Electrocardiogram classification method of chaotic neural network with complex weight

Abstract

The application relates to the technical field of signal processing, in particular to a chaotic neural network with complex-valued weights and application of the chaotic neural network in electrocardiogram classification. First, a complex Logistic chaotic mapping with complex-valued parameters is proposed, and bifurcation diagrams, Lyapunov exponents and chaotic attractors of the complex Logistic chaotic mapping are analyzed. Second, the ergodicity of CLCM and a new neuron function are used to optimize the weights of the CNN. Then, the method is verified by using the MIT-BIH database. Through band-pass filtering and double-threshold processing, the electrocardiogram signal is processed into a signal with a single waveform and a more prominent signal, which is used as the input of the designed CNN. The results show that the accuracy of the CNN with complex weights for electrocardiogram classification is improved. The complex weight chaotic neural network has the ability to prevent the network from falling into a local minimum, improves the recognition accuracy of the electrocardiogram, and has a high recognition accuracy.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and more specifically to an electrocardiogram (ECG) classification method using a chaotic neural network with complex weights and its application in ECG classification. Background Technology

[0002] Electrocardiography (ECG) plays a crucial role in the diagnosis of arrhythmias, myocardial ischemia, and premature ventricular contractions (PVCs). However, ECG abnormalities are diverse and highly variable. Images of the same disease can appear drastically different. Accurate diagnosis requires physicians to possess extensive knowledge and clinical experience. For a long time, physicians have been engaged in a large volume of ECG diagnostic work, making them prone to misdiagnosis due to fatigue. Therefore, automated ECG recognition has been a hot research topic in the field of artificial intelligence, greatly promoting the progress and development of healthcare.

[0003] Existing ECG signal pattern recognition methods are typically based on traditional neural networks. For example, using directed acyclic graph convolutional neural networks (DNNs) for heartbeat classification can automatically extract multi-scale features from different layers of the convolutional neural network; deep neural networks are used to detect and classify arrhythmias in dynamic ECGs. By accurately testing or prioritizing the most urgent situation, the false diagnosis rate in ECG analysis can be reduced. However, these methods are prone to getting trapped in local minima. To overcome the drawbacks of local minima, chaotic neural networks (CNNs) have emerged. CNNs can better simulate and reproduce the real brain structure and function, providing a solid foundation for exploring human brain processing mechanisms, especially issues of thought and consciousness. Therefore, research on chaotic neural networks will have wide practical applications in engineering and brain science. However, existing chaotic neural networks have poor recognition accuracy, making it difficult to achieve more precise recognition results. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a chaotic neural network with complex weights for electrocardiogram (ECG) classification and its application in ECG classification. The chaotic neural network with complex weights has the ability to prevent the network from getting trapped in local minima, and its application in ECG classification improves the accuracy of ECG classification.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] An electrocardiogram (ECG) classification method using a chaotic neural network with complex-valued weights employs a complex-valued logistic chaotic mapping (CLCM). CLCM extends the variables of the logistic mapping from the real domain to the complex domain, increasing the ergodicity of the chaotic system. The mathematical model of CLCM is defined as follows:

[0007]

[0008] Where w n =x n +jy n It is a state variable in the complex field. Represents an imaginary number, z n This represents the output sequence, where a and b are system parameters, a is a real number, and b = b1 + jb2 is a complex parameter.

[0009] W n Separating the real and imaginary parts yields a 3D-CLCM:

[0010]

[0011] When b2 = 1.5, the chaotic interval of the CLCM is -1.3 < b1 < 1.3, -0.1 < a < 8.9. Compared with the one-dimensional Logistic mapping, it has more variables and parameters and a wider range of chaos.

[0012] Furthermore, the ECG classification method using a chaotic neural network with complex weights introduces a steepness factor function into the sigmoid function, generating a new activation function model as a function of all neurons. The equation of the new neuron function is shown below:

[0013]

[0014] Where f is the frequency of the sine function, η and β are both positive parameters, η represents the initial phase, and ε(t) is the steepness factor function (ε(t)>0).

[0015] Select one of the following example functions:

[0016]

[0017] Simulations were conducted using a two-layer feedforward network structure with 20 hidden units, a maximum of 800 iterations, and an η = 1.8 loss function as shown below:

[0018] E=(yf(x)) 2 ,

[0019] Where y represents the predicted value and f(x) represents the actual output value.

[0020] As the loss function decays, the network gradually approaches a stable equilibrium point through a continuous chaotic bifurcation process from a bi-periodic bifurcation to a fixed point. The chaotic ergodic search mechanism of the chaotic neural network with complex weights has the ability to prevent the network from getting trapped in local minima.

[0021] Furthermore, this invention combines the ergodicity of CLCM with the conjugate gradient method to propose a learning algorithm for chaotic neural networks, including:

[0022] Step 1: Set a positive number M, set the range set I = [-M, M], and define W0 ∈ I. m As the initial weights of the CNN, W0 = X0 + Y o j is a complex variable; the next iteration result of W0 is calculated using the conjugate gradient method, denoted as . When k = 0, let

[0023] Step 2, set Among them W k (i) (i=1,...,m) is W k The i-th component, L(·), is a function of CLCM; the conjugate gradient method is used to calculate... And Let W be the name of the project. k+1 The next iteration;

[0024] Step 3, if the function If true, then set Otherwise, W * Remain unchanged;

[0025] Step 4, if W * If no change is observed after several iterations, the algorithm terminates; otherwise, k = k + 1, and the process returns to step 2.

[0026] Furthermore, the application of the ECG classification method with complex-valued weighted chaotic neural networks described in this invention in ECG classification specifically includes:

[0027] (1) Digital Filtering

[0028] First, the ECG signal is preprocessed through baseline removal, noise reduction, and signal segmentation steps; then, classical digital filtering methods are used for digital filtering.

[0029] (2) Adaptive threshold

[0030] To make the heartbeat waveform pattern more uniform, after bandpass filtering, the graph is then subjected to dual-slope processing. This involves finding the maximum and minimum average slopes within a certain range on the left and right sides of the point, respectively. Then, the maximum slope on the left is subtracted from the minimum slope on the right, and vice versa, and the maximum of the two is obtained. The range of slope values ​​to be found is set to 0.015s to 0.060s on both sides, which is set as an empirical parameter. The dual thresholds can change well with the signal, thus correctly detecting the position of the QRS wave.

[0031] (3) Heartbeat extraction and heartbeat classification

[0032] When locating heartbeats, missed heartbeats are ignored, while both incorrectly detected and correctly detected heartbeats are truncated. The learning algorithm of the chaotic neural network is robust, and a relatively small number of incorrectly detected heartbeats will not have a significant impact on the results. After adaptive thresholding, the heartbeat signal contains L1 points to the left and L2 points to the right. That is, the length of each truncated heartbeat is L1+L2 points. It is classified into 4 variables in the workspace: "Normal (N)", "Left Bundle Branch Block (LBBB)", "Right Bundle Branch Block (RBBB)" and "Ventricular Premature Beat (PVC)".

[0033] This invention first proposes a complex logistic chaotic map (CLCM) with complex-valued parameters, and analyzes its bifurcation graph, Lyapunov exponent, and chaotic attractor. Secondly, the ergodicity of CLCM and a novel neuron function are used to optimize the weights of a CNN. The method is then validated using the MIT-BIH database. By using bandpass filtering and double thresholding, the ECG signal is processed into a more homogeneous and prominent waveform, which is then used as input to the designed CNN. The CNN with complex weights shows a certain improvement in the accuracy of electrocardiogram (ECG) classification.

[0034] Technical effects of the present invention:

[0035] Compared with existing technologies, the ECG classification method of the present invention, which uses a chaotic neural network with complex weights and its application in ECG classification, has the following advantages:

[0036] (1) This invention proposes a complex-valued Logistic chaotic map, namely a complex Logistic chaotic map (CLCM) in complex fields, which has the ability to prevent the network from getting trapped in local minima. Its bifurcation graph, Lyapunov exponent and chaotic attractor are analyzed in detail. Then, CLCM is used to calculate the weights to improve the global optimization capability of the proposed complex-valued weighted chaotic neural network.

[0037] (2) This invention introduces a steepness factor function into the Sigmoid function, which makes the activation function exhibit non-monotonic behavior and more chaotic dynamic characteristics, thereby improving the global optimization capability of complex weighted CNN.

[0038] (3) Based on the MIT-BIH ECG classification database, this invention uses classification methods such as complex weighted chaotic neural networks to conduct simulation experiments. The results show that complex weighted chaotic neural networks improve the recognition accuracy of ECGs and have a high recognition accuracy rate. Attached Figure Description

[0039] Figure 1 This is a bifurcation diagram showing how the variable of the present invention changes with parameter b;

[0040] Figure 2 This is a Lyapunov index diagram for this invention;

[0041] Figure 3 This is a 3D-CLCM attractor diagram of the present invention;

[0042] Figure 4 This is a time evolution diagram of the weights and loss function of this invention;

[0043] Figure 5 This is a flowchart of the learning algorithm of the present invention;

[0044] Figure 6 This is a diagram of the CLCM weighted feedback structure of the present invention;

[0045] Figure 7 This is a flowchart of the electrocardiogram signal processing of the present invention;

[0046] Figure 8 The waveforms of signal 103 before and after filtering in this invention are shown.

[0047] Figure 9 This is the waveform diagram after the present invention has undergone dual-slope processing;

[0048] Figure 10 This is a waveform diagram after the sliding window integration process of this invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0050] Example 1:

[0051] This embodiment relates to an electrocardiogram (ECG) classification method using a chaotic neural network with complex-valued weights. It employs a complex-valued logistic chaotic mapping (CLCM). CLCM extends the variables of the logistic mapping from the real domain to the complex domain, increasing the ergodicity of the chaotic system. The mathematical model of CLCM is defined as follows:

[0052]

[0053] Where wn =x n +jy n It is a state variable in the complex field. Represents an imaginary number, z n This represents the output sequence, where a and b are system parameters, a is a real number, and b = b1 + jb2 is a complex parameter.

[0054] W n Separating the real and imaginary parts yields a 3D-CLCM:

[0055]

[0056] Bifurcation diagrams depict the process from bifurcation to chaos and are of great significance for analyzing chaotic characteristics; the bifurcation diagram of variables b1∈(-1.33,1.33) and a∈(-0.1,8.9) as a function of parameter b is shown below. Figure 1 As shown, the initial values ​​are (x1, y1, z1) = (0.2, 0.4, 0.1). The bifurcation diagram clearly reflects the entire chaotic process. When a large number of irregularly distributed points appear on the bifurcation diagram, it indicates that the system is chaotic.

[0057] Figure 2 The diagram shows the Lyapunov exponent of the system as a function of parameters b1 and a when b2 = 1.5. The attractor diagram for the 3D-CLCM is shown below. Figure 3 As shown, where a = 1, b1 = 0.5, b2 = 1.5, from Figure 3 It can be seen that the particles move in complex shapes within a finite region; when -1.3 < b1 < 1.3 and -0.1 < a < 8.9, the 3D-CLCM exhibits chaotic behavior.

[0058] Compared with the one-dimensional Logistic mapping, the CLCM of this invention has more variables and parameters, and its chaotic interval is -1.3 < b1 < 1.3, -0.1 < a < 8.9, which is a wider range of chaos.

[0059] This invention introduces a steepness factor function into the Sigmoid function, generating a new activation function model that serves as a function for all neurons. The equation for the new neuron function is shown below:

[0060]

[0061] Where f is the frequency of the sine function, η and β are both positive parameters, η represents the initial phase, and ε(t) is the steepness factor function (ε(t)>0).

[0062] Select one of the following example functions:

[0063]

[0064] Simulations were conducted using a two-layer feedforward network structure with 20 hidden units, a maximum of 800 iterations, and an η = 1.8 loss function as shown below:

[0065] E=(yf(x)) 2 ,

[0066] Where y represents the predicted value and f(x) represents the actual output value.

[0067] The time evolution graphs of weights and loss functions are as follows: Figure 4 As shown, Figure 4 (a) is the time evolution plot of a single weight. Figure 4 (b) represents the loss function for all neurons. It can be seen that as the loss function decays, the network gradually approaches a stable equilibrium point through a continuous chaotic bifurcation process from a bi-periodic bifurcation to a fixed point. Since neural networks cannot repeatedly traverse all possible states based on their evolutionary behavior, they suffer from the limitation of local minima. The ergodicity of chaotic search helps overcome the limitation of distributed ergodicity in general stochastic algorithms, preventing the network from getting trapped in local minima. Therefore, the chaotic ergodic search mechanism of chaotic neural networks with complex weights has the ability to prevent the network from getting trapped in local minima.

[0068] like Figure 5 and Figure 6 As shown, this invention combines the ergodicity of CLCM with the conjugate gradient method to propose a chaotic ergodic search method with complex-valued weights, including:

[0069] Step 1: Set a large positive number M, set the range set I = [-M, M], and define W0 ∈ I. m As the initial weights of the CNN, W0 = X0 + Y o j is a complex variable. The next iteration result of W0 is calculated using the conjugate gradient method, denoted as... When k = 0, let

[0070] Step 2, set Among them W k (i) (i=1,...,m) is W k The i-th component, L(·), is a function of CLCM. It is calculated using the conjugate gradient method. And Let W be the name of the project. k+1 The next iteration;

[0071] Step 3, if the function If true, then set Otherwise, W * Remain unchanged;

[0072] Step 4, if W* If no change is observed after several iterations, the algorithm terminates; otherwise, k = k + 1, and the process returns to step 2.

[0073] Example 2:

[0074] This embodiment relates to the application of an electrocardiogram (ECG) classification method using a chaotic neural network with complex weights in ECG classification.

[0075] The most commonly used database in the field of electrocardiography is the MIT-BIH arrhythmia database, which contains 48 records, lasting 30 minutes, with a total of 648,000 sampling points and 109,500 heartbeats, of which abnormal heartbeats account for about 30%.

[0076] The QRS complex is the most prominent and sharpest in every frequency band of every heartbeat, making it easier to detect than other bands. The peaks (or troughs) of the QRS complex are known as "singularities," exhibiting steep slopes and non-differentiable points. Based on this characteristic, various processing methods can be used for detection, such as filtering and wavelet transform. After preprocessing the data, heartbeat signals are extracted, and the chaotic neural network is trained and tested to achieve basic recognition and classification of heartbeat signals.

[0077] like Figure 7 As shown, the electrocardiogram signal undergoes four processing steps: digital filtering, adaptive thresholding, heartbeat extraction, and heartbeat classification.

[0078] (1) Digital Filtering

[0079] First, the ECG signal is preprocessed through three simple steps: baseline removal, noise reduction, and signal segmentation. ECG filtering algorithms generally require low computational cost and good real-time performance. At the same time, ECG filtering algorithms can filter out interference as much as possible, providing good data for accurate analysis.

[0080] Digital filtering methods can be broadly classified into three categories: classical digital filtering methods (such as wavelet transform and bandpass filtering), adaptive filtering methods (such as mathematical morphology), and modern high-tech filtering methods (such as neural networks). The simulation employed a classical digital filtering method.

[0081] The database uses signal number 103 as an example. The signal undergoes a 40th-order finite impulse response (FIR) bandpass filter, with a passband of 15–25 Hz, roughly equivalent to the frequency band of a QRS wave. The waveforms of signal number 103 before and after filtering are as follows: Figure 8 As shown in the figure, after filtering, the P-wave and T-wave are significantly weakened, a large amount of noise is eliminated, and the QRS wave characteristics are more obvious.

[0082] (2) Adaptive threshold

[0083] To make the heartbeat waveform pattern more uniform, after bandpass filtering, the graph is then subjected to "dual slope" processing. This involves finding the maximum and minimum average slopes within a certain range to the left and right of each point, respectively. Then, the maximum slope on the left is subtracted from the minimum slope on the right, and vice versa, and the maximum of the two is calculated. The range for finding these slopes is set to 0.015s to 0.060s on both sides, and these are considered empirical parameters. The resulting waveforms before and after processing are as follows: Figure 9 As shown in the figure. Therefore, it can be concluded that the dual threshold can change well with the signal, thus correctly detecting the position of the QRS wave.

[0084] Due to filtering or slope calculation factors, the waveform amplitude decreases with each step, but excessively small amplitude is detrimental to detection. Here, a sliding window integration is used. This method increases the absolute amplitude and further smooths the waveform. The width of the sliding window is set to 17 sampling points, an empirical parameter. After integration, the waveform amplitude increases significantly. Therefore, the waveform becomes more uniform, and the changes in the QRS wave are more prominent. The processed waveform is as follows: Figure 10 As shown.

[0085] (3) Heartbeat extraction and heartbeat classification

[0086] When locating heartbeats, false positives and false negatives are common. False negatives can be ignored, while both falsely and correctly detected heartbeats are cropped. The learning algorithm of the chaotic neural network is robust; a small number of false positives will not significantly affect the results. After adaptive thresholding, the heartbeat signal contains 100 points to the left and 150 points to the right, meaning each cropped heartbeat has a length of 250 points. Four variables can be found in the workspace: "Normal (N)", "Left Bundle Branch Block (LBBB)", "Right Bundle Branch Block (RBBB)", and "Ventricular Premature Beat (PVC)".

[0087] In this experiment, bandpass filtering and double thresholding were first used to process the data. Then, 20,000 heartbeat signals were randomly divided into training and test sets. The random selection of the training and test sets was achieved by randomly shuffling the sample indices using the randperm function. Then, 14,000 samples corresponding to the indexes were selected as the training set, and the remainder were used as the test set.

[0088] Table 1. Electrocardiogram Recognition Results

[0089]

[0090] The identification results of the ECG samples are shown in Table 1, and the sample distribution of the prediction results, represented by "Conf_Mat", is shown in Table 2. "Conf_Mat" is an abbreviation for "confusion matrix" and is used to represent the sample distribution of the classification results.

[0091] Table 2 Confusion Matrix

[0092]

[0093]

[0094] Open the matrix named "Conf_Mat" in the workspace, as shown in Table 2. Categories 1, 2, 3, and 4 represent N, PVC, RBBB, and LBBB, respectively. The diagonal line represents the number of correctly predicted categories, and the rest represent the number of incorrectly predicted categories.

[0095] For example, in row 2 and column 4 of (2,4), 9 premature beats were incorrectly identified as left bundle branch block, which is the highest number of errors. This is because premature beats and left bundle branch block can behave more similarly. The number in (4,3) is 0, meaning that no left bundle branch block was incorrectly identified as right bundle branch block. This indicates that the differences between them are greater, making them easier to identify. By analyzing the confusion matrix, the performance of the classifier and the sample distribution can be analyzed more carefully.

[0096] ECG classification criteria are overall accuracy (Se) and average positive detection rate (P). + The composite index F1 is calculated using the following formula:

[0097] Se = TP / (TP + FN) × 100%

[0098] P + =TP / (TP+FP)×100%

[0099]

[0100] In the formula, TP represents the number of items in the category that are correctly classified; FN represents the number of items in the category that are misclassified into other categories; and FP represents the number of heartbeats that do not belong to the category but are classified into the category by the classifier.

[0101] Based on the above metrics, the accuracy of heart rate classification achieved by this method is compared with that of other methods. As shown in Table 3, the overall accuracy of this method is 99.10%, which is the best among all methods. Meanwhile, the accuracy of conventional convolutional neural networks is 98.26%, backpropagation neural networks are 97.97%, support vector machines are 96.69%, and chaotic neural networks with real-valued logistic chaotic mappings are 98.85%.

[0102] It is worth noting that chaotic neural networks, whether using real-valued or complex-valued logistic chaotic mappings, can overcome the problem of neural networks easily getting trapped in local minima, thus improving the ability to classify heart rate. However, the dynamics of complex chaotic systems are more complex than those of real chaotic systems. The real and imaginary parts of complex chaotic systems are independent, increasing the ergodicity of the chaotic mapping. Therefore, complex chaotic systems improve the recognition rate of ECG signals and have higher recognition accuracy.

[0103] Table 3 Comparison of the results of the proposed chaotic neural network and known literature.

[0104]

[0105] This invention proposes a complex-valued logistic chaos model and utilizes its ergodicity to select weights; then, the conjugate gradient method is employed to determine the search direction. Furthermore, a steepness factor function is introduced into the sigmoid activation function, making the activation function non-monotonic and effectively improving the global search capability of the CNN. This invention applies this method to heartbeat pattern recognition, achieving excellent results with a recognition rate as high as 99.10%. The recognition indices for the four ECG beats are all high and stable, with an average positive detection rate of 99.09% and a comprehensive index of 99.09%.

[0106] Compared with other heartbeat classification methods, this method significantly improves the overall recognition accuracy, average positive detection rate, and comprehensive index. The results show that the ECG classification method model with complex-weighted chaotic neural networks in this invention has good ergodicity and global optimization ability, making it suitable for heartbeat recognition.

Claims

1. An electrocardiogram (ECG) classification method using a chaotic neural network with complex weights, characterized in that, include: (1) Digital Filtering First, the ECG signal is preprocessed through baseline removal, noise reduction, and signal segmentation steps; Digital filtering employs classic digital filtering methods; (2) Adaptive threshold To make the heartbeat waveform pattern more uniform, after bandpass filtering, the graph is then subjected to dual-slope processing. This involves finding the maximum and minimum average slopes within a certain range on the left and right sides of the point, respectively. Then, the maximum slope on the left is subtracted from the minimum slope on the right, and vice versa, and the maximum of the two is obtained. The range of slope values ​​to be found is set to 0.015s to 0.060s on both sides, which is set as an empirical parameter. The dual thresholds can change well with the signal, thus correctly detecting the position of the QRS wave. (3) Heartbeat extraction and heartbeat classification When locating heartbeats, missed heartbeats are ignored, while both incorrectly detected and correctly detected heartbeats are truncated. After adaptive threshold processing, the heartbeat signal contains L1 points to the left and L2 points to the right. That is, the length of each truncated heartbeat is L1+L2 points. It is classified into 4 variables in the workspace: "normal", "left bundle branch block", "right bundle branch block" and "ventricular premature beat". The Complex-Valued Logistic Chaotic Mapping (CLCM) is employed. CLCM extends the variables of the Logistic Mapping from the real domain to the complex domain, increasing the ergodicity of the chaotic system. The mathematical model of CLCM is defined as follows: Where w n =x n +jy n It is a state variable in the complex field. Represents an imaginary number, z n This represents the output sequence, where a and b are system parameters, a is a real number, and b = b1 + jb2 is a complex parameter. w n Separating the real and imaginary parts yields a 3D-CLCM: When b2 = 1.5, the chaotic interval of the CLCM is -1.3 < b1 < 1.3, -0.1 < a < 8.9; By introducing a steepness factor function into the sigmoid function, a new activation function model is generated as a function of all neurons. The equation of the new neuron function is shown below: Where f is the frequency of the sine function, η and β are both positive parameters, η represents the initial phase, and ε(t) is the steepness factor function (ε(t)>0).

2. The electrocardiogram classification method using a chaotic neural network with complex weights according to claim 1, characterized in that, Select one of the following example functions: Simulations were conducted using a two-layer feedforward network structure with 20 hidden units, a maximum of 800 iterations, and an η = 1.8 loss function as shown below: E=(y-f(x)) 2 , Where y represents the predicted value and f(x) represents the actual output value; as the loss function decays, the network gradually approaches a stable equilibrium point through a continuous chaotic bifurcation process from a bi-period bifurcation to a fixed point. The chaotic ergodic search mechanism of the chaotic neural network with complex weights has the ability to prevent the network from getting trapped in local minima.

3. The electrocardiogram classification method using a chaotic neural network with complex weights according to claim 2, characterized in that, Combining the ergodicity of CLCM with the conjugate gradient method, a chaotic ergodic search method with complex-valued weights is proposed, including: Step 1: Set a positive number M, set the range set I = [-M, M], and define W0 ∈ I. m As the initial weights of the CNN, W0 = X0 + Y o j is a complex variable; the next iteration result of W0 is calculated using the conjugate gradient method, denoted as . When k = 0, let Step 2, set Among them W k (i) (i=1,...,m) is W k The i-th component, L(·), is a function of CLCM; the conjugate gradient method is used to calculate... And Let W be the name of the project. k+1 The next iteration; Step 3, if the function If true, then set Otherwise, W * Remain unchanged; Step 4, if W * If no change is observed after several iterations, the algorithm terminates; otherwise, k = k + 1, and the process returns to step 2.

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