain spatial and temporal correlation with each other, and the correlation between the lead signals is ignored when the physiological signals are treated as a plurality of independent signal sources. And a reasonable tensor data organization form can restore the system state of a single signal source to a greater extent.
Furthermore, another motivation for tensor data representation is that tensors have some unique properties that can help effectively mine the internal features of data, such as CANDECOMP/parafacc decomposition (CPD) and Tucker Decomposition (TD). Based on the above consideration, tensors have been primarily applied in the field of biomedical signals, for example, tensor representations of electroencephalogram data have been applied more in the aspects of multidirectional blind source separation, feature extraction, classification, dimension reduction, multidirectional clustering and the like.
However, the inventor finds in research that in the current sleep stage research, more methods are based on feature extraction of single-lead or multi-lead physiological signals, few sleep stage methods based on tensor data processing exist, and in few sleep stage methods based on tensor data processing, a tensor decomposition method is mainly applied, and there is no document to carry out sleep stage work by extracting the complexity of tensor data. Moreover, a method for accurately estimating the complexity of tensor data is also lacked in the current literature.
In short, in many tensor data processing schemes, an entropy method for evaluating complexity of tensor data is not embodied, and physiological signals are not extracted by using complexity of tensor data, so that the feature extraction accuracy of the current physiological signals is low due to the fact that the complexity of the internal structure of the tensor is not considered, and certain errors are brought to later applications such as classification.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a sleep physiological signal feature extraction method based on tensor complexity, and feature extraction is realized through spatial data complexity or predictability of tensor based on data representation of tensor.
In order to achieve the above object, one or more embodiments of the present invention provide the following technical solutions:
the sleep physiological signal feature extraction method based on tensor complexity comprises the following steps:
acquiring a sleep physiological signal and converting a multi-lead time sequence of the sleep physiological signal into tensor expression;
the sleep physiological signal is expressed as an N-order tensor which consists of N-order sub-tensors;
and determining the magnitude of the approximate entropy of the N-order tensor by judging the difference magnitude between each element in each sub-tensor and each element in the global sub-tensor, and taking the approximate entropy of the tensor as the characteristic of the sleep physiological signal extraction.
According to the further technical scheme, the extracted sleep physiological signal tensor approximate entropy characteristics are input to a classifier which is trained in advance for classification, and the sleep stage corresponding to the sleep physiological signal is determined.
According to a further technical scheme, after the characteristics are obtained, firstly, variance detection and independent sample t detection of tensor approximate entropies of sleep tensors in different sleep states are carried out to judge whether the tensor approximate entropies and the sleep states have obvious correlation and obvious difference or not, if yes, the extracted characteristics are input into a pair of multi-support vector machine classifiers to carry out sleep state classification, and the accuracy of sleep stages is output.
According to the further technical scheme, for the N-order tensor, a similarity comparison threshold parameter is given, an embedding dimension is determined to be used for dividing the dimension of the sub-tensor, and according to the embedding dimension, m continuous points are sequentially taken in N directions of the tensor to form the N-order sub-tensor;
calculating the distance between any two N-order sub-tensors under the condition that the embedding dimension is m, and determining the distance by the maximum difference value of corresponding position elements between the two sub-tensors;
calculating the number of N-order sub tensors meeting set conditions and calculating the ratio of the number of the N-order sub tensors to the number of all the sub tensors;
defining an average similarity rate when the embedding dimension is m;
and calculating an average similarity ratio when the embedding dimension is m +1, and calculating tensor approximate entropy of the N-order tensor based on the average similarity ratio to be used as the feature extracted from the sleep physiological signal.
In order to achieve the above object, one or more embodiments of the present invention provide the following technical solutions:
on the other hand, a sleep physiological signal feature extraction system based on tensor complexity is disclosed, which comprises:
the signal acquisition module is used for acquiring the sleep physiological signal;
the signal processing module is used for converting the multi-lead time sequence of the sleep physiological signal into tensor expression;
the signal characteristic extraction module is used for expressing the sleep physiological signal as an N-order tensor, and the N-order tensor is composed of N-order sub-tensors; and determining the magnitude of the approximate entropy of the N-order tensor by judging the difference between the elements in each sub-tensor and each element in the global sub-tensor, and taking the approximate entropy of the tensor as the characteristic of the sleep physiological signal extraction.
The sleep stage module is used for inputting the extracted tensor approximate entropy characteristics of the sleep physiological signals into a pre-trained classifier for classification and determining the sleep stage corresponding to the sleep physiological signals.
In the signal feature extraction module, for an N-order tensor, a similarity comparison threshold parameter is given, an embedding dimension is determined for dividing the dimension of the molecular tensor, and according to the embedding dimension, m continuous points are sequentially taken in N directions of the tensor to form an N-order sub-tensor;
calculating the distance between any two N-order sub-tensors under the condition that the embedding dimension is m, and determining the distance by the maximum difference value of corresponding position elements between the two sub-tensors;
calculating the number of N-order sub tensors meeting set conditions and calculating the ratio of the number of the N-order sub tensors to the number of all the sub tensors;
defining an average similarity rate when the embedding dimension is m;
and calculating an average similarity ratio when the embedding dimension is m +1, and calculating tensor approximate entropy of the N-order tensor based on the average similarity ratio to be used as the feature extracted from the sleep physiological signal.
The above one or more technical solutions have the following beneficial effects:
according to the technical scheme, the complexity of the tensor is evaluated by calculating the conditional probability of the neighborhood similarity inside the sleep physiological signal tensor, the complexity is used as the characteristic signal for dividing the sleep stage, the correlation among lead signals of the sleep physiological signal can be well reserved by utilizing the mode of evaluating the complexity of the tensor, the extracted characteristic can accurately reflect the internal characteristic of the sleep physiological signal data, and then the sleep stage is more accurate in the subsequent classification processing.
Based on the fact that an entropy method is generally applied to time sequences or two-dimensional images, the technical scheme of the disclosure provides the entropy method capable of accurately evaluating the spatial complexity of tensor data, and the entropy method is applied to sleep stages, and compared with a traditional entropy method, the sleep stage accuracy of tensor approximate entropy is higher.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a schematic diagram illustrating the calculation of tensor approximate entropy according to an embodiment of the present invention;
FIG. 2 is a diagram of a three-dimensional ordinary tensor constructed from a one-dimensional time series according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the construction of a third-order sleep tensor from polysomnography data in a't/dt/s' manner according to an embodiment of the present invention;
FIG. 4(A) is a graph of the trend of the approximate entropy of the tensor over the four common tensors when r is between 0.05 and 2.00;
FIG. 4(B) is an enlarged view of the area of FIG. (A) when the TensorApEn value of the embodiment of the present invention is from-0.5 to 1.5;
fig. 5(a) is a histogram of shadow errors of tensor approximate entropy in six sleep states according to an embodiment of the present invention, where the histogram includes from the top left corner to the bottom right corner: wake, S1, S2, S3, S4 and REM;
fig. 5(B) is a graph of approximate entropy mean variation of tensors in six sleep states of B2 according to this embodiment, where each of the B1 and B3 is an enlarged region of the B2 graph at different values of r;
FIG. 6(A) ANOVA test between any pair of sleep states;
fig. 6(B) independent sample t-tests between any pair of sleep states, the pixel size in each sub-graph characterizing the p-value of the test, the corresponding pixel being labeled ' × ' in fig. 6(a) when the p-value is greater than 0.05 and ' in fig. 6(B) when the p-value is greater than 0.0033;
FIG. 7: the approximate entropies of four common time series are changed along with the change of different r values;
FIG. 8: tensors of different dimensions compute the computational complexity of tensor approximation entropy.
Detailed Description
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular is intended to include the plural unless the context clearly dictates otherwise, and further it is to be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of the stated features, steps, operations, devices, components, and/or combinations thereof.
The embodiments and features of the embodiments of the invention may be combined with each other without conflict.
Example one
The embodiment discloses a sleep physiological signal feature extraction method based on tensor complexity, and provides a new feature extraction method for tensor-based data representation by exploring tensor spatial data complexity or predictability, which specifically comprises the following steps: acquiring a sleep physiological signal and converting a multi-lead time sequence of the sleep physiological signal into tensor expression;
the sleep physiological signal is expressed as an N-order tensor which consists of N-order sub-tensors;
and determining the magnitude of the approximate entropy of the N-order tensor by judging the difference magnitude between each element in each sub-tensor and each element in the global sub-tensor, and taking the approximate entropy of the tensor as the characteristic of the sleep physiological signal extraction.
In a specific embodiment, in order to evaluate the performance of tensor approximate entropy in distinguishing different Sleep states, a public Sleep database Sleep-EDF is also selected. The database contained 61 samples from two studies, with data labeled SC collected from a study evaluating the effect of age factors on sleep quality from 1987 to 1991, with samples from 25 to 101 years of age of healthy caucasian; data additionally labeled ST was collected from a study to assess the effect of administration of a neuroleptic on sleep quality, and the test samples were caucasian diagnosed with mild sleep disturbance.
In order to construct the third-order sleep tensor, three-lead physiological data with the sampling frequency of 100Hz in a database are selected, wherein the three-lead physiological data comprise Fpz-Cz electroencephalogram signals, Pz-Oz electroencephalogram signals and horizontal electro-oculogram signals. Each group of sleep data was calibrated by experienced professional physicians giving sleep status every 30S according to R & K criteria, and contains a total of 6 sleep states including wakefulness (W), non-rapid eye movement periods (S1, S2, S3, S4), and rapid eye movement period REM. Since each sleep record contains polysomnography data in a large number of wake states before and after falling asleep, only 30 minutes of wake data before and after falling asleep were selected in order to balance the data volume of the respective sleep states. In addition, in order to remove baseline drift and linear trend, a 4-order Butterworth band-pass filter is designed to filter the signal, and the cut-off frequencies are 0.5Hz and 30Hz respectively.
The tensor approximate entropy is calculated as follows:
(1) for an N-order tensor
Figure BDA0002461304240000061
A threshold parameter r is compared given the similarity and an embedding dimension m is determined for partitioning the sub-tensor dimensions.
(2) In tensor according to embedding dimension mXSequentially taking m continuous points in each of the N directions to form an N-order sub-tensor
X m(i1，i2，…，iN)＝X(i1：i1+m-1，i2：i2+m-1，…，iN：iN+ m-1), the dimension of each sub-tensor is
Figure BDA0002461304240000062
Thereby in total generating
Figure BDA0002461304240000063
Figure BDA0002461304240000064
A number N of order sub-tensors.
(3) And calculating the distance between any two N-order sub-tensors under the condition that the embedding dimension is m, wherein the distance is determined by the maximum difference value of corresponding position elements between the two sub-tensors.
Dm(X m(i1，i2，…，iN)，X m(j1，j2，…，jN))
＝max|X(i1+k1，i2+k2，…，iN+kN)
-X(j1+f1，j2+f2，…，jN+fN)|
Wherein k is1，k2，…，kN＝0，1，2，…，m-1；f1，f2，…， f N0, 1, 2, …, m-1. It should be noted that there is a self-matching in the calculation of the tensor approximate entropy, i.e. i is not excluded1＝j1，i2＝j2，…iN＝jNThis is similar to the conventional time series approximate entropy calculation process.
(4) For each one
i1∈[1，2，…，I1-m+1]，i2∈[1，2，…，I2-m+1]，…，iN∈ [1，2，…，IN-m+1]Calculating the number of N-order sub-tensors satisfying the following conditions and calculating the ratio of the number of the N-order sub-tensors to the number of the total sub-tensors
Figure BDA0002461304240000071
Wherein j1∈[1，2，…，I1-m+1]，j2∈[1，2，…，I2-m+1]，…，jN∈[1，2，…，IN- m+1]，std(X) Tensor representing order NXStandard deviation of all elements in (a). This process is calledX m(i1，i2，…，iN) The process of template matching of (a) is,
Figure BDA0002461304240000072
representing any one of the sub-tensorsX m(j1，j2，…，jN) The probability of match with the template.
(5) Define the average similarity ratio at embedding dimension m:
Figure BDA0002461304240000073
(6) repeating the steps (1) to (5) to calculate the average similarity rate psi when the embedding dimension is m +1m+1(r)。
Tensor of order N
Figure BDA0002461304240000074
The tensor approximation entropy of (d) is calculated as follows:
TensorApEn(X)＝Ψm+1(r)-Ψm(r)
i1is referred to as tensorXIn I1Ith in the direction1An element, j1Is referred to as tensorXIn I1J th in direction1An element, i2Is referred to as tensorXIn I2Ith in the direction2An element, j2Is referred to as tensorXIn I2J th in direction2Elements, and so on.
Fig. 1 shows a schematic diagram of a method for calculating tensor approximate entropy, and in order to more clearly show the method for calculating tensor approximate entropy, a third-order tensor is taken as an example in the schematic diagram. Regarding the selection of the embedding dimension m and the threshold r for similarity comparison, the internal complexity of the N-th order tensor can be evaluated to the maximum when m is 2, but the selection of the parameter r needs to be selected differently according to different application environments. In this disclosure, setting m to 2 and discussing mainly the effect of the parameter r on the ordinary tensor and the sleep tensor when selecting different values. From the information entropy point of view, the idea of tensor approximate entropy is to determine the magnitude of information entropy of one tensor by judging the difference magnitude between each element in each sub-tensor and each element in the global sub-tensor. If a sub-tensorX m(i1，i2，…，iN) The difference from other sub-tensors is large, and D is satisfiedm(X m(i1，i2，…，iN)，X m(j1，j2，…，jN))＜r×std(X) Sub tensor of order NX m(j1，j2，…，jN) The number of the information entropy codes is small, and the information amount corresponding to the information entropy codes is larger.
To evaluate the generalization ability of tensor approximate entropy, the evaluation index of the tensor approximate entropy on a common tensor is tested firstly. Therefore, according to the present disclosure, four ordinary tensors are first constructed through four conventional time sequences, in order to conveniently show the data structure of the tensors, the dimensions of the four ordinary tensors constructed in this section are all three-order, and the size of the tensor is R50×50×50. An intuitive schematic of constructing a three-dimensional tensor from a one-dimensional time series is shown in figure 2. TensorX 1From a pulse signal of length 50
Figure RE-GDA0002533241030000081
Figure RE-GDA0002533241030000082
Is constructed. Pulse signal y1In tensorX 1And the arrangement was replicated 50 times in the I1 direction and I2 and I3 directions, respectively. Second tensorX 2From a sinusoidal signal y2Sin (2 × pi × 20 × n), structure mode and tensorX 1Constructed in a similar manner, y2In tensionX 2And the arrangement was replicated 50 times in the I1 direction and I2 and I3 directions, respectively. In addition, tensorX 3From a trigonometric function y containing two frequency components30.6 × sin (2 × pi × 50 × n) +0.3 × sin (2 × pi × 120 × n), in order to further increase tensorX 3Only inX 3For sequence y in the direction of I23A simple copy alignment is made and the displacement is increased in the direction of I3. At the same time, the fourth tensorX 4White gaussian noise is present in each direction, as shown in fig. 2 (d).
FIG. 2: a three-dimensional ordinary tensor diagram is constructed from a one-dimensional time series. Time series y1Corresponding tensorX 1(ii) a Time series y2Corresponding tensorX 2(ii) a Time series y3Corresponding tensorX 3(ii) a Time series y4Corresponding to the amount of tensionX 4。
Constructing a sleep tensor from the polysomnography data:
there are several methods available in the existing literature to convert the multi-lead time series into a tensor form, one of the common methods is to perform time-frequency analysis on the time series to obtain frequency domain information of the time series, thereby constructing a tensor of 'lead × time domain × frequency domain', in addition, another method for constructing a tensor is based on Hankel decomposition, and the multi-lead physiological signals related to a plurality of samples under test can also be organized into a tensor of 'sample × lead × time domain', however, the above three common methods for constructing tensor representation have a significant problem, since the above three methods construct a third-order tensor by expanding the third-dimensional data, the data volume will increase significantly, which brings a huge burden to later-time-domain-based data processing, therefore, to avoid introducing expanded data while ensuring the rationality of the data structure, the other two new methods for constructing the tense are worth using, which are respectively 'dt/s' and's/s/t' and the three methods for constructing a sleep signal structure by using a three-channel electrical signal structure, which is shown by a three-channel electrical signal structure, I-t-time domain structure, I-t, which is shown by a three channel structure of a three channel electrical signal structure (I-z electrical signal structure) which is shown by a three channel structure, I-z electrical signal structure, I-z structure, I's, I-z structure, which is shown by a three channel structure, I-z electrical signal structure, I's, a three channel structure, which is shown by a three channel structure, which is shown by a three channel structure, a three channel structure which is shown by a method for which is a method for example, a method for which is shown by a method forAccordingly, X1, X2, and X3 in FIG. 3 represent Fpz-Oz EEG, Pz-Oz EEG, and horizontal electro-ocular data, respectively. Kth 'slice' X in sleep tensor generated by't/dt/s' methodkCan be expressed as:
Figure BDA0002461304240000101
for each slice in the sleep data, the duration is 30s, the sampling frequency is 100Hz, and the resultant tensor has a size of each 'slice' of
Figure BDA0002461304240000102
Each row contains 1s of data. Thus, each sleep segment containing three channels of data can be sized in a manner of't/dt/s
Figure BDA0002461304240000103
For the 59481 sleep slices in table 5.1 we can convert this into 59481 sleep tensors in total, with each sleep tensor having the sleep state designation given by the specialist. The calibration data is used as classified ground truth, namely labeling of sleep state classification, and a classifier is learned and trained based on the calibration data and used for evaluating a classification result.
FIG. 3: a third order sleep tensor is constructed from the polysomnography data in the manner of't/dt/s'. Three 'slices' X1 to X3 in the tensor are respectively constructed by single-channel sleep data, and the three tensors are arranged in the I3 direction to form three-order tensors. Wherein each 'slice' is constructed as shown by the red solid line in the figure, the sleep data of a single channel is cut into segments of length N, the first segment of data is represented by x1(1)to x1(N) arranged from left to right in the tensor, corresponding to a second segment of data x1(N+1)to x1(2N) are arranged right to left in the tensor, and so on the single channel sleep data is constructed in a serpentine fashion as one 'slice' in the tensor.
Consistency analysis of tensor approximate entropy:
in the definition of the tensor approximation entropy, it is indicated that there are two parameters to be determined, namely the embedding dimension m and the similarity comparison threshold r. Since m selects a definite value 2, the consistency of tensor approximate entropy when selecting different similarity comparison threshold r is mainly discussed. Given two tensorsXAndYthe consistency of tensor approximate entropy is defined as follows: if r is present0∈ r make tensorXIs more complex than tensorYI.e. TensorApEn x (r0)＞TensorApEn Y (r0) For all rk∈ r all satisfy TensorApEn x (rk)＞TensorApEn Y (rk) Then the tensor approximation entropy can be considered to have good consistency.
The consistency analysis can be generalized as the following equation:
Figure BDA0002461304240000111
discriminative power analysis of tensor approximate entropy
Similarly, the identification capability of tensor approximate entropy when selecting different similarity comparison threshold r is mainly discussed. Considering n different tensorsX 1，X 2，…，X nAssuming that its complexity is progressively increased, if for all rk∈ r tensor approximate entropies all satisfy:
Figure BDA0002461304240000112
the tensor approximate entropy is considered to be well discriminative.
Statistical test of tensor approximate entropy
1) ANOVA test of variance
To investigate whether the tensor approximate entropy has significant correlation with different sleep states, we performed ANOVA test on the tensor approximate entropy in different sleep states. Two conditions, normal distribution and homogeneity of variance, are required to be verified before the ANOVA test is performed. If the conditions are met, a one-way ANOVA test is performed, otherwise a parametric test and a non-parametric test are performed. Since there is debate in the literature as to whether parametric or non-parametric tests should be performed when variance homogeneity is not satisfied, we present both parametric and non-parametric test results in this disclosure when variance homogeneity is not satisfied. All tests considered significant correlation if and only if the p-value was less than 0.05.
A) Non-parametric inspection
In the case where the data does not satisfy homogeneity of variance, the independent sample Kruskal-Wallis test is commonly used to test whether there is significant correlation between data in place of one-way ANOVA. This method, proposed by William Kruskal and w.
B) Parameter testing
In addition to non-parametric tests, some parametric tests are equally applicable to cases where the data does not satisfy the homogeneity of variance. In this disclosure, we performed both the Welch and Brown-Forsythe tests to further confirm the results of the non-parametric tests. The Welch test refers to a test of whether the mean values of each group are equal using the statistics of the Welch distribution. The Welch distribution is similar to the F distribution, and the homogeneity of variance is not required by the Welch test, so when the distribution of the dependent variable does not meet the requirement of the homogeneity of variance, the Welch test is more stable than the variance analysis. Similarly, the Brown-Forsythe test refers to a test of whether the mean values of each group are equal using the statistics of the Brown-Forsythe distribution. The Brown-Forsythe distribution also approximates the F distribution, but the Brown-Forsythe test also has no requirement on the homogeneity of variance, so the Brown-Forsythe test is more reliable than the analysis of variance when the distribution of the dependent variables does not meet the requirement on the homogeneity of variance.
4.8. Independent sample t test
To further explore whether tensor approximation entropy has significant differences between different sleep states, the present disclosure simultaneously performs independent sample t-tests of the data. Generally, the p-value when t-test is performed on independent samplesData were considered significantly different when less than 0.05. However, since the present disclosure considers a total of 6 different sleep states, it also encompasses
Figure BDA0002461304240000121
The pair of sleep states, and therefore some probability factors, may also lead to a conclusion of a significant difference in this case. To compensate for the effects of this factor, we performed Bonferroni's correction to evaluate whether there was a significant difference with a more rigorous criterion, and data were considered significant differences if and only if the p-value was less than 0.0033 (0.05/15). After Bonferroni's correction, confidence is higher if there is still a significant difference in tensor approximate entropy.
Consistency and identification capability analysis of tensor approximate entropy on common tensor
The space structure diagram of the four ordinary tensors is shown in fig. 2, and it is obvious that there is a relatively obvious difference in space complexity between the four tensors, and the difference is shown in fig. 2X 1ToX 4The complexity increases in order. In order to evaluate the consistency and the identification capability of the tensor approximate entropy on the common tensor, the tensor approximate entropy of the four common tensors under the condition that r takes different values is respectively calculated, the value range of r is 0.10 to 2.00, and the step length is 0.05. The trend of tensor approximation entropy with r is shown in fig. 4. TensorX 1The tensor approximation entropy of (A) is kept constant at 0.1036 when different r values are taken, and the tensor isX 2Sum tensorX 3The approximate entropy of the tensor is similar with the variation trend of r, but
Figure BDA0002461304240000131
Is always greater than
Figure BDA0002461304240000132
Meanwhile, when the value of r is small, tensor is obtainedX 4Approximate entropy of tensor of
Figure BDA0002461304240000133
Is the smallest of the four tensors, whenWhen the value of r is more than 0.5,
Figure BDA0002461304240000134
the value of (b) is the largest. As is apparent from fig. 4, the tensor approximate entropy shows good consistency and identification capability when r is 0.7 to 2.0. However, this consistency and discrimination ability is weakened when the r value is less than 0.5. In addition, we can also find that when the r value is greater than 0.7
Figure BDA0002461304240000135
Is always less than
Figure BDA0002461304240000136
This is generally recognized by usX 2Is more complex thanX 1In contradistinction, a discussion and explanation of this point will be given in detail in the fourth subsection.
FIG. 4: (A) the tensor approximates the trend of variation of entropy over four common tensors when r takes values between 0.05 and 2.00. (B) The area of plot (A) is magnified for TensorApEn values from-0.5 to 1.5.
Consistency of tensor approximate entropy on sleep tensor and discriminability analysis:
the six sleep states analyzed and the corresponding number of sleep slices can be seen in table 5.1. Based on the given tensor construction method't/dt/s', we converted the sleep slices in table 5.1 into 59481 sleep tensors with dimensions of 30 × 100 × 3. We fix the embedding dimension m to 2, and increase the value of the step length r from 0.1 to 2.0 by taking 0.1, and calculate the tensor approximate entropy of each sleep tensor, and the variation trend of the calculation result along with the value of r is shown in fig. 5. A histogram of shading errors of tensor approximate entropy in each sleep state is given in fig. 5(a), while a mean variation curve of tensor approximate entropy for six sleep states is given in fig. 5 (B). It can be clearly seen that the tensor approximate entropy changes smoothly with different values of r, and each shadow error histogram shows spindle-shaped changes, when the value of r approaches to both ends, the standard deviation ratio of the tensor approximate entropy is smaller, and when the value of r is the median size, the standard deviation ratio of the tensor approximate entropy is larger. In fig. 5(B), the variation curves of tensor approximate entropy can be roughly classified into three major categories, wherein the variation trends of S2, S3 and S4 are similar, the variation trend of S1 is similar to that of REM, and the variation trend of Wake phase is a single category, which is further verified in statistical test. With respect to consistency of tensor approximate entropy over sleep tensor and discriminative power, tensor approximate entropy behaves as: when the value of r is less than 0.5,
TensorApEnWake＞TensorApEnS1/REM＞TensorApEnS2/S3/S4when the value of r is less than 1.1, TensorApEnS2/S3/S4＞TensorApEnWake＞TensorApEnS1/REM。
FIG. 5: (A) the shadow error histogram of tensor approximate entropy under six sleep states is respectively as follows from the upper left corner to the lower right corner: wake, S1, S2, S3, S4, and REM. (B) b 2: tensor approximation entropy mean value change graphs in six sleep states, and b1 and b3 are enlarged images of areas of the b2 under different r values.
And (4) analyzing a statistical test result:
prior to the ANOVA test, a priori conditions need to be verified, and the results show that the variance of tensor approximation entropy does not satisfy homogeneity, so we give the parametric ANOVA test and the non-parametric ANOVA test separately, including the independent samples Kruskal-Wallis test and the Welch and Brown-Forsythe test, with the results shown in table 5.2. The original assumption of the ANOVA test is that tensor approximate entropies in six sleep states all come from the same distribution, but p values of the parametric test and the nonparametric test are less than 0.05(p is 0), so that the original assumption is rejected through the ANOVA test, namely the tensor approximate entropies have significant correlation with the sleep states.
Meanwhile, in order to further explore the significant correlation between tensor approximate entropy and sleep states, i respectively give ANOVA tests between any two sleep state pairs, and the results are shown in fig. 6. Since we compare the correlation between each sleep state and the other five sleep states separately, while r contains 20 different values from 0.1 to 2.0, 100 (20 × 5) pixels are contained in each sub-graph in fig. 6, where each pixel value represents the magnitude of the p value of the ANOVA test, and the corresponding pixel is labeled as 'x' when the p value is greater than 0.05. It should be noted that for the same sleeping state pair, the corresponding p values at the same r value are the same, such as S1 and REM and S1. 66 of the 600(100 × 6) pixels in fig. 6(a) are labeled '×', meaning that more than 89% of the ANOVA tests can assume a significant correlation between tensor approximate entropy and corresponding sleep state pairs. The results in another 11% of the ANOVA tests showed no significant correlation, including between S1 and REM when r takes a particular value, and there was a gradual progression in the magnitude of the p value as the r value was incremented. This indicates that there is no significant correlation between individual sleep states when r takes a particular value, but the global ANOVA test indicates that tensor approximation entropy does have a significant correlation with sleep states. In fact, this conclusion also explains the mean change curve in fig. 5(b 2).
Meanwhile, the independent sample t test results are shown in the same manner in fig. 6(B), with the difference that the evaluation index is stricter if and only if the p-value is less than 0.0033
Figure BDA0002461304240000152
When there is a significant difference between the corresponding sleep state pairs, the corresponding pixel is marked' when the p value is greater than 0.0033 indicating that there is no significant difference. As can be clearly seen by comparing fig. 6(B) and 6(a), fewer pixels are labeled 'and the color of the pixels is lighter, and only 32 of 600 pixels are labeled' indicating that even though the evaluation index is more stringent in the independent sample t-test, there are still 94.67% of the independent sample t-test results indicating that the tensor approximate entropy has significant differences between different sleep states. Similar to the ANOVA test, the results for p-values greater than 0.0033 in the t-test also focused between S1 and REM, indicating that there was no significant difference between S1 and REM when r was taken to a particular value.
TABLE 1.6 non-parametric ANOVA and parametric ANOVA tests in sleep states
Figure BDA0002461304240000151
FIG. 6: (A) ANOVA test between any pair of sleep states. (B) Independent samples t-test between arbitrary sleep state pairs. The pixel size in each sub-graph characterizes the examined p-value, with the corresponding pixel labeled 'in graph (a) when the p-value is greater than 0.05 and' in graph (B) when the p-value is greater than 0.0033.
In this section, to be able to evaluate the internal complexity of the tensor, the present disclosure proposes a new entropy measure method: the tensor approximates entropy. This section evaluates the consistency and discriminative power of tensor approximate entropy on the normal tensor and sleep tensor, respectively, while tensor approximate entropy is proven to have significant correlation with sleep states and significant differences between different sleep states.
The existence of significant correlation with sleep states and significant differences between different sleep states is a prerequisite for sleep state classification, and is used to ensure that tensor approximate entropy can be used for sleep state classification.
Wherein when the value of r is greater than 0.7,X 2is less than the approximate entropy of the tensorX 1But is generally recognized asX 2Is more complex thanX 1. In order to explore the credibility of the result, the structure is further providedX 1～X 4Four time series y of1～y4Approximate entropy. The similarity comparison threshold r is also increased from 0.05 to 2.0 in steps of 0.05, and the result is shown in fig. 7. It should be noted that the trend of the four curves in fig. 7 is about the same as that of the curve in fig. 5(a), and when the r value is greater than 0.7, the time series y2Is always less than y1This is similar to the tensor of FIG. 5(A) when the r value is greater than 0.7X 2Is less than the tensorX 1And (5) the consistency is achieved. This further proves that the tensor approximation entropy result proposed by the present disclosure is trustworthy. Meanwhile, the reason why this phenomenon occurs is that although the time series y1Or tensorX 1Most of the elements are 0, but once sentThe change is a mutation from 0 to 1, but in time sequence y2Or tensorX 2Only slight variations exist between adjacent elements. In addition, the phenomenon that the time series approximate entropy changes suddenly along with the change of the r value can be found, but the problem is well relieved in tensor approximate entropy.
In addition to this, the computational complexity of tensor approximation entropy is also a concern. As can be seen from the definition formula (5-2) of the tensor approximate entropy, it is necessary to generate the approximate entropy in each calculation
Figure BDA0002461304240000161
The sub-tensors are compared with each other. Thus, the computational complexity of tensor approximate entropy grows exponentially with the size of the tensor dimension. To explore the relationship between the computation complexity of tensor approximate entropy and the dimension of tensor dimension, we constructed a plurality of tensors with different dimension sizes in the same mode, wherein each tensor has its own dimension size
Figure BDA0002461304240000171
The tensors generated by the method are all cubic in space structure, but the generated tensors are not required to be arranged at 125000(50 × ×), the tensor approximate entropies of all tensors are calculated on a CPU and a GPU respectively, and program running time is recorded, and the result is shown in FIG. 8.
Clinical data is usually analyzed in the form of one-dimensional time series or two-dimensional images, but since physiological data is usually generated in the form of three-dimensional data, original information of signals can be better reserved by organizing the data in the form of tensor, and particularly, the position relation between leads is often lost in the one-dimensional time series or the two-dimensional images. Entropy measures have proven to be an important measure of complexity for time series as well as images, and have also been widely applied to clinical physiological data. However, a complexity measurement method for tensor still lacks in the numerous entropy measurement methods, and in such a background, the disclosed technical solution proposes an entropy measurement method for evaluating the complexity inside the tensor and is named as tensor approximate entropy.
Tensor approximation entropy the complexity of the tensor is evaluated by computing the conditional probability of neighborhood similarity inside the tensor. Specifically, the tensor approximate entropy is determined by the similarity among the sub-tensors inside the tensor, and if a large number of similar or even identical sub-tensors exist inside the tensor, the corresponding tensor approximate entropy is smaller, which means that the internal complexity of the tensor is smaller. In the definition of tensor approximate entropy, two parameters need to be determined, namely an embedding dimension m and a similarity comparison threshold r, wherein the embedding dimension m determines the dimension of the sub-tensors, and the similarity comparison threshold r controls the similarity standard among the sub-tensors. In the present disclosure, m is 2 to maximally explore the internal structure of the tensor, and the influence on the approximate entropy of the tensor when different similarity comparison threshold values r are selected is mainly discussed.
In order to test consistency and identification capability of tensor approximate entropy, tensor approximate entropies of 4 types of common tensors and 6 types of sleep tensors are calculated respectively, wherein the common tensors are constructed by 4 common time sequences, and the sleep tensors are constructed by polysomnography data in a sleep state. The test result shows that the tensor approximate entropy shows good consistency and identification capability on the common tensor and the sleep tensor, the parametric ANOVA test and the non-parametric ANOVA test both show that the tensor approximate entropy has obvious correlation with 6 sleep states, and the independent sample t test shows that the tensor approximate entropy has obvious difference between the 6 sleep states.
The disclosed result shows that the tensor approximate entropy is an effective and reliable method for evaluating the internal complexity of the tensor, and meanwhile, the application range of entropy measurement is expanded by the work.
In particular, the application of tensor approximation entropy in sleep stages is detailed below:
tensor approximation entropy has been demonstrated to have significant differences between different sleep states, thus further demonstrating the application of tensor approximation entropy in sleep staging work. Since the tensor approximate entropy shows significant differences between any two sleep state alignments when r takes 0.6 or 0.9, this subsection verifies at the same time that r takes 0.6 and 0.9, respectively. The classifier selects a pair of multi-support vector machines OVR SVMs (One-Versus-Rest SVMs). In the independent sample training and testing mode, tables 1 and 2 give the sleep state classification results when r is 0.6 and 0.9, respectively.
Table 1 independent sample training and test classification results when r is 0.6
Figure BDA0002461304240000181
Table 2 independent sample training and test classification results when r is 0.9
Figure BDA0002461304240000191
Comparing tables 1 and 2, it can be seen that when r is 0.6 and 0.9, respectively, the classification accuracy of tensor approximation entropy is relatively close in sleep stage. Meanwhile, compared with the results of other existing sleep staging methods in the table 3, the sleep staging method based on tensor approximate entropy can be found to be remarkably improved in the classification accuracy ACC and Cohen's kappa indexes, and the classification accuracy rates which can be achieved in the classification of 2-6 are respectively 96.84%, 91.87%, 85.43%, 83.76% and 80.73%.
Table 3 five classification performance comparison with other existing methods
Figure BDA0002461304240000192
Figure BDA0002461304240000201
Example II
Disclosed is a sleep physiological signal feature extraction system based on tensor complexity, comprising:
the signal acquisition module is used for acquiring the sleep physiological signal;
the signal processing module is used for converting the multi-lead time sequence of the sleep physiological signal into tensor expression;
the signal characteristic extraction module is used for expressing the sleep physiological signal as an N-order tensor, and the N-order tensor is composed of N-order sub-tensors; and determining the magnitude of the approximate entropy of the N-order tensor by judging the difference between the elements in each sub-tensor and each element in the global sub-tensor, and taking the approximate entropy of the tensor as the characteristic of the sleep physiological signal extraction.
The sleep stage module is used for inputting the extracted sleep physiological signal tensor approximate entropy characteristics to a pre-trained classifier for classification and determining the sleep stage corresponding to the sleep physiological signal.
In the signal feature extraction module, for an N-order tensor, a similarity comparison threshold parameter is given, an embedding dimension is determined to be used for dividing the dimension of the molecular tensor, and according to the embedding dimension, m continuous points are sequentially taken in each of N directions of the tensor to form an N-order sub-tensor;
calculating the distance between any two N-order sub-tensors under the condition that the embedding dimension is m, and determining the distance by the maximum difference value of corresponding position elements between the two sub-tensors;
calculating the number of N-order sub tensors meeting set conditions and calculating the ratio of the number of the N-order sub tensors to the number of all the sub tensors;
defining an average similarity rate when the embedding dimension is m;
and calculating an average similarity ratio when the embedding dimension is m +1, and calculating tensor approximate entropy of an N-order tensor based on the average similarity ratio to be used as the feature extracted from the sleep physiological signal.
It will be appreciated by those skilled in the art that the modules or steps of the invention described above may be implemented using general purpose computing apparatus, or alternatively, they may be implemented using program code executable by computing apparatus, whereby the modules or steps may be stored in a memory device and executed by computing apparatus, or separately fabricated into individual integrated circuit modules, or multiple modules or steps thereof may be fabricated into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts based on the technical solutions of the present invention. Forms are still within the scope of the present invention.

Claims (10)

1. The sleep physiological signal feature extraction method based on tensor complexity is characterized by comprising the following steps of:
acquiring a sleep physiological signal and converting a multi-lead time sequence of the sleep physiological signal into tensor expression;
the sleep physiological signal is expressed as an N-order tensor which consists of N-order sub-tensors;
and determining the magnitude of the approximate entropy of the N-order tensor by judging the difference magnitude between each element in each sub-tensor and each element in the global sub-tensor, and taking the approximate entropy of the tensor as the characteristic of the sleep physiological signal extraction.
2. The method as claimed in claim 1, wherein after the tensor approximate entropy feature of the sleep physiological signal is obtained, firstly, variance test and independent sample t test of tensor approximate entropy of the sleep tensor under different sleep states are performed to determine whether the tensor approximate entropy and the sleep state have significant correlation and significant difference, if yes, the extracted feature is input to a pair of multi-support vector machine classifiers to classify the sleep state, and the sleep stage corresponding to the sleep physiological signal is determined.
3. The method for extracting sleep physiological signal features based on tensor complexity as claimed in claim 1, wherein for an N-th order tensor, a similarity comparison threshold parameter is given, an embedding dimension is determined for dividing a molecular tensor dimension, and according to the embedding dimension, m continuous points are sequentially taken in each of N directions of the tensor to form an N-th order sub-tensor;
calculating the distance between any two N-order sub-tensors under the condition that the embedding dimension is m, and determining the distance by the maximum difference value of corresponding position elements between the two sub-tensors;
calculating the number of N-order sub tensors meeting set conditions and calculating the ratio of the number of the N-order sub tensors to the number of all the sub tensors;
defining an average similarity rate when the embedding dimension is m;
and calculating an average similarity ratio when the embedding dimension is m +1, and calculating tensor approximate entropy of an N-order tensor based on the average similarity ratio to be used as the feature extracted from the sleep physiological signal.
4. The method for extracting sleep physiological signal features based on tensor complexity as claimed in claim 1, wherein when the sleep physiological signal is collected, three-lead physiological data with the sampling frequency of 100Hz are selected, and the three-lead physiological data comprise Fpz-Cz electroencephalogram signals, Pz-Oz electroencephalogram signals and horizontal electrooculogram signals;
each group of sleep data is subjected to sleep state calibration according to the R & K standard;
each set of sleep data includes an arousal state W, a non-rapid eye movement period, and a rapid eye movement period REM.
5. The method as claimed in claim 1, wherein the acquired sleep physiological signal is filtered to remove baseline drift and linear trend.
6. The method for extracting sleep physiological signal features based on tensor complexity as claimed in claim 1, wherein the tensor approximate entropy is calculated as follows:
TensorApEn(X)＝Ψm+1(r)-Ψm(r)
therein, Ψm(r)、Ψm+1(r) is the average similarity ratio when the embedding dimensions are m, m +1, the N-order tensorX。
7. The method as claimed in claim 1, wherein the sleep physiological signal feature extraction method based on tensor complexity is characterized in that EEG and EOG signals in the sleep physiological signal are constructed into sleep tensor representation by using't/dt/s'.
8. Sleep physiological signal feature extraction system based on tensor complexity, characterized by includes:
the signal acquisition module is used for acquiring the sleep physiological signal;
the signal processing module is used for converting the multi-lead time sequence of the sleep physiological signal into tensor expression;
the signal characteristic extraction module is used for expressing the sleep physiological signal as an N-order tensor, and the N-order tensor is composed of N-order sub-tensors; and determining the magnitude of the approximate entropy of the N-order tensor by judging the difference magnitude between each element in each sub-tensor and each element in the global sub-tensor, and taking the approximate entropy of the tensor as the characteristic of the sleep physiological signal extraction.
9. The system as claimed in claim 8, further comprising a sleep stage module for inputting the extracted sleep physiological signal tensor approximate entropy features into a pre-trained classifier for classification, and determining the sleep stage corresponding to the sleep physiological signal.
10. The system for extracting sleep physiological signal features based on tensor complexity as claimed in claim 8, wherein in the signal feature extraction module, for an N-th order tensor, a similarity comparison threshold parameter is given, an embedding dimension is determined for dividing the dimension of the molecular tensor, and according to the embedding dimension, m continuous points are sequentially taken in each of N directions of the tensor to form an N-th order sub-tensor;
calculating the distance between any two N-order sub-tensors under the condition that the embedding dimension is m, and determining the distance by the maximum difference value of corresponding position elements between the two sub-tensors;
calculating the number of N-order sub tensors meeting set conditions and calculating the ratio of the number of the N-order sub tensors to the number of all the sub tensors;
defining an average similarity rate when the embedding dimension is m;
and calculating an average similarity ratio when the embedding dimension is m +1, and calculating tensor approximate entropy of an N-order tensor based on the average similarity ratio to be used as the feature extracted from the sleep physiological signal.
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