Multi-line graph clustering method based on time-frequency domain difference entropy and view angle weight self-adaption

Abstract

The invention discloses a multi-line graph clustering method based on time-frequency domain difference entropy and view angle weight self-adaption, which comprises the following steps of: dividing multi-line graph data into a plurality of time domain view angles according to an energy interval, extracting time-frequency domain characteristics of the multi-line graph data of each time domain view angle, calculating difference entropy of each time-frequency domain characteristic, and clustering the time-frequency domain characteristics of each time-frequency domain; combining all the difference entropies into a difference entropy vector; a feature extraction module is constructed and used for extracting time domain features in the multi-line graph data of different time domain view angles; taking the time domain features of all the time domain view angles as a time domain view angle combination, taking the difference entropy vector as a time-frequency domain view angle combination, and taking the time domain features of all the time domain view angles and the difference entropy vector as a combined view angle combination; and performing soft clustering on each visual angle combination, dynamically adjusting the soft clustering weight of each visual angle combination through a weight control module, and performing weighted fusion on a soft clustering result according to the weight to obtain a final clustering result.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-line graph clustering, and in particular to a multi-line graph clustering method based on time-frequency domain differential entropy and viewpoint weight adaptation. Background Art

[0002] Multi-line graph analysis and clustering are of great significance in scientific research. Their powerful ability to uncover underlying patterns and structures in data provides strong support for researchers to accurately identify similarities and efficiently perform classification tasks. This significantly facilitates in-depth analysis of complex phenomena, thereby improving the accuracy and efficiency of data interpretation.

[0003] Currently, the industry has developed a variety of methods for clustering multi-line graph analysis. Traditional machine learning clustering methods rely on iterative calculations, focusing on mining the distribution characteristics of data points in Euclidean space to achieve classification; deep clustering methods, with the powerful feature extraction and dimensionality reduction capabilities of deep neural networks, obtain the latent spatial characteristics of data, showing unique advantages in high-dimensional data clustering scenarios. However, when dealing with complex high-dimensional data, the amount of computation required by traditional machine learning algorithms increases exponentially, and the reliability of distance calculations between data points is difficult to guarantee; although deep clustering methods have advantages in processing high-dimensional data, they are not capable of extracting complex correlation information between curves. Therefore, multi-perspective clustering methods have emerged, focusing on examining data from different perspectives in order to obtain a more comprehensive clustering perspective.

[0004] Although the current multi-view clustering method can capture the correlation between curves, the current mainstream method ignores the noise interference between perspectives in order to improve the learning ability of different perspective representations, which greatly reduces the clustering stability and seriously restricts its effective application in the field of multi-line graph clustering. Summary of the Invention

[0005] The present invention proposes a multi-line graph clustering method based on time-frequency domain differential entropy and perspective weight adaptation, which solves the problem that the existing technology ignores the noise interference between perspectives, resulting in low clustering stability.

[0006] To solve the above technical problems, the present invention provides a multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation, comprising the following steps:

[0007] Step S1: Divide the multi-line graph data into multiple time domain perspectives according to the energy interval, extract the time-frequency domain features of the multi-line graph data of each time domain perspective, calculate the differential entropy of each time-frequency domain feature, and combine all the differential entropies into a differential entropy vector;

[0008] Step S2: constructing a feature extraction module, wherein the feature extraction module is used to extract time domain features from the multi-line graph data of each time domain perspective;

[0009] Step S3: The time domain features of all time domain perspectives are combined as a time domain perspective, the differential entropy vector is combined as a time-frequency domain perspective, and the time domain features and differential entropy vectors of all time domain perspectives are combined as a joint perspective;

[0010] Step S4: Soft clustering is performed on each perspective combination respectively, and the soft clustering weight of each perspective combination is dynamically adjusted through the weight control module. The soft clustering results are weighted and fused according to the weight to obtain the final clustering result.

[0011] Preferably, the expression for calculating the differential entropy of each time-frequency domain feature in step S1 is:

[0012]

[0013] Where, Multi-line graph data under the time domain perspective s The differential entropy of is the differential entropy function; express The probability density function of .

[0014] Preferably, the expression of the feature encoder of the feature extraction module in step S2 is:

[0015]

[0016] Where, is the multi-line graph data under the time domain perspective s, each time domain perspective has x independent curves; f s for Time domain features; MLP is a multi-layer perceptron; F s is the feature encoder corresponding to the time domain perspective s.

[0017] Preferably, in step S2, the sum of squared errors is used as the feature reconstruction loss of the feature extraction module, and the expression of the feature reconstruction loss is:

[0018]

[0019] Where, L s is the feature reconstruction loss; s is the total number of time domain perspectives; l2 is the length of the longest time domain feature sequence in all time domain perspectives; D j is the decoder corresponding to the time domain perspective j; is the multi-line graph data under the time domain perspective j; f j for Time domain characteristics; Represents the calculation of the vector two norm, that is, the Euclidean distance.

[0020] Preferably, the soft clustering for each perspective combination in step S4 includes the following steps: calculating the confidence that the samples in each perspective combination belong to each cluster center, dividing the samples according to the confidence, and implementing soft clustering. The expression of the soft clustering process is:

[0021] α=norm(C soft (J(D)));

[0022] Where α is the soft clustering result; norm() represents the [0,1] normalization of the vector; C soft is a soft clustering function; J represents joint embedding, which is used to fuse different perspectives and is implemented by a learnable multi-layer perceptron dimensionality reduction; D is the perspective combination.

[0023] Preferably, in step S4, consistency loss is used as the constraint of the soft clustering, and the expression of the consistency loss is:

[0024]

[0025] Where, L c is the consistency loss; τ is the control factor; n is the number of samples; α sc is the soft clustering result of the joint perspective combination; α de is the soft clustering result of the time-frequency domain perspective combination; α t It is the soft clustering result of the time domain perspective combination; Represents the calculation of the vector two norm, that is, the Euclidean distance.

[0026] Preferably, the expression for weighted fusion of the soft clustering results according to the weights in step S4 is:

[0027]

[0028] Where S out is the clustering result; Softmax is the activation function; W is the fully connected parameter of the weight control module; α c is the joint vector of the soft clustering results of all view combinations; H is the conjugate transpose of the matrix; b is the bias of the weight control module; C() is the clustering module; α sc is the soft clustering result of the joint perspective combination; α de is the soft clustering result of the time-frequency domain perspective combination; α t It is the soft clustering result of the time domain perspective combination.

[0029] Preferably, after obtaining the final clustering result in step S4, the parameters of the feature extraction module and the weight control module are optimized by alternating optimization training, including the following steps:

[0030] Step S41: Freeze the parameters of the weight control module and optimize the parameters of the feature extraction module by minimizing the sum of squared errors and consistency loss;

[0031] Step S42: Freeze the parameters of the feature extraction module and optimize the parameters of the weight control module by minimizing the total clustering loss.

[0032] Preferably, the expression of the total clustering loss in step S42 is:

[0033] L sc =L c +L D +L s ;

[0034] L D =L1+L2+L3;

[0035]

[0036] In the above formula, L sc is the total clustering loss; L c is the consistency loss; L D is the soft clustering loss; L s is the feature reconstruction loss; L1 is the inter-cluster separability and intra-cluster compactness loss; L2 is the cluster orthogonality loss; L3 is the simplex proximity loss; k is the number of clusters; n is the number of samples; κ ab is the Gaussian kernel matrix; f i 、f j are the representation vectors of sample i and sample j respectively; γ is a hyperparameter; α ai , α aj , α bi , α bj , α i , α j k-dimensional vector assigned to the cluster; e j is a simple standard vector; m ai 、m aj 、m bi 、m bj Assign vectors to clusters and e j Similarity matrix between ; Represents the calculation of the Euclidean distance of vectors.

[0037] Preferably, in step S41, the parameters of the feature extraction module are optimized by gradient descent, and the expression of the optimization process is:

[0038] ω·α c =argmin ω∈Ω L sc (w,ω);

[0039] Where ω is the parameter in Ω; αc is the joint vector of the soft clustering results of all view combinations; argmin represents the search for the value that minimizes the total clustering loss; w is the parameter of the weight control module; Ω is the parameter of the feature extraction module; L sc (w,ω) is the total clustering loss.

[0040] The benefits of the present invention include at least:

[0041] 1. Divide the multi-line graph data into time domain perspectives according to energy intervals, and extract the time-frequency domain features of each time domain perspective. Deeply explore the characteristics of the multi-line graph at different time scales, avoid information omissions caused by single time dimension analysis, make feature extraction more comprehensive, and provide rich and multi-level time domain information for subsequent clustering;

[0042] 2. We constructed three perspective combinations: time domain perspective combination, time-frequency domain perspective combination, and joint perspective combination. These combinations comprehensively depict the characteristics of multi-line graph data from different perspectives. By combining time domain features with differential entropy vectors and fully integrating time domain and time-frequency domain information, we provide a more comprehensive and multi-dimensional data foundation for cluster analysis, helping to discover more complex and hidden patterns and structures in the data.

[0043] 3. The soft clustering weights of different perspective combinations are dynamically adjusted, and the soft clustering results are weighted and fused according to the weights. Weights are automatically assigned according to the importance of the data under different perspectives, giving full play to the advantages of each perspective combination, so that the clustering results more accurately reflect the true structure of the data, and enhancing the adaptability and robustness of the method to complex data distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of a method flow in an embodiment of the present invention;

[0045] Figure 2 This is an example diagram of original multi-line graph data according to an embodiment of the present invention;

[0046] Figure 3 This is a visualization example diagram of the multi-line graph data after division and standardization according to an embodiment of the present invention;

[0047] Figure 4 Schematic diagram of the training process of the clustering model according to an embodiment of the present invention;

[0048] Figure 5 Schematic diagram of the results of material clustering using this method. DETAILED DESCRIPTION

[0049] The following is a clear and complete description of the technical solutions in the embodiments of the present invention, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0050] like Figure 1 As shown, an embodiment of the present invention provides a multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation, comprising the following steps:

[0051] Step S1: Divide the multi-line graph data into multiple time domain perspectives according to the energy interval, extract the time-frequency domain features of the multi-line graph data of each time domain perspective, calculate the differential entropy of each time-frequency domain feature, and combine all the differential entropies into a differential entropy vector.

[0052] Step S2: constructing an independent feature extraction module for each time domain perspective, where the feature extraction module is used to extract time domain features of the multi-line graph data at different time domain perspectives.

[0053] Step S3: The time domain features of all time domain perspectives are combined as the time domain perspective, the differential entropy vector is combined as the time-frequency domain perspective, and the time domain features and differential entropy vectors of all time domain perspectives are combined as the joint perspective.

[0054] Step S4: Soft clustering is performed on each perspective combination respectively, and the soft clustering weight of each perspective combination is dynamically adjusted through the weight control module. The soft clustering results are weighted and fused according to the weight to obtain the final clustering result.

[0055] Specifically, the embodiment of the present invention uses the band structure diagrams of 12954 materials on the Materials Project website as an example to perform multi-line graph clustering. The original data of the band structure diagram is as follows: Figure 2 The vertical axis of the band structure diagram represents the electron energy, and the horizontal axis represents the high symmetry points of the crystal in the reciprocal lattice space, which usually reflect the physical and chemical properties of the material.

[0056] For the band structure diagram data, all curves with energy mean in [-4, 4] are retained as the original multi-line diagram data. The original multi-line diagram data is divided into different perspective combinations, and the time-frequency domain differential entropy is extracted as an independent time-frequency domain enhanced perspective. For the original multi-line diagram data set D = {X1,…,X n},sample Indicates that the original multi-line graph data is divided into s different time domain perspectives according to the vertical axis energy mean. In the embodiment of the present invention, s is set to 8, and each time domain perspective has x independent curves. In the embodiment of the present invention, x is 12, and different curves are regarded as different data channels. The time domain perspective of sample X can be expressed as Extract the time-frequency domain features of the multi-line graph data of each time domain perspective and calculate the time-frequency domain features The differential entropy of , all differential entropies are combined into a differential entropy vector D de ={f de}.

[0057] Among them, the waveform The differential entropy of It can be expressed as:

[0058]

[0059] Where, Multi-line graph data under the time domain perspective s The differential entropy of is the differential entropy function; express The probability density function of .

[0060] When the random variables of the waveform discrete values of the multi-line graph data obey the Gaussian distribution N(μ,σ 2 ), the differential entropy The calculation can be simplified to:

[0061]

[0062] Where t is the time; is the probability density function of the time series with time as the horizontal axis; e is the natural logarithm; μ is the expectation of the probability density function; σ is the standard deviation of the probability density function.

[0063] The differential entropy vector f de As a time-frequency domain perspective.

[0064] The length of the curve sequence of the band structure diagram of different materials varies from 50 to 150, which is determined by the scale of the material in the reciprocal lattice space. Therefore, it is necessary to align and standardize the grouped curves. The alignment operation will make the curves with shorter sequence lengths Aligned by linear interpolation l2 represents the length of the longest sequence in the data set. In the embodiment of the present invention, l2=150. The aligned data set can be expressed as:

[0065]

[0066] Where M is the interpolation matrix; t i is the interpolation parameter, t i It is a value between 0 and 1, used to control the interpolation weight, and is set to 0.5 in the embodiment of the present invention.

[0067] Perform Z-SCORE normalization on the aligned curves:

[0068]

[0069] In the above formula, μ represents the mean of the aligned curve data; σ represents the standard deviation of the aligned curve data; I i is the i-th curve data; I i,norm is the i-th curve data after normalization.

[0070] The new curve I obtained after Z-SCORE standardization has a mean of 0, a variance of 1, and is dimensionless. Figure 3 shown.

[0071] Construct a feature encoder to learn the dimensionality reduction representation of the time series waveform. For the time series waveforms with different perspective combinations after preprocessing, construct a feature encoder with independent parameters:

[0072]

[0073] Where, is the multi-line graph data under the time domain perspective s, each time domain perspective has x independent curves; f s for The time domain characteristics of the present invention are set to f s The output dimension is 32; MLP is a multi-layer perceptron; F s It is the feature encoder corresponding to the time domain perspective s, responsible for information fusion of the waveform channel, and then completes the dimensionality reduction through the MLP fully connected layer.

[0074] The feature encoder uses the sum of squared errors as the feature reconstruction loss to optimize the feature encoder's dimensionality reduction representation capability. The training goal of dimensionality reduction representation learning is to ensure that the representation vector after dimensionality reduction retains the original data information as much as possible. The expression of feature reconstruction loss is:

[0075]

[0076] Where, L s is the feature reconstruction loss; s is the total number of time domain perspectives; D j is the decoder corresponding to the time domain perspective j; is the multi-line graph data under the time domain perspective j; Represents the calculation of the vector two norm, that is, the Euclidean distance.

[0077] The feature reconstruction loss is for each encoder F s Constructed the corresponding decoder D s ,This feature reconstruction loss aggregates the sum of squared errors of all view combinations as the final constraint target.

[0078] After using the feature extractor to extract the time domain features of the multi-line graph data at different time domain perspectives, the time domain features of all time domain perspectives are used as the time domain perspective combination, the differential entropy vector is used as the time-frequency domain perspective combination, and the time domain features and differential entropy vector of all time domain perspectives are used as the joint perspective combination. Thus, the three perspective combinations are: D t ={f1,…,f s}、D de ={f de} and D sc ={f1,…,f s ,f de}.

[0079] For the three perspective combinations D t 、D de and D sc Clustering is performed, and each perspective combination is sent to an independent joint clustering module J() to achieve soft clustering C soft (). The results of soft clustering are represented as soft assignment matrices α of size (n, k) t , α de and α sc , each row of the soft assignment matrix is normalized to the interval (0,1), representing the affinity vector of a certain sample data to all k cluster centers. de For example, the clustering process is expressed as:

[0080] α de =norm(C soft (J(D de )));

[0081] Where norm() represents the normalization operation.

[0082] Using consistency loss L c As a constraint for soft clustering, L c Composed of two mean square errors, we hope that α t With α sc The expression is close to α de . Consistency loss L c The expression is:

[0083]

[0084] Where τ is the control factor used to compress L c The value of τ is set so that it does not excessively affect the total clustering loss. In the embodiment of the present invention, τ is set to 0.05; n represents the number of samples; Represents the calculation of the vector two norm, that is, the Euclidean distance.

[0085] At the same time, a weight control module is designed to fuse the soft clustering results of different perspective combinations:

[0086]

[0087] Where S out is the clustering result; Softmax is the activation function; W is the fully connected parameter of the weight control module; α c is the joint vector of the soft clustering results of all perspective combinations; H is the conjugate transpose of the matrix; b is the bias of the weight control module; C() is the clustering module.

[0088] After random initialization, the final results of the above parameters are fixed through training. After the training, the weight of the soft clustering results of each view combination on the final result is shown in Table 1.

[0089] Table 1 Weight values of each perspective combination

[0090] Perspective Combination Weight value <![CDATA[α t ]]> 0.3033 <![CDATA[α de ]]> 0.4133 <![CDATA[α sc ]]> 0.2833

[0091] Multiple losses are used to jointly constrain the joint clustering module, measure the model performance during the training process, and use the alternating minimum optimization method to train the model. If the total loss is greater than the set threshold, step S2 is repeated, otherwise the process ends. In the embodiment of the present invention, the alternating minimum optimization strategy training is used to prevent the model from being affected by the initial parameters and falling into a local optimal solution. Specifically, the following steps are included:

[0092] Step S41: Freeze the parameters of the weight control module and optimize the parameters of the feature extraction module by minimizing the sum of squared errors and consistency loss.

[0093] Step S42: Freeze the parameters of the feature extraction module and optimize the parameters of the weight control module by minimizing the total clustering loss.

[0094] The loss function based on divergence is used as the soft clustering loss. The soft clustering loss includes three items: L1 emphasizes the separability between clusters and the loss of intra-cluster compactness; L2 is the cluster orthogonality loss, which encourages cluster orthogonality; L3 is the simplex approximation loss, which makes the result close to the simplex. Assume that the clustering module C() consists of a fully connected layer activated by a softmax layer, and obtains the k-dimensional vector of cluster assignment

[0095] The first loss aims to make the representations of samples from different clusters farther apart in the latent space, while making the representations of samples from the same cluster more compact in the latent space:

[0096]

[0097] κ ij =exp(-‖h i -hj ‖ 2 / (2γ 2 ));

[0098] Where k is the number of clusters; κ ab is the Gaussian kernel matrix; γ is the hyperparameter; α ai , α aj , α bi , α bj is the k-dimensional vector assigned to the cluster; n is the number of samples; f i 、f j are the representation vectors of sample i and sample j respectively.

[0099] The second loss encourages the assignment vectors of each object to be as orthogonal as possible:

[0100]

[0101] Where, α i , α j k-dimensional vector assigned to the cluster.

[0102] The third loss brings the allocation vector of each object closer to the simplicial canonical form:

[0103]

[0104] Where m ai 、m aj 、m bi 、m bj Assign vectors to clusters and e j Similarity matrix between j is a simple standard vector.

[0105] The goal of the soft clustering loss is to minimize the sum of the above three losses L D =L1+L2+L3. At the same time, considering the loss of the feature encoder for training the dimensionality reduction representation and the consistency loss of the soft clustering, the total loss of the clustering model is the sum of the three losses:

[0106] L sc (w,ω)=L c +L D +L s ;

[0107]

[0108] In the above formula, L sc (w,ω) is the total clustering loss; w is the parameter in W; W is the parameter of the weight control module; ω is the parameter in Ω; Ω is the parameter of the feature extraction module; n is the number of samples.

[0109] As can be seen from the above formula, the embodiment of the present invention decomposes the multi-view clustering problem into two sub-problems, updates the parameters of Ω and W respectively, freezes the other part, and updates Ω and W alternately.

[0110] First, pre-train the relevant parameters Γ of the feature extractor and optimize the loss L of the feature encoder s , and obtain the reduced-dimensional representation of the time series waveform. For the sub-problem min ω∈Ω (), the freezing parameter W, according to ω·α c =argmin ω∈Ω L sc (w,ω), the gradient descent convergence optimization is performed on the feature extractor. Similarly, the convergence of the weight control module is achieved by freezing the parameter Ω and optimizing the subproblem min w∈W () is obtained. In this training framework, when learning the parameter Ω, the model can be regarded as a conventional multi-view clustering model, which obtains complementary information from three different latent spaces. Then, the learned soft clustering results are fixed, and the weight parameter W is optimized so that the model automatically selects the appropriate soft clustering results for fusion. It is worth noting that the soft clustering results given by the model are fixed during the optimization of the parameter W. In order to prevent unnecessary interference, in the optimization subproblem min ω∈Ω (), for L sc The consistency loss L in (w,ω) c , let the hyperparameter τ = 0. Therefore, the entire model can automatically select features and obtain stable clustering effects. The training process of the clustering network is as follows Figure 4 shown.

[0111] After completing the model training, the CH score (Calinski-Harabasz Index, CHI) and DB index (Davies-Bouldin Index, DBI) were used to evaluate the clustering performance of the model.

[0112]

[0113] In the above formula, trace() represents the sum of squared distances, which is weighted by the size of the cluster; BCSM is the inter-cluster discrete matrix, and WCSM is the intra-cluster discrete matrix, representing the intra-cluster and inter-cluster covariance matrices; s i 、s j is the average distance from the sample points in the cluster to the cluster center; d ij is the center distance between two clusters.

[0114] The larger the CH score, the better the clustering performance of the model. The smaller the DB score, the greater the difference between clusters and the clearer the division between clusters. It measures the distance between clusters.

[0115] In order to verify the performance of the clustering method proposed in the embodiment of the present invention, the clustering results of the method of the embodiment of the present invention in four independent experiments were compared with the results of k-means clustering. The constraint loss and its evaluation results are shown in Table 2. Examples of similar materials found after clustering are shown in Table 2. Figure 5 As shown. The vertical axis of subgraph (a) is the soft clustering allocation vector α i The horizontal axis is the gravimetric capacity (A·H), an important parameter for measuring battery material performance, which calibrates the amount of electricity that can be released per unit mass of the corresponding material. The vertical axis of sub-graph (b) is the electron energy; the horizontal axis indicates the high symmetry points of the crystal in the reciprocal lattice space, which usually reflect the physical and chemical properties of the material. Figure 5 It can be seen that, based on the material LiFePO4 (Pca2_1), the two types of battery materials represented by LiCoPO4 and LiFePO4 (Pnma) showed very similar performance. Both of the above representative materials have been proven to be good battery anode materials. Figure 5 Continuing to explore new anode materials within the range of materials found can save a lot of trial and error costs.

[0116] Table 2 Band structure diagram prediction results and performance table

[0117] Experiment number Loss value CH score DBI k-means -- 224 1.45 Experiment 1 1.449 653 1.07 Experiment 2 1.491 644 1.04 Experiment 3 1.526 669 1.09 Experiment 4 1.478 648 1.06

[0118] The clustering method proposed in this embodiment of the present invention adds differential entropy in the time-frequency domain as a feature-enhancing perspective to multiple perspectives composed of different time series waveforms. Furthermore, a weight-controlled soft clustering mechanism is introduced to safely leverage the complementary information between different perspectives and prevent new perspectives from interfering with the clustering results. Unlike mainstream methods that directly fuse the representations of multiple perspectives before clustering, this mechanism groups the perspectives and adaptively adjusts the weights of the soft clustering results of the perspective combinations. This allows the model to automatically select the clustering results from the combinations with richer information for fusion, eliminating the interference of noise between perspectives.

[0119] By introducing differential entropy in the time-frequency domain, feature expression is enhanced and clustering accuracy is improved. By using differential entropy in the time-frequency domain as an independent feature enhancement perspective, it can effectively capture the dynamic changes of data in the time-frequency domain, making up for the shortcomings of traditional single-perspective clustering methods in feature expression and significantly improving clustering accuracy.

[0120] By dividing the data into multiple perspective combinations, the noise interference between perspectives is reduced, the excessive influence of a single perspective on the clustering results is avoided, and the clustering effect is improved.

[0121] A weight control module was designed to fuse soft clustering vectors from multiple perspectives to produce a joint clustering result. This module dynamically adjusts weights based on the importance of different perspectives, effectively reducing the model's sensitivity to random initialization parameters and significantly improving its stability. Furthermore, the weight control module can fuse soft clustering vectors from multiple perspectives, effectively alleviating the problem of data sparsity in high-dimensional spaces, avoiding drastic fluctuations in clustering results, and improving the robustness of clustering results.

[0122] The technical features of the above embodiments may be combined in any manner. To simplify the description, not all possible combinations of the technical features in the above embodiments are described. Only preferred embodiments of the present invention are presented. While the description is relatively specific and detailed, it should not be construed as limiting the scope of the present invention. As long as there are no conflicts in the combination of these technical features, they should be considered to be within the scope of this specification.

[0123] It should be noted that, for those skilled in the art, various modifications and improvements can be made without departing from the scope of the present invention, and these modifications and improvements fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation, characterized in that: The following steps are involved: Step S1: Divide the multi-line graph data into multiple time domain perspectives according to the energy interval, extract the time-frequency domain features of the multi-line graph data of each time domain perspective, calculate the differential entropy of each time-frequency domain feature, and combine all the differential entropies into a differential entropy vector; Step S2: constructing a feature extraction module, wherein the feature extraction module is used to extract time domain features from the multi-line graph data of each time domain perspective; Step S3: The time domain features of all time domain perspectives are combined as a time domain perspective, the differential entropy vector is combined as a time-frequency domain perspective, and the time domain features and differential entropy vectors of all time domain perspectives are combined as a joint perspective; Step S4: Soft clustering is performed on each perspective combination respectively, and the soft clustering weight of each perspective combination is dynamically adjusted through the weight control module. The soft clustering results are weighted and fused according to the weight to obtain the final clustering result.

2. The multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation according to claim 1, characterized in that: The expression for calculating the differential entropy of each time-frequency domain feature in step S1 is: Where, Multi-line graph data under the time domain perspective s The differential entropy of is the differential entropy function; express The probability density function of .

3. The multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation according to claim 1, characterized in that: The expression of the feature encoder of the feature extraction module in step S2 is: Where, is the multi-line graph data under the time domain perspective s, each time domain perspective has x independent curves; f s for Time domain characteristics; MLP is a multi-layer perceptron; F s is the feature encoder corresponding to the time domain perspective s.

4. The multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation according to claim 1, characterized in that: In step S2, the sum of squared errors is used as the feature reconstruction loss of the feature extraction module. The expression of the feature reconstruction loss is: Where, L s is the feature reconstruction loss; s is the total number of time domain perspectives; l2 is the length of the longest time domain feature sequence in all time domain perspectives; D j is the decoder corresponding to the time domain perspective j; is the multi-line graph data under the time domain perspective j; f j for Time domain characteristics; Represents the calculation of the vector two norm, that is, the Euclidean distance.

5. The multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation according to claim 1, characterized in that: The soft clustering is performed on each view combination in step S4, including the following steps: calculating the confidence that the samples in each view combination belong to each cluster center, dividing the samples according to the confidence, and implementing soft clustering. The expression of the soft clustering process is: α=norm(C soft (J(D))); Where α is the soft clustering result; norm() represents the normalization operation, which normalizes the model output to the range of [0,1]; C soft is a soft clustering function; J represents joint embedding, which fuses different perspective combinations by learning a multi-layer perceptron; D is the perspective combination.

6. The multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation according to claim 1, characterized in that: In step S4, consistency loss is used as the constraint of the soft clustering. The expression of the consistency loss is: Where, L c is the consistency loss; τ is the control factor; n is the number of samples; α sc is the soft clustering result of the joint perspective combination; α de is the soft clustering result of the time-frequency domain perspective combination; α t is the soft clustering result of the time domain perspective combination; || || m2 Represents the calculation of the vector two norm, that is, the Euclidean distance.

7. The multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation according to claim 1, characterized in that: The expression for weighted fusion of the soft clustering results according to the weights in step S4 is: Where S out is the clustering result; Softmax is the activation function; W is the fully connected parameter of the weight control module; α c is the joint vector of the soft clustering results of all view combinations; H is the conjugate transpose of the matrix; b is the bias of the weight control module; C() is the clustering module; α sc is the soft clustering result of the joint perspective combination; α de is the soft clustering result of the time-frequency domain perspective combination; α t It is the soft clustering result of the time domain perspective combination.

8. The multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation according to claim 1, characterized in that: After the final clustering result is obtained in step S4, the parameters of the feature extraction module and the weight control module are optimized through alternating optimization training, including the following steps: Step S41: Freeze the parameters of the weight control module and optimize the parameters of the feature extraction module by minimizing the sum of squared errors and consistency loss; Step S42: Freeze the parameters of the feature extraction module and optimize the parameters of the weight control module by minimizing the total clustering loss.

9. The multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation according to claim 8, characterized in that: The expression of the total clustering loss in step S42 is: L sc =L c +L D +L s ; <h2 style=";text-align:left;direction:ltr">L<h2 style=";text-align:left;direction:ltr"> D <h2 style=";text-align:left;direction:ltr"> (L1+L2+L3) In the above formula, L sc is the total clustering loss; L c is the consistency loss; L D is the soft clustering loss; L s is the feature reconstruction loss; L1 is the inter-cluster separability and intra-cluster compactness loss; L2 is the cluster orthogonality loss; L3 is the simplex proximity loss; k is the number of clusters; n is the number of samples; κ ab is the Gaussian kernel matrix; f i 、f j are the representation vectors of sample i and sample j respectively; γ is a hyperparameter; α ai , α aj , α bi , α bj , α i , α j k-dimensional vector assigned to the cluster; e j is a simple standard vector; m ai 、m aj 、m bi 、m bj Assign vectors to clusters and e j Similarity matrix between ; Represents the calculation of the Euclidean distance of vectors.

10. The multi-line graph clustering method based on time-frequency domain differential entropy and view weight adaptation according to claim 8, characterized in that: In step S41, the parameters of the feature extraction module are optimized by gradient descent. The expression of the optimization process is: oh·a c =argmin ω∈Ω L sc (w,ω); Where ω is the parameter in Ω; α c is the joint vector of the soft clustering results of all view combinations; argmin represents the search for the value that minimizes the total clustering loss; w is the parameter of the weight control module; Ω is the parameter of the feature extraction module; L sc (w,ω) is the total clustering loss.

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