Electrocardiogram classification method based on graph regularization structure constraint low-rank sparse representation

Abstract

The invention discloses a structure constraint low-rank sparse representation arrhythmia classification method based on tag embedded graph regularization, and belongs to the field of electrocardiosignal processing. The method comprises the following steps: constructing a training data set and a label matrix; a graph Laplacian matrix is constructed based on the label matrix, local structure information and label information of the electrocardiosignals are fully utilized to construct a low-rank sparse representation model fusing a local constraint item and a graph regularization item, and a discriminative dictionary is obtained through dictionary learning; and finally, performing low-rank sparse representation on a test sample by using the learned dictionary, and completing classification according to a minimum reconstruction error principle. According to the method, by introducing a tag embedded graph regularization item, the model keeps a local manifold structure of data and enhances intra-class compactness and inter-class separability in a sparse representation learning process, so that the classification accuracy of electrocardiosignals, particularly arrhythmia classes, is remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of signal processing, specifically relating to a cardiac arrhythmia classification algorithm based on structurally constrained low-rank sparse representation with label embedding graph regularization, applicable to the classification of electrocardiogram signals. Background Technology

[0002] The locality and label information of training samples play an important role in representation learning classification. Wang et al. (Locality and structure regularized low rank representation for hyperspectral image classification. IEEE Transactions on Geoscience and Remote Sensing, 2019. 57(2): p. 911-923) proposed a locality and structure regularized low rank representation model to utilize the low-dimensional manifold structure of hyperspectral images and apply non-negative constraints to learn discriminative representation coefficients. Li et al. (Li, R., et al., Robust ECG biometrics using GNMF and sparse representation. Pattern Recogn Lett, 2020. 129: p. 70-76) proposed a novel robust ECG biometrics recognition method based on graph regularized non-negative matrix factorization (GNMF) and sparse representation. In GNMF, an affinity graph is constructed to encode geometric and label information in order to obtain more discriminative features. Wang et al. (Wang, X., Y.Han and Y. Deng, CSGSA-Net: Canonical-structured graph sparse attention network for fetal ECG estimation. Biomedical Signal Processing and Control, 2023. 82: p. 104556) proposed a typical structured graph sparse attention network for fetal ECG estimation. The spatial graph sparse attention module aims to estimate the fetal ECG signal masked by the maternal ECG signal by learning the waveform features of the fetal ECG, while the channel graph sparse attention module aims to distinguish the feature waveform from noise by capturing the details of the fetal ECG signal.Yin et al. (Yin, HF, XJ Wu and J. Kittler, Facerecognition via locality constrained low rank representation and dictionary learning. arxiv preprint arxiv, 2019: p. 1912.03145) introduced local constraint terms in the low-rank decomposition process to preserve local geometric structure and proposed a Locally Constrained Low-Rank Representation and Dictionary Learning (LCLRRDL) algorithm for image classification.

[0003] However, existing low-rank sparse representation dictionary learning algorithms do not simultaneously consider the local structural information and label information of training samples during the learning process, or they do not consider the distributional differences of similar sample data. Therefore, their classification performance needs to be improved. Since classifier performance metrics are crucial in the automatic diagnosis of arrhythmias, researching methods to improve classification accuracy is particularly important. Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in the prior art by proposing a cardiac arrhythmia classification algorithm based on structure-constrained low-rank sparse representation (SCLSR-LEGR) with label embedding graph regularization. Building upon the low-rank sparse representation model, this algorithm fully utilizes the local structural information of electrocardiogram (ECG) signals to construct local constraint terms. Simultaneously, it innovatively constructs a graph Laplacian matrix using label information, ensuring that the learned sparse representation minimizes intra-class compactness and maximizes inter-class separability. A dictionary is learned through a dictionary learning algorithm, and finally, the sparsity coefficients of the test samples are calculated using the low-rank sparse representation model. Classification is then performed based on minimizing the reconstruction error.

[0005] This invention is achieved through the following technical solutions.

[0006] The present invention discloses a cardiac arrhythmia classification algorithm based on structure-constrained low-rank sparse representation (SCLSR-LEGR) with label embedding graph regularization, comprising the following steps:

[0007] (1) Construct an h*n dimensional training dataset The label information matrix of the training dataset Test dataset ;

[0008] (2) Based on tag information matrix Construct the graph Laplacian matrix L;

[0009] Given a set of samples x i and xj Let x represent the i-th and j-th columns of matrix X. i and x j The similarity is denoted as A. ij If x i and x j If they are samples of the same type, set A. ij The similarity matrix A is 1.

[0010]

[0011] The Laplacian matrix B of the tag embedding graph is defined as:

[0012]

[0013] B=GA. A is a similar matrix, and G is a diagonal matrix. .

[0014] (3) Construct a structurally constrained low-rank sparse representation model based on the label embedding graph Laplacian matrix, and obtain the learning dictionary D through training.

[0015]

[0016] Represents local constraint terms. Represents the Hadama product Represents the nuclear norm. express Norm, This represents the trace of the matrix. α, γ, and λ are regularization parameters, and β is a weighting parameter.

[0017] By introducing three auxiliary variables J, L, and C, the above formula can be restated as follows:

[0018]

[0019] The augmented Lagrangian function of the above formula is:

[0020]

[0021] Y1, Y2, Y3, and Y4 are augmented Lagrange multipliers, and μ is the penalty parameter. Let J denote the inner product of matrices. k Z k L k C k E k and D K It is the optimization variable, and the number of iterations k (k=0,1,2,…).

[0022] Update J, fix Z, L, C, E, and D:

[0023]

[0024] ,

[0025]

[0026] Update Z, fix J, L, C, E, and D:

[0027]

[0028] Update L, fix J, Z, C, E, and D:

[0029]

[0030] Update C, fix J, Z, L, E, and D:

[0031]

[0032] Update E, fix J, Z, L, C, and D:

[0033]

[0034] remember p i Let the i-th column of matrix P be represented as follows:

[0035]

[0036] Update D, fix J, Z, L, C, and E:

[0037]

[0038] D is obtained through iterative updates.

[0039] (4) Based on the trained learning dictionary D, the sparsity coefficients of the test samples are calculated through the low-rank sparse representation model (LRSR). The test samples are classified according to minimizing the reconstruction error. A structural constraint low-rank sparse representation classification algorithm (SCLSR-LEGRC) based on label embedding graph regularization is proposed.

[0040] For test samples Using a low-rank sparse representation model, the sparse coefficients z of the test sample y are calculated by learning the dictionary D. The low-rank sparse representation model is defined as follows:

[0041]

[0042] Assume there are k classes of test samples, denoted as {D} k}, k=1,2,…,K,D kLet be a specific training sample matrix of class k. , Based on a specific training sample matrix D of class k k It can be represented as follows

[0043]

[0044] z k express The partial sparse coefficients associated only with the k-th class. Finally, The label can be determined by minimizing the reconstruction error.

[0045]

[0046] This invention creatively proposes a cardiac arrhythmia classification algorithm based on structure-constrained low-rank sparse representation (SCLSR-LEGR) with label embedding graph regularization. Building upon the low-rank sparse representation model, it fully utilizes the local structural information of electrocardiogram (ECG) signals to construct local constraint terms. Simultaneously, it innovatively constructs a graph Laplacian matrix using label information, ensuring that the learned sparse representation minimizes intra-class compactness and maximizes inter-class separability. A dictionary D is obtained through a dictionary learning algorithm, and finally, the sparsity coefficients of the test samples are calculated using the low-rank sparse representation model. Classification is then performed based on minimizing the reconstruction error. Attached Figure Description

[0047] Figure 1 This is an ECG classification scheme based on structural constraints of low-rank sparse representation using label embedding graph regularization.

[0048] Figure 2 The effect of parameters α and λ on classification accuracy.

[0049] Figure 3 The effect of parameters γ and β on classification accuracy. Detailed Implementation

[0050] The present invention will be further described below with reference to embodiments.

[0051] In this embodiment, the data was sourced from the MIT-BIH arrhythmia database. 10,400 heartbeats were used as the training sample set, and 54,590 heartbeats as the test sample set. Heartbeat signals were categorized into five classes according to the Association for the Advancement of Medical Devices (AAMI) standard ANSI / AAMIEC57:1998 / (R)2008: normal heartbeats (N), atrial premature beats and supraventricular ectopic beats (S), ventricular premature beats and ventricular ectopic beats (V), fusion of ventricular and normal heartbeats (F), and unclassifiable or unknown heartbeats (Q). The model was evaluated based on performance metrics such as sensitivity (SEN), positive predictive value (PPV), F1, and accuracy (Acc).

[0052] (1) Feature extraction: The ECG signals in the MIT-BIH database are segmented into equal lengths. That is, after the R-peak is detected, the 99 samples before the R-peak, the 180 samples after the R-peak, and the R-peak itself, totaling 280 samples, are considered as one heartbeat. Then, the level 4 detail subband coefficients and level 4 approximate subband coefficients are extracted as features through wavelet transform to construct the dataset.

[0053] (2) Construct an h*n dimensional training dataset The label information matrix of the training dataset Test dataset .

[0054] (3) Based on tag information matrix Constructing the graph Laplacian matrix ;

[0055] (4) Innovatively constructing a structurally constrained low-rank sparse representation model based on the label embedding graph Laplacian matrix, and obtaining a learning dictionary D through training.

[0056] (5) Based on the trained learning dictionary D, the sparsity coefficients of the test samples are calculated through the low-rank sparse representation model, and the samples are classified according to minimizing the reconstruction error.

[0057] (6) Classification performance indicators:

[0058] Sensitivity Sensitivity represents the percentage of samples where the actual result is positive, and the predicted result is also positive. Higher sensitivity indicates a lower rate of missed diagnoses; its mathematical definition is shown in the formula.

[0059]

[0060] Positive predictive value (PPV): The percentage of samples predicted as positive that also turn out to be positive. It reflects the probability that a sample belongs to that category. A higher accuracy indicates a lower rate of false positives. Its mathematical definition is shown in the formula.

[0061]

[0062] Value: Proposed based on accuracy and sensitivity, this value provides an overall evaluation of both. Higher accuracy and higher sensitivity are both better. Its mathematical definition is shown in the formula.

[0063]

[0064] Accuracy (Accuracy): This is the most intuitive metric for measuring model performance. A higher accuracy indicates better overall model performance. Its mathematical definition is shown in the formula.

[0065]

[0066] In this system, true positives (TP) represent the number of heartbeats correctly predicted by the classifier to be without arrhythmia (i.e., normal). False positives (FP) represent the number of arrhythmic heartbeats that were classified as normal. True negatives (TN) represent the number of correctly predicted arrhythmic heartbeats. False negatives (FN) quantify the total number of normal heartbeats that were misclassified as arrhythmias.

[0067] (7) Parameter settings:

[0068] The effects of parameters α and λ on classification accuracy are as follows: Figure 2 As shown, when α=10 -3 Furthermore, the classification accuracy reaches its maximum value when λ=1.

[0069] The effects of parameters γ and β on classification accuracy are as follows: Figure 3 As shown, when γ=10 -7 And β=10 -7 At that time, the classification accuracy reached its maximum value.

[0070] Table 1 shows the classification results of the Low-Rank Representation and Dictionary Learning Algorithm Based on Local Constraints (LCLRRDL). It can be seen that the classification accuracy of LCLRRDL is 98.69%, with 53,874 ECG signals correctly classified and 716 incorrectly classified. Specifically, 360 N-class ECG signals, 229 S-class ECG signals, 20 V-class ECG signals, 24 F-class ECG signals, and 83 Q-class ECG signals were incorrectly classified, resulting in an error rate of 1.31%.

[0071] Table 1 Classification results of LCLRRDL algorithm

[0072]

[0073] Table 2 shows the classification results of the Structure-Constrained Low-Rank Sparse Representation (SCLSR-LEGR) model based on the label embedding graph Laplacian matrix. It can be seen that the classification accuracy of SCLSR-LEGR is 99.73%, with 54,441 ECG signals correctly classified and 149 incorrectly classified. Specifically, 8 Class S ECG signals, 72 Class V ECG signals, 4 Class F ECG signals, and 65 Class Q ECG signals were incorrectly classified, resulting in an error rate of 0.27%. The classification accuracy of this method is significantly better than that of the LCLRRDL algorithm.

[0074] Table 2 Classification results of SCLSR-LEGR algorithm

[0075] .

Claims

1. An electrocardiogram (ECG) classification method based on graph regularization-constrained low-rank sparse representation, characterized in that, Includes the following steps: (1) Construct an h*n dimensional training dataset The label information matrix of the training dataset Test dataset ; (2) Based on tag information matrix Construct the graph Laplacian matrix; Given a set of samples x i and x j Represents the i-th and j-th columns of matrix X; x i and x j The similarity is denoted as A. ij If x i and x j If they are samples of the same type, set A. ij The similarity matrix A is defined as: (The value is 1; the similarity matrix A is defined as:) The Laplacian matrix B of the tag embedding graph is defined as: B=GA; A is a similar matrix, and G is a diagonal matrix. ; (3) Construct a structurally constrained low-rank sparse representation model based on the label embedding graph Laplacian matrix, and obtain the learning dictionary D through training: Represents local constraint terms. Represents the Hadama product Represents the nuclear norm. express Norm, The trace of the matrix is ​​represented by α, γ, and λ, which are regularization parameters, and β is a tradeoff parameter. By introducing three auxiliary variables J, L, and C, the above formula is restated as follows: The augmented Lagrangian function of the above formula is: Y1, Y2, Y3, Y4 are augmented Lagrange multipliers, and μ is the penalty parameter; Let J denote the inner product of matrices; denoted as J k Z k L k C k E k and D K The optimization variable is the number of iterations k (k=0,1,2,…); Update J, fix Z, L, C, E, and D: Update Z, fix J, L, C, E, and D: Update L, fix J, Z, C, E, and D: Update C, fix J, Z, L, E, and D: Update E, fix J, Z, L, C, and D: Update D, fix J, Z, L, C, and E: D is obtained through iterative updates; (4) Based on the trained learning dictionary D, the sparsity coefficients of the test samples are calculated through the low-rank sparse representation model LRSR. The test samples are classified according to minimizing the reconstruction error. A structural constraint low-rank sparse representation classification algorithm SCLSR-LEGRC based on label embedding graph regularization is proposed. For test samples Using a low-rank sparse representation model, the sparse coefficients z of the test sample y are calculated by learning the dictionary D; the low-rank sparse representation model is defined as follows: Assume there are k classes of test samples, denoted as {D} k }, k=1,2,…,K,D k Let be a specific training sample matrix of class k; denoted as , Based on a specific training sample matrix D of class k k It is expressed as follows: z k express Only the partial sparse coefficients associated with the k-th class; finally, The labels are determined by minimizing the reconstruction error: 。

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