High-dynamic TWA multi-channel detection method based on tensor decomposition and machine learning

Abstract

The invention belongs to the field of electrocardiosignal detection, and relates to a tensor decomposition and machine learning-based high-dynamic TWA multi-channel detection method, which comprises the following steps of: acquiring a plurality of multi-channel ECG signals and preprocessing to obtain a plurality of TWA alternating signals; constructing a short-time dynamic data set according to the plurality of TWA alternating signals; performing tensor decomposition on each tensor in the short-time dynamic data set to obtain a decomposition factor data set; performing feature extraction on decomposition factors in the decomposition factor data set to obtain a feature factor data set; training a machine learning model by using the feature factor data set; acquiring an ECG signal, calculating a characteristic factor of the ECG signal, and inputting the characteristic factor of the ECG signal into the trained machine learning model to obtain a detection result; according to the method, the short-time dynamic data set with the label is constructed by considering the short-time dynamic characteristics of the TWA, a short-time high-dynamic training sample is provided for TWA research, and the problems of data scarcity or label inaccuracy and the like possibly existing due to dependence on a real data set are avoided.

Description

Technical Field

[0001] The present invention belongs to the field of electrocardiogram signal detection, and relates to a high-dynamic TWA multi-channel detection method based on tensor decomposition and machine learning. Background Art

[0002] Currently, multi-channel analysis methods for T wave alternans (TWA) utilize the correlation between channels to improve the detection effect, such as the method combining periodic component analysis and fractional Fourier transform with tensor decomposition. Recently, integrated data methods, dictionary learning methods, convolutional neural networks, etc. combined with machine learning have also been proposed, improving the detection accuracy.

[0003] However, the existing methods still face limitations. They do not consider the short-time dynamic characteristics of TWA, lack a unified detection standard and annotation database. Shallow neural network algorithms and some machine learning methods do not consider multi-channel correlation information and are difficult to be used clinically. Summary of the Invention

[0004] To solve the above problems of the existing technology, the present invention adopts a high-dynamic TWA multi-channel detection method based on tensor decomposition and machine learning, including:

[0005] S1. Obtain multiple multi-channel ECG signals and perform preprocessing to obtain multiple TWA alternating signals;

[0006] S2. Construct a short-time dynamic data set according to the multiple TWA alternating signals; the short-time dynamic data set includes two types of tensors: tensors with TWA and tensors without TWA;

[0007] S3. Perform tensor decomposition on each tensor in the short-time dynamic data set to obtain a decomposition factor data set;

[0008] S4. Extract features from the decomposition factors of each tensor in the decomposition factor data set to obtain a feature factor data set;

[0009] S5. Use the feature factor data set to train a machine learning model to obtain a trained machine learning model;

[0010] S6. Obtain a multi-channel ECG signal, calculate the feature factors of the ECG signal, and input the feature factors of the ECG signal into the trained machine learning model to obtain a detection result.

[0011] Advantageous Effects:

[0012] 1. The present invention considers the short-term dynamic characteristics of TWA. Through PCA mapping, the backup signal is mapped to the real TWA signal to obtain the transformed signal, and dynamic transformation, truncation, and noise addition are performed on the transformed signal to obtain a labeled short-term dynamic data set. The short-term dynamic data set provides short-term high-dynamic training samples for TWA research, avoiding problems such as data scarcity or inaccurate labels that may exist when relying on real data sets; 2. In a short-term high-dynamic environment, tensors have advantages in expressing the correlation of multi-dimensional data. Therefore, the present invention performs tensor decomposition on the tensor of the TWA signal, and extracts the characteristic factor matrix associated with the tensor in the heartbeat and sampling point dimensions according to the decomposed factors, thereby improving the effect of noise suppression and the effect of extracting short-term high-dynamic information, and can better exert the detection ability of machine learning for short-term high-dynamic weak signals, improving the TWA detection effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flowchart of a high-dynamic TWA multi-channel detection method based on tensor decomposition and machine learning provided by an embodiment of the present invention;

[0014] Figure 2 It is a flowchart of the construction of a short-term dynamic data set provided by an embodiment of the present invention;

[0015] Figure 3 It is an X-lead dynamic TWA tensor projection diagram provided by an embodiment of the present invention;

[0016] Figure 4 It is the first-beat dynamic TWA tensor projection diagram provided by an embodiment of the present invention;

[0017] Figure 5 It is the 150th sampling point dynamic TWA tensor projection diagram provided by an embodiment of the present invention;

[0018] Figure 6 It is the tensor factor diagram (a) of the TWA signal in the heartbeat projection direction, the tensor factor diagram (b) in the sampling point projection direction, and the tensor factor diagram (c) in the lead projection direction provided by an embodiment of the present invention;

[0019] Figure 7 It is the tensor factor diagram (a) of the non-TWA signal in the heartbeat projection direction, the tensor factor diagram (b) in the sampling point projection direction, and the tensor factor diagram (c) in the lead projection direction provided by an embodiment of the present invention;

[0020] Figure 8 It is the T-CNN / C-CNN model structure diagram provided by an embodiment of the present invention;

[0021] Figure 9 It is the MNN model structure diagram provided by an embodiment of the present invention;

[0022] Figure 10 This is a graph showing the accuracy results of different features and methods under em noise provided by the embodiments of the present invention;

[0023] Figure 11 This is a graph showing the accuracy results of different features and methods under ma noise provided by the embodiments of the present invention;

[0024] Figure 12 This is a graph showing the accuracy results of different features and methods under gs noise provided by the embodiments of the present invention;

[0025] Figure 13 This is a graph showing the accuracy results of different features and methods under all noises provided by the embodiments of the present invention;

[0026] Figure 14 This is a graph showing the comparison results of different methods under real data provided by the embodiments of the present invention. Detailed implementation manners

[0027] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0028] As Figure 1 shown, the embodiments of the present invention provide a high-dynamic TWA multi-channel detection method based on tensor decomposition and machine learning, including the following steps:

[0029] S1. Obtain E multi-channel ECG signals and perform preprocessing to obtain E TWA alternating signals;

[0030] The preprocessing of the multi-channel ECG signals includes: successively performing interference cancellation, heartbeat alignment, and background T-wave cancellation on the multi-channel ECG signals to obtain TWA alternating signals where e is the index of the TWA alternating signal, K represents the number of consecutive heartbeats of the ECG signal (i.e., the number of heartbeat cycles), N represents the number of sampling points in each heartbeat cycle, and L represents the number of leads of the ECG signal.

[0031] The interference cancellation includes: dividing the ECG signal into 1.3-second windows, finding the 25% median points in each window of the ECG signal, averaging the median points of each window of the ECG signal to determine the baseline level, removing the baseline drift of the ECG signal according to the baseline level, and then using a third-order Butterworth band-pass filter from 0.3 Hz to 40 Hz to remove the baseline drift and high-frequency noise of the ECG signal.

[0032] Heartbeat alignment includes: locating the QRS wave and T wave of the ECG signal after interference cancellation; selecting the leads for alignment based on the located QRS wave and T wave, and finding reliable reference points in the selected leads. Select a representative template heartbeat from multiple heartbeat cycles of the ECG signal, and adjust the reference points according to the template heartbeat; verify the heartbeat cycles in the ECG signals of each lead and remove abnormal heartbeat cycles.

[0033] Background T wave cancellation: Extract the TWA waveform of the ECG signal after heartbeat alignment through the spectral method of the TWAnalyser (T wave alternans analyser), eliminate the background T wave by beat-by-beat subtraction, suppress the low-frequency components, and obtain the initial TWA alternans signal. The initial TWA alternans signal Flattened into a TWA alternans signal

[0034] S2. According to E TWA alternans signals Construct a short-term dynamic dataset; the short-term dynamic dataset includes TWA tensors with and without TWA tensors.

[0035] As Figure 2 shown, constructing a short-term dynamic dataset according to the TWA alternans signal includes:

[0036] S21. Randomly select F TWA alternans signals from the TWA alternans signal According to the selected F TWA alternans signals Construct F kinds of alternative signals where f is the index of the selected TWA alternans signal.

[0037] Construct alternative signal B f including: performing TWA reshaping on the selected TWA alternans signal by each heartbeat to obtain the reshaped TWA signal Replace the abnormal waveforms in the TWA signal with the mean waveform to obtain the TWA signal after waveform replacement Perform mean normalization on the TWA signal after waveform replacement Perform normalization on the mean-normalized TWA signal Perform replication on the normalized TWA signal to obtain an alternative signal with an amplitude of 1 uv

[0038] Performing TWA reshaping on the TWA alternans signal includes: The TWA alternans signal of each lead is a vector of length KN, and the TWA alternans signal of each lead Reshape it into a K×N matrix for each heartbeat to obtain the reshaped TWA signal

[0039] For the TWA signal after waveform replacement Performing mean normalization includes: the signal of each lead Is a K×N matrix, for the signal of each lead Take the mean of each column to obtain the mean-normalized TWA signal

[0040] Copying the normalized TWA signal includes: the TWA signal of one heartbeat after normalization Copy it into K heartbeats, and make the even heartbeats the inverse of the odd heartbeats to obtain the backup signal

[0041] S22. According to F backup signals B f Perform transformation on E TWA alternating signals T e To obtain H TWA tensors Where, H = E×F;

[0042] According to F backup signals B f Perform transformation on E TWA alternating signals T e The transformation includes:

[0043] S221. Normalize each of the E TWA alternating signals respectively to obtain E true TWA signals

[0044] S222. Map F types of backup signals B f To each true TWA signal A e To obtain H = E×F types of transformed signals Where, h is the index of the transformed signal C h Of;

[0045] Map the backup signal B f To the true TWA signal A e Includes:

[0046] Estimate the spatial correlation of the true TWA signal A e Of

[0047] A is a zero-mean random process with spatial correlation, then its spatial correlation can be estimated as:

[0048]

[0049] To obtain the required principal components, construct and solve The eigenvector equation to obtain the eigenvector matrix

[0050]

[0051] where Λ represents the diagonal eigenvalue matrix, and Ψ e represents the eigenvector matrix. The matrix Ψ e defines an orthonormal transformation, which is applied to B f to obtain the transformed signal C h :

[0052] C h = B f Ψ e

[0053] where the transformed signal C h is the clean TWA background, and the l-th lead contains the l-th principal component of A e .

[0054] S223. Perform dynamic transformation on H transformed signals C h respectively to obtain H TWA tensors;

[0055] Tensorize the transformed signal C h into and multiply the signal of each lead by the dynamic matrix to obtain a TWA tensor with spatially correlated dynamic changes

[0056]

[0057] G h = diag(a, b, …)

[0058] where K represents the number of consecutive heartbeats involved in the detection (i.e., the number of heartbeat cycles), N represents the number of sampling points in each heartbeat cycle, and L represents the number of signal channels; the diagonal matrix a and b are numbers of different sizes, ranging from (0, 100], and by changing the size of G h the amplitude range can be set to dynamically change randomly from 0 to 100 uV.

[0059] The projection diagrams of the TWA tensor in three projection directions are shown in Figure 3 , Figure 4 , Figure 5 .

[0060] S23. For H TWA tensors Perform truncation and noise addition separately to obtain a short-term dynamic data set.

[0061] For the TWA tensor Performing truncation and noise addition includes: Considering the short-term non-stationary characteristics of the real signal, a 32-sliding window w is used to truncate the TWA tensor to obtain the truncated TWA tensor Noise is added to the truncated TWA tensor to obtain the TWA tensor with added noise Using the TWA tensor with added noise subtract the corresponding truncated TWA tensor to obtain the TWA tensor without TWA; The TWA tensor with added noise is used as the TWA tensor with TWA. Combine the TWA tensors with TWA and those without TWA to obtain a short-term dynamic data set.

[0062] Through the above steps, the short-term dynamic data set provides short-term high-dynamic training samples. Using the short-term dynamic data set for machine learning training can improve the detection accuracy.

[0063] In one embodiment, 4 kinds of standby signals B are constructed. The 4 kinds of standby signals B are mapped to 10 real TWA signals A through PCA mapping to obtain 40 different transformed signals. Perform dynamic transformation on the 40 different transformed signals to obtain 40 TWA tensors; Use a 32-sliding window to truncate the 40 TWA tensors respectively to obtain 40 TWA tensors with different lengths. Perform matrix transformation on the 40 TWA tensors with different lengths to obtain 40 TWA tensors with different amplitudes. Add noise to the 40 TWA tensors with different amplitudes to obtain the final 40 TWA tensors. The noise includes Gaussian (gs), electrode movement (em), and muscle activity (ma). Add noise with different ANRs in the range of -30 to 5 dB to the 40 different TWA tensors. Use the TWA tensor with added noise to subtract the TWA tensor before adding noise to obtain the TWA tensor without TWA, and finally construct a TWA tensor data set with an amplitude of 0 to 100 uv, a signal-to-noise ratio of -30 to 5, an interval of 4, a heart beat of 7 to 32, and 38,400 tensor numbers Among them, the tensors without TWA and with TWA each account for half.

[0064] S3. Perform tensor decomposition on each tensor in the short-term dynamic data set to obtain a decomposition factor data set;

[0065] After obtaining the tensors with TWA and without TWA, they need to be decomposed. The decomposition methods for tensors can be Tucker decomposition and CP decomposition.

[0066] Among them, performing Tucker decomposition on a third-order tensor includes:

[0067]

[0068] Among them, × p (p = 1, 2, 3) represents the p-mode product between the tensor and the matrix, indicating that each p-mode fiber of the tensor is multiplied by the matrix. is the core tensor of the i-th tensor. and represent the decomposition factor matrices of the i-th tensor in the heartbeat, sampling point, and lead projection directions. R1, R2, and R3 are the three dimensions of the core tensor, all equal to the number of leads L.

[0069] Among them, performing CP decomposition on a third-order tensor includes:

[0070]

[0071] Among them, λ i,r is a scalar weight, s i,r , b i,r , c i,r are the r-th vectors of the decomposition factor matrices of s i,r representing the i-th tensor in the heartbeat, sampling point, and lead projection directions respectively. R is the rank of the decomposition.

[0072] As Figure 6 , Figure 7 shown, the decomposition factors in the projection direction of the heartbeat dimension are composed of aligned adjacent TWA matrices, and its projection can best detect the presence of TWA; the decomposition factors in the projection direction of the sampling point dimension are composed of the waveforms of the TWA matrix. Therefore, the projection contains signal and noise waveform information. The decomposition factors in the projection direction of the lead dimension represent different channels of the TWA tensor.

[0073] S4. Feature extraction is performed on the decomposition factors of each tensor in the decomposition factor dataset to obtain a feature factor dataset.

[0074] Performing feature extraction on the decomposition factors of each tensor in the decomposition factor dataset includes:

[0075] S41. Multiply the core tensor of the i-th tensor as a weight factor by the corresponding decomposition factors U i , V i respectively to obtain a feature factor matrix

[0076] When the decomposition method is CP decomposition, scalar weights are multiplied by the corresponding decomposition factors.

[0077] S42. Perform cubic interpolation on each column of the eigenfactor matrix U i ′ to obtain an eigenfactor matrix U of size i ″;

[0078] S43. Concatenate the eigenfactor matrices U i ″ and V i ′ along the heartbeat dimension to obtain the eigenfactor matrix of the i-th tensor

[0079] By performing tensor decomposition on the tensor of the TWA signal as described above and extracting the eigenfactor matrices associated with the tensor along the heartbeat and sampling point dimensions, the effect of noise suppression and the effect of extracting short-term high-dynamic information are improved, thereby better exerting the detection ability of machine learning for short-term high-dynamic weak signals and enhancing the TWA detection effect.

[0080] S5. Use the eigenfactor dataset to train a machine learning model to obtain a trained machine learning model;

[0081] The machine learning model can be a CNN (Convolutional Neural Network), RF (Random Forest), or KNN (K-Nearest Neighbor Algorithm).

[0082] When the machine learning model is a CNN, divide the eigenfactor dataset into a training set, a test set, and a validation set, and the ratio between them is 7:1.5:1.5. Set the learning rate of the cosine annealing algorithm to be from 0.01 to 0.0001, the batch size to be 200, and the loss function to be the cross-entropy loss.

[0083] S6. Obtain multi-channel ECG signals, calculate the eigenfactors of the ECG signals, and input the eigenfactors of the ECG signals into the trained machine learning model to obtain a detection result; where the detection result is whether there is a TWA signal.

[0084] Calculating the eigenfactors of the ECG signals includes: performing the above-mentioned preprocessing, tensor decomposition, and feature extraction on the ECG signals to obtain the eigenfactors.

[0085] Due to the non-stationary and high-dynamic characteristics of TWA, it is very difficult to simulate through a model, which leads to certain deviations in the simulation. Therefore, in one embodiment, real data will be used for simulation to fine-tune the trained neural network. Specifically, the ECG signals using leads X, Y, and Z in the PTB database are used, and the ECG signals are preprocessed according to step S1. A sliding window of 32 is used to intercept signal tensors of different lengths, obtaining 339 diseased signals and 268 healthy signals, which are divided into a training set, a validation set, and a test set. The trained neural network is trained and validated according to the training set and the validation set to obtain a fine-tuned neural network, and then the test set is used for testing. The results are as Figure 14 shown.

[0086] According to different decomposition methods, the methods proposed in the present invention are defined as T-CNN, C-CNN, T-RF, C-RF, T-KNN, and C-KNN; where T represents Tucker decomposition and C represents CP decomposition; traditional signal processing methods such as Time Method (TM), Spectral Method (SM), Modified Moving Average Method (MMA), Laplacian Likelihood Ratio (LLR), and Complex Demodulation (CD) are used to process the ECG signals to obtain a feature set Using the feature set Train a convolutional neural network, and define this method as the MNN algorithm.

[0087] As Figure 8 shown, T-CNN / C-CNN includes two convolutional layers Conv, one Flatten layer, and two linear layers Linear; as Figure 9 shown, the convolutional neural network model of the MNN algorithm includes: one convolutional layer, one Flatten layer, and two linear layers Linear.

[0088] Figure 10 , Figure 11 , Figure 12 and Figure 13 are the accuracy results of T-CNN, C-CNN, T-RF, C-RF, T-KNN, C-KNN, and MNN algorithms under different noises respectively. Among them, vs RF, vs KNN, vs MNN respectively represent the accuracy of T-CNN minus RF, KNN, and MNN. From the simulation results, compared with the RF and KNN methods based on digital signal processing, it can be seen that the methods proposed in the present invention have the following advantages:

[0089] (1) Stronger noise suppression performance: As can be seen from the detection results, the anti-noise performance of the present invention is better than that of RF and KNN. This is mainly due to the fact that the present invention decomposes the tensor and learns the correlation between the decomposed tensors, achieving the effect of noise suppression.

[0090] (2) Stronger dynamic tracking ability: The present invention constructs a short-time dynamic data set based on the TWA alternating signal, breaking the traditional assumption of stable signals and noise, and giving the degree of freedom of beat-by-beat change in the time domain. Therefore, the present invention has stronger detection performance.

[0091] The above embodiments further elaborate on the purpose, technical solutions, and advantages of the present invention. It should be understood that the above embodiments are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made to the present invention within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A high-dynamic TWA multi-channel detection method based on tensor decomposition and machine learning, characterized in that: include: S1, acquiring multiple multi-channel ECG signals and preprocessing them to obtain multiple TWA alternating signals; S2, constructing a short-time dynamic data set based on multiple TWA alternating signals; The short-term dynamic dataset includes two types of tensors: tensors with TWA and tensors without TWA; S3, performing tensor decomposition on each tensor in the short-term dynamic data set to obtain a decomposition factor data set; S4, performing feature extraction on the decomposition factors of each tensor in the decomposition factor data set to obtain a feature factor data set; S5. Use the feature factor data set to train the machine learning model to obtain a trained machine learning model; S6. Obtain multi-channel ECG signals, calculate characteristic factors of the ECG signals, input the characteristic factors of the ECG signals into the trained machine learning model, and obtain detection results.

2. The high dynamic TWA multi-channel detection method based on tensor decomposition and machine learning according to claim 1, characterized in that: Preprocessing the multi-channel ECG signal includes: performing interference elimination, heartbeat alignment and background T wave elimination on the multi-channel ECG signal in turn to obtain a TWA alternating signal. Wherein, e is the index of the TWA alternating signal, K represents the number of consecutive heart beats of the ECG signal, that is, the number of heartbeat cycles, N represents the sampling points contained in each heartbeat cycle, and L represents the number of leads of the ECG signal.

3. The high dynamic TWA multi-channel detection method based on tensor decomposition and machine learning according to claim 1, characterized in that: The short-term dynamic data set constructed based on multiple TWA alternating signals includes: S21, in TWA alternating signal T e Randomly select multiple TWA alternating signals Multiple TWA alternating signals according to selection Construct multiple backup signals B f ; Wherein, e is the index of the TWA alternating signal, and f is the index of the selected TWA alternating signal; S22, according to multiple backup signals B f For each TWA alternating signal T e Transform to obtain multiple TWA tensors S23. For each TWA tensor After truncation and noise addition, a short-term dynamic data set is obtained.

4. The high dynamic TWA multi-channel detection method based on tensor decomposition and machine learning according to claim 3 is characterized in that: Construct backup signal B f Includes: TWA alternating signal for selected Perform TWA reshaping to obtain the reshaped TWA signal The reshaped TWA signal The abnormal waveform in is replaced with the mean waveform to obtain the TWA signal after waveform replacement. TWA signal after waveform replacement Perform averaging and average the TWA signal Normalize the normalized TWA signal Copy and obtain the backup signal B f .

5. The high dynamic TWA multi-channel detection method based on tensor decomposition and machine learning according to claim 3, characterized in that: According to various backup signals B f For each TWA alternating signal T e The transformations include: S221, for each TWA alternating signal T e Normalize them separately to get multiple real TWA signals A e ; S222, multiple spare signals B are mapped by PCA f Mapped to each real TWA signal A e , and obtain multiple transformation signals C h ; Where h is the transformation signal C h The index of S223, for each conversion signal C h Perform dynamic transformations respectively to obtain multiple TWA tensors 6. The high dynamic TWA multi-channel detection method based on tensor decomposition and machine learning according to claim 5, characterized in that: The backup signal B is transformed into f Mapping to the real TWA signal A e Includes: Estimation of the true TWA signal A e Spatial correlation Build and solve The eigenvector equation of e ; The eigenvector matrix Ψ e and backup signal B f Multiply them to get the transformed signal C h .

7. The high dynamic TWA multi-channel detection method based on tensor decomposition and machine learning according to claim 5, characterized in that: For the transformed signal C h Dynamic transformation includes: transforming the signal Tensorization, get tensor Building a dynamic matrix The tensor and the dynamic matrix G h Multiply them together to get the TWA tensor Wherein, K represents the number of consecutive heart beats of the ECG signal, N represents the sampling points contained in each heart beat cycle, and L represents the number of leads of the ECG signal.

8. The high dynamic TWA multi-channel detection method based on tensor decomposition and machine learning according to claim 3, characterized in that: For each TWA tensor The truncation and noise addition include: using a sliding window to the TWA tensor Intercept and obtain the intercepted TWA tensor In TWA tensor Add noise to get the TWA tensor after adding noise Using the TWA tensor after adding noise Subtract the corresponding truncated TWA tensor Get the TWA tensor The tensor without TWA, the TWA tensor after adding noise As TWA tensor There are TWA tensors; put all TWA tensors The tensors with TWA and without TWA are combined to obtain the short-term dynamic data set.

9. The high dynamic TWA multi-channel detection method based on tensor decomposition and machine learning according to claim 1, characterized in that: Tensor decomposition of the tensor of the short-term dynamic data set includes: Among them, × p (p=1,2,3) represents the p-module product between a tensor and a matrix, is the core tensor of the ith tensor, and represents the decomposition factor of the i-th tensor in the direction of heart beat, sampling point and lead projection. R1, R2 and R3 are the three dimensions of the core tensor. K represents the number of consecutive heart beats of the ECG signal, that is, the number of heart cycles. N represents the sampling points contained in each heart cycle. L represents the number of leads of the ECG signal.

10. The high dynamic TWA multi-channel detection method based on tensor decomposition and machine learning according to claim 9, characterized in that: Feature extraction for each tensor decomposition factor includes: S41. The core tensor of the i-th tensor Multiply by the corresponding decomposition factor U i 、V i , get the characteristic factor matrix U i ′、V i ′; S42, factor matrix U' i Each column of is interpolated three times, resulting in a value of The characteristic factor matrix U i ″; S43, factor matrix U i ″、V i ′ is concatenated according to the heartbeat dimension to obtain the characteristic factor matrix Y of the i-th tensor i .

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