Label propagation algorithm based on triple integration similarity

Abstract

The invention discloses a label propagation algorithm based on triple integration similarity. The method comprises the following steps of: 1, respectively representing an original data set as similarity graphs under three different visual angles based on three measures of distance, correlation coefficient and density, and representing all known label information in the data set as a label matrix by using one-hot coding; 2, respectively solving three corresponding local similarity graphs and three local kernel matrixes; 3, solving a final triple integration similarity graph through an iteration mode; 4, performing corresponding transformation on off-diagonal elements and diagonal elements in the triple integration similarity graph to obtain a standard propagation matrix; and 5, spreading label information from a labeled sample to a non-labeled sample in an iteration mode, wherein the maximum index corresponding to each sample in the label matrix is the category to which the sample is divided. The method has the advantages that the adaptability to the distribution condition of a data set is better, the adaptability to data distribution is higher, and the robustness is higher.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a label propagation algorithm based on triple integration similarity. Background Technology

[0002] In many machine learning tasks, such as object recognition and biomedical classification, acquiring labeled samples is extremely costly and time-consuming. In recent years, semi-supervised classification learning, specifically designed for tasks where labeled samples are scarce, has received widespread attention. For semi-supervised classification learning tasks, the proportion of labeled samples in the dataset is far lower than that of unlabeled samples, making it impossible to build a reasonable classifier using traditional supervised methods. Therefore, semi-supervised classification learning must be based on reasonable assumptions and allocate the scarce label information to a large number of unlabeled samples. Typically, mainstream semi-supervised classification learning methods are based on clustering or manifold assumptions. For clustering assumptions, relevant methods assume that samples within the same cluster have the same label, and the decision boundary between different categories should be located in a low-density region of the samples. Typical methods include transformed support vector machines, support tensor machines based on low-rank approximations, and local spline regression, etc. These methods usually establish specific constraints and criteria, resulting in non-convex or NP-hard learning objectives. On the other hand, the manifold assumption implies that samples within the same manifold have the same label. Methods based on the manifold assumption typically use graphs to represent samples in the dataset, where each sample is represented as a node, and the similarity between nodes is given by edges and their corresponding weights. Then, supported by physical or statistical laws, these methods cleverly utilize the similarity in the graph to construct a propagation matrix with iterative properties. After appropriately enhancing the separability of the propagation matrix, the labels are gradually and smoothly propagated from a very small number of labeled samples to a large number of unlabeled samples through matrix inversion or approximate iterative updates. Typically, this semi-supervised classification method based on similarity graph construction and propagation rules is called label propagation. Existing label propagation methods include harmonic function algorithms, Fick's law-assisted propagation algorithms, k-part graph algorithms, graph transition algorithms, and minimum cut algorithms, among others.

[0003] While existing manifold-based label propagation methods have achieved high semi-supervised classification performance on some test tasks, they are inherently subject to strict assumptions and limitations regarding the original distribution of the data because the generation of similarity maps relies on a single-view metric. For example, Fick's law-assisted propagation algorithms specify Euclidean distance as the sole metric for generating the initial similarity map, making them only sensitive to distance. Harmonic function algorithms, which generate similarity maps based on Gaussian functions, are still only applicable to datasets following a Gaussian distribution, even though the hyperparameters of the Gaussian function are adjustable. In the real world, not all available datasets follow a Gaussian distribution or are solely related to Euclidean distance. Local density, topological properties, and many other attributes also significantly influence the likelihood of label propagation between sample pairs. Since the propagation matrix in manifold-based label propagation methods is obtained from the initial similarity map through operations such as inversion, multiplication, and division, the properties of the similarity map essentially determine the probability of subsequent propagation between sample pairs. Relying solely on a single metric to generate the initial similarity map is one of the important reasons for the low classification accuracy of existing label propagation methods on real-world datasets.

[0004] Therefore, a good label propagation method should not only focus on the formulation of complex propagation rules and their corresponding physical / statistical interpretations, but also on the learning of similarity graphs. In recent years, some researchers have made preliminary efforts to fill the gap in similarity graph learning. For example, robust adaptive embedded label propagation and automatically weighted label propagation based on robust triple matrix recovery attempt to combine adaptive weight learning with label propagation. However, adaptive weights do not change the initial properties of a given graph. Furthermore, efficient regularized label propagation learning frameworks incorporate regularization of label propagation into graph convolutional networks and achieve very impressive semi-supervised classification results. However, in label propagation-related research, the question of how to reasonably use multiple metrics to evaluate similarity graphs remains unresolved. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a label propagation algorithm based on triple integration similarity, which addresses the problems of existing semi-supervised classification learning label propagation methods, such as lack of similarity graph learning, low accuracy of real data classification, and high running complexity due to matrix inversion.

[0006] To address the aforementioned technical problems, the label propagation algorithm based on triple integration similarity of the present invention includes the following steps:

[0007] Step 1. Based on distance, correlation coefficient and density, the original dataset is represented as similarity graphs from three different perspectives, and all known label information in the dataset is represented as a label matrix using one-hot encoding;

[0008] Step 2. Based on the similarity graphs obtained in Step 1 from the three different perspectives, solve for the corresponding three natural kernel matrices. Based on the similarity graphs obtained in Step 1 from the three different perspectives and the K-nearest neighbor method, solve for the corresponding three local similarity graphs and three local kernel matrices respectively.

[0009] Step 3. Based on the natural kernel matrix and local kernel matrix obtained in Step 2, set the initialization state matrix, the maximum number of iterations and the iteration termination condition, and solve the final triple integrated similarity graph by iterative method. Any off-diagonal element in the triple integrated similarity graph simultaneously contains sample pair information based on distance, correlation coefficient and density.

[0010] Step 4. Based on the topological properties of the Hessian matrix, transform the off-diagonal and diagonal elements of the triple integrated similarity graph obtained in Step 3 to obtain the standard propagation matrix, which fully preserves the distance, correlation coefficient, and density information of any sample pair while meeting the requirements of label propagation.

[0011] Step 5. Based on the label matrix represented by the one-hot encoding obtained in Step 1 and the propagation matrix obtained in Step 4, the label information is propagated from labeled samples to unlabeled samples through an iterative process using the propagation rule assisted by Fick's law. The iteration terminates when the maximum number of iterations is reached or the convergence condition is met. At this time, the maximum value index corresponding to each sample in the label matrix is ​​the category to which the sample is classified.

[0012] Step 1 specifically includes step 1.1: All data in the dataset... The samples were divided into labeled sample sets based on whether they were labeled or unlabeled. and unlabeled sample set ,in , , , and All include dimensional features, and Total number of categories;

[0013] Step 1.2: From a distance perspective, plot all samples using an undirected weighted graph. It means that among them ,and Adjacency matrix any element in Calculated using the following Gaussian kernel function:

[0014]

[0015] in and All Any element in , , The bandwidth of the Gaussian kernel function is set to the median of the Euclidean distances between all sample pairs, resulting in the adjacency matrix. As the first layer of initial similarity graph;

[0016] Step 1.3: From the perspective of correlation coefficient, plot all samples using an undirected weighted graph. It means that among them ,and Adjacency matrix any element in The Pearson correlation coefficient is obtained from the following formula:

[0017]

[0018] in and All Any element in , , for The variance of the adjacency matrix obtained As a second initial similarity graph;

[0019] Step 1.4: From a density perspective, plot all samples using an undirected weighted graph. It means that among them , Adjacency matrix any element in It is calculated using the following Gaussian kernel function based on local distance:

[0020]

[0021] in and All Any element in , , The bandwidth of the Gaussian kernel function based on local distance is set to the median of the local distances between all sample pairs, resulting in the adjacency matrix. As a third initial similarity graph; For the sample The local distance is given by the following formula:

[0022]

[0023] Where positive integers It is a user-defined hyperparameter representing the size of the local neighborhood, while Indicates sample Divorce No. The Euclidean distance between the nearest samples;

[0024] Step 1.5: Convert the label values ​​of all labeled samples to... Unique thermal coding Store the samples, setting the label value for all unlabeled samples to [value]. Zero-dimensional matrix ,Will and The one-hot encoded representation is obtained by concatenating the components. Tag matrix ;

[0025] Step 2 specifically includes step 2.1: based on the three initial similarity maps obtained in step 1. Calculate the corresponding natural kernel matrix respectively , where any element is given by the following formula:

[0026]

[0027] Make ;

[0028] Step 2.2: Based on the three adjacency matrices obtained in Step 1 The K-nearest neighbor method is used to calculate the corresponding local similarity graphs. any element Given by the following formula:

[0029]

[0030] Step 2.3: Based on the local similarity map obtained in Step 2.2 Calculate the corresponding local kernel matrix respectively , where any element Given by the following formula:

[0031]

[0032] Step 3 specifically includes step 3.1: Based on the three natural kernel matrices obtained in step 2.1, for any Set the initial state matrix Set the maximum number of iterations. Set the iteration termination condition Among them, positive numbers Hyperparameters provided by the user;

[0033] Step 3.2: Based on the three natural kernel matrices obtained in Step 2.1 and the three local kernel matrices obtained in Step 2.3, use an iterative approach for any... Solve for any time interval. state matrix The iteration method is given by the following formula:

[0034]

[0035] Step 3.3: According to the iteration method in Step 3.2, when Or the iteration termination condition is met. When the iteration terminates, for any The state matrix is ​​fixed or converges to The final triple integration similarity graph is then calculated using the following formula. :

[0036]

[0037] Step 1 specifically includes step 4.1: based on the triple-integrated similarity graph obtained in step 3.3. Set hyperparameters The triple-integrated similarity graph any off-diagonal element Transform into ;

[0038] Step 4.2: To satisfy the topological properties of the Hessian matrix, let the triple integrated similarity graph... any diagonal element And hyperparameters Must meet ;

[0039] Step 4.3: Based on the transformation rules in Steps 4.1 and 4.2, obtain the propagation matrix that satisfies the topological properties of the Hessian matrix. As shown below:

[0040]

[0041] Step 5 specifically includes step 5.1: representing the unique-hot encoding obtained in step 1. Tag matrix and the propagation matrix obtained in step 4.3 Based on the propagation rules aided by Fick's law, a learning rate is set. The following iterative formula can be used to calculate any time step. soft label vector at time :

[0042]

[0043] Step 5.2: Set the maximum number of iterations Termination threshold Set the iteration termination condition When the number of iterations Or the iteration termination condition is met. When the iteration terminates, the soft tag vector is recorded. Predicted category for any sample It can be given by the following formula:

[0044]

[0045] in soft label vector The OK.

[0046] Advantages of this invention:

[0047] 1. By taking three different perspectives—distance, similarity, and density—a comprehensive evaluation of a given dataset can be conducted, which can effectively avoid error propagation between sample pairs of different classes. The triple integration of similarity graph learning is not limited by the single metric of distance, and has better adaptability to the distribution of the dataset, making it more robust.

[0048] 2. In order to effectively improve the accuracy of semi-supervised classification, the symmetric matrix fusion technique is used to integrate the initial similarity maps from different perspectives. After formulating the final propagation probability matrix based on the properties of the Hessian matrix, the three segmentation characteristics of the data are still maintained. Therefore, the present invention has higher accuracy than the existing LP algorithm in semi-supervised classification tasks.

[0049] 3. In order to effectively improve the running speed of the algorithm, an iterative method combining Fick's law and KNN graph representation is adopted, which effectively avoids matrix inversion operations in the optimization process, thereby achieving fast convergence of the algorithm. Therefore, this invention has a faster running speed than existing semi-supervised LP algorithms. Attached Figure Description

[0050] Figure 1 This is a flowchart of the label propagation algorithm based on triple integration similarity of the present invention. Detailed Implementation

[0051] The label propagation algorithm based on triple integration similarity of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] Example:

[0053] The label propagation algorithm based on triple integration similarity includes the following steps:

[0054] Step 1. Based on distance, correlation coefficient and density, the original dataset is represented as similarity graphs from three different perspectives, and all known label information in the dataset is represented as a label matrix using one-hot encoding;

[0055] Step 1.1: Extract all data from the dataset. The samples were divided into labeled sample sets based on whether they were labeled or unlabeled. and unlabeled sample set ,in , , , and All include dimensional features, and This represents the total number of categories.

[0056] Step 1.2: From a distance perspective, plot all samples using an undirected weighted graph. It means that among them ,and Adjacency matrix any element in Calculated using the following Gaussian kernel function:

[0057]

[0058] in and All Any element in , , The bandwidth of the Gaussian kernel function can be simply set as the median of the Euclidean distances between all sample pairs, resulting in the adjacency matrix. This serves as the first layer of initial similarity graph.

[0059] Step 1.3: From the perspective of correlation coefficient, plot all samples using an undirected weighted graph. It means that among them ,and Adjacency matrix any element in The Pearson correlation coefficient is obtained from the following formula:

[0060]

[0061] in and All Any element in , , for The variance of the adjacency matrix obtained As a second initial similarity graph.

[0062] Step 1.4: From a density perspective, plot all samples using an undirected weighted graph. It means that among them ,and Adjacency matrix any element in It is calculated using the following Gaussian kernel function based on local distance:

[0063]

[0064] in and All Any element in , , The bandwidth of the Gaussian kernel function based on local distance can be simply set to the median of the local distances between all sample pairs, resulting in the adjacency matrix. As a third initial similarity graph, For the sample The local distance can be given by the following formula:

[0065]

[0066] Where positive integers It is a user-defined hyperparameter representing the size of the local neighborhood, while Indicates sample Divorce No. The Euclidean distance between the nearest samples.

[0067] Step 1.5: Convert the label values ​​of all labeled samples to... Unique thermal coding Store the samples, and set the label values ​​for all unlabeled samples to 0. Zero-dimensional matrix ,Will and The one-hot encoded representation is obtained by concatenating the components. Tag matrix .

[0068] Step 2. Based on the similarity graphs obtained in Step 1 from the three different perspectives, solve for the corresponding three natural kernel matrices. Based on the similarity graphs obtained in Step 1 from the three different perspectives and the K-nearest neighbor method, solve for the corresponding three local similarity graphs and three local kernel matrices respectively.

[0069] Step 2.1: Based on the three initial similarity graphs obtained in Step 1 Calculate the corresponding natural kernel matrix respectively , where any element is given by the following formula:

[0070]

[0071] Make ;

[0072] Step 2.2: Based on the three adjacency matrices obtained in Step 1 The K-nearest neighbor method is used to calculate the corresponding local similarity graphs. any element Given by the following formula:

[0073]

[0074] Step 2.3: Based on the local similarity map obtained in Step 2.2 Calculate the corresponding local kernel matrix respectively , where any element Given by the following formula:

[0075]

[0076] Step 3. Based on the natural kernel matrix and local kernel matrix obtained in Step 2, set the initialization state matrix, the maximum number of iterations and the iteration termination condition, and solve the final triple integrated similarity graph by iterative method. Any off-diagonal element in the triple integrated similarity graph simultaneously contains sample pair information based on distance, correlation coefficient and density.

[0077] Step 3.1: Based on the three natural kernel matrices obtained in Step 2.1, for any Set the initial state matrix Set the maximum number of iterations. Set the iteration termination condition Among them, positive numbers Hyperparameters provided by the user;

[0078] Step 3.2: Based on the three natural kernel matrices obtained in Step 2.1 and the three local kernel matrices obtained in Step 2.3, use an iterative approach for any... Solve for any time interval. state matrix The iteration method is given by the following formula:

[0079]

[0080] Step 3.3: According to the iteration method in Step 3.2, when Or the iteration termination condition is met. When the iteration terminates, for any The state matrix is ​​fixed or converges to The final triple integration similarity graph is then calculated using the following formula. :

[0081]

[0082] Step 4. Based on the topological properties of the Hessian matrix, transform the off-diagonal and diagonal elements of the triple integrated similarity graph obtained in Step 3 to obtain the standard propagation matrix, which fully preserves the distance, correlation coefficient, and density information of any sample pair while meeting the requirements of label propagation.

[0083] Step 4.1: Based on the triple integration similarity graph obtained in Step 3.3 Set hyperparameters The triple-integrated similarity graph any off-diagonal element Transform into ;

[0084] Step 4.2: To satisfy the topological properties of the Hessian matrix, let the triple integrated similarity graph... any diagonal element And hyperparameters Must meet ;

[0085] Step 4.3: Based on the transformation rules in Steps 4.1 and 4.2, obtain the propagation matrix that satisfies the topological properties of the Hessian matrix. As shown below:

[0086]

[0087] 5. Based on the label matrix represented by the one-hot encoding obtained in step 1 and the propagation matrix obtained in step 4, the label information is propagated gradually and smoothly from labeled samples to unlabeled samples through an iterative process, based on the propagation rule assisted by Fick's law. When the iteration process reaches the maximum number of iterations or meets the convergence condition, the iteration terminates. At this time, the maximum value index corresponding to each sample in the label matrix is ​​the category to which the sample is classified.

[0088] Step 5.1: Based on the one-hot encoding obtained in Step 1... Tag matrix and the propagation matrix obtained in step 4.3 Based on the propagation rules aided by Fick's law, a learning rate is set. The following iterative formula can be used to calculate any time step. soft label vector at time :

[0089]

[0090] Step 5.2: Set the maximum number of iterations Termination threshold Set the iteration termination condition When the number of iterations Or the iteration termination condition is met. When the iteration terminates, the soft tag vector is recorded. Predicted category for any sample It can be given by the following formula:

[0091]

[0092] in soft label vector The OK.

[0093] To further illustrate the beneficial effects of the present invention, the following comparative experiments were conducted.

[0094] This invention uses Mincut [Joachims T. Transductive learning via spectral graph partitioning[C]. In Proceedings of the 20th International Conference on Machine Learning, 2003: 290-297.], HF [Zhu X, Ghahramani Z, Lafferty J D. Semi-supervised learning using gaussian fields and harmonic functions[C]. In Proceedings of the 20th International Conference on Machine Learning, 2003: 912-919.], FLAP [Gong C, Tao D, Fu K, Yang J. Fick’s law assisted propagation for semisupervised learning[J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 26(9): 2148-2162.], AELP-WL [Zhang Z, Li F, Jia L, Qin J, Zhang L, Yan S. Robust adaptive embedded label propagation with weight learning for inductive classification[J]. IEEE Transactions on Neural Networks and Learning Systems, 2017, 29(8): 3388-3403.], ALP-TMR [Zhang H, Zhang Z, Zhao M, Ye Q, Zhang M, Wang M. Robust triple-matrix-recovery-based auto-weighted label propagation for classification[J].[IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(11): 4538-4552.] The method of this invention was experimentally validated on 15 UCI benchmark datasets for semi-supervised classification tasks. Each comparison method was run 20 times on each dataset under the same experimental conditions. The average accuracy and standard deviation are shown in Table 1, and the average running time (in seconds) is shown in Table 2. According to the experimental results, the method of this invention achieved the highest accuracy and fastest running speed on most UCI datasets, which fully demonstrates the beneficial effects of this invention.

[0095] Table 1. Accuracy of different semi-supervised classification methods on the UCI dataset

[0096] Datasets The method of the present invention HF FLAP Mincut AELP-WL ALP-TMR LERP Amazon 0.7529±0.0054 0.6370±0.0105 <![CDATA[ 0.7462±0.0058 ]]> 0.6654±0.0082 0.7271±0.0154 0.7389±0.0133 0.7431±0.0192 Amphibians 0.7135±0.0196 0.6457±0.0143 0.7058±0.0188 0.6245±0.0133 0.7011±0.0385 <![CDATA[ 0.7102±0.0364 ]]> 0.7094±0.0257 audit 0.9083±0.0025 0.8541±0.0051 0.8677±0.0030 0.8563±0.0046 0.8754±0.0094 0.8837±0.0103 <![CDATA[ 0.8981±0.0084 ]]> Avila 0.9304±0.0037 0.9004±0.0077 0.9145±0.0042 0.8872±0.0060 0.9156±0.0142 0.9110±0.0168 <![CDATA[ 0.9219±0.0082 ]]> epilepsy 0.9401±0.0015 0.8978±0.0027 0.9010±0.0016 0.8591±0.0011 <![CDATA[ 0.9231±0.0067 ]]> 0.9170±0.0085 0.9059±0.0063 fertility <![CDATA[ 0.7937±0.0195 ]]> 0.7038±0.0396 0.7652±0.0227 0.7269±0.0355 0.7459±0.0338 0.7362±0.0397 0.8044±0.0298 German 0.7836±0.0088 0.7257±0.0167 <![CDATA[ 0.7747±0.0090 ]]> 0.7311±0.0146 0.7671±0.0174 0.7725±0.0166 0.7721±0.0231 HCV 0.9135±0.0192 0.8935±0.0321 0.8835±0.0199 0.8537±0.0344 0.8976±0.0257 0.9025±0.0299 <![CDATA[ 0.9035±0.0221 ]]> HTRU2 <![CDATA[ 0.9114±0.0060 ]]> 0.8695±0.0088 0.9026±0.0077 0.8661±0.0064 0.8865±0.0121 0.9056±0.0169 0.9409±0.0032 madelon 0.5974±0.0072 0.5856±0.0099 0.5943±0.0067 0.5927±0.0085 0.5933±0.0168 <![CDATA[ 0.6102±0.0235 ]]> 0.6294±0.0191 Parkinson 0.8750±0.0035 0.8254±0.0126 0.8475±0.0094 0.7971±0.0102 0.8436±0.0235 0.8316±0.0212 <![CDATA[ 0.8594±0.0076 ]]> Roman 0.8850±0.0095 0.8406±0.0093 0.8235±0.0109 0.7963±0.0085 0.8578±0.0160 0.8644±0.0112 <![CDATA[ 0.8734±0.0101 ]]> seeds 0.9804±0.0062 0.9053±0.0054 0.9629±0.0043 0.9215±0.0077 0.9614±0.0072 <![CDATA[ 0.9759±0.0064 ]]> 0.9527±0.0144 Synchronous <![CDATA[ 0.8055±0.0177 ]]> 0.7380±0.0259 0.7492±0.0184 0.7250±0.0159 0.7570±0.0254 0.7319±0.0271 0.8253±0.0277 wine 0.9675±0.0013 0.9445±0.0024 0.9578±0.0011 0.9269±0.0017 0.9632±0.0076 0.9562±0.0073 <![CDATA[ 0.9609±0.0115 ]]>

[0097] Table 2. Running time (seconds) of different semi-supervised classification methods on the UCI dataset.

[0098] Datasets The method of the present invention HF FLAP Mincut AELP-WL ALP-TMR LERP Amazon <![CDATA[ 1.78 ]]> 4.30 1.74 5.52 3.62 3.75 35.33 Amphibians 0.45 0.59 <![CDATA[ 0.49 ]]> 0.63 1.27 1.39 8.10 audit 2.05 2.44 <![CDATA[ 2.12 ]]> 2.95 6.63 6.58 24.72 Avila 6.36 19.81 <![CDATA[ 7.32 ]]> 27.22 18.94 16.33 110.59 epilepsy 9.28 34.99 <![CDATA[ 10.57 ]]> 75.62 29.80 25.63 168.95 fertility <![CDATA[ 0.11 ]]> 0.13 0.08 0.21 0.80 0.94 6.89 German <![CDATA[ 1.92 ]]> 4.64 1.78 4.82 11.97 9.59 29.76 HCV 0.90 1.98 <![CDATA[ 0.92 ]]> 1.09 2.03 1.96 11.77 HTRU2 12.95 75.54 <![CDATA[ 13.32 ]]> 102.71 36.30 29.49 176.58 madelon <![CDATA[ 4.73 ]]> 31.72 4.25 25.28 21.02 19.30 224.68 Parkinson 1.46 3.27 <![CDATA[ 1.50 ]]> 4.64 10.39 9.91 55.89 Roman 10.50 78.43 <![CDATA[ 12.74 ]]> 117.55 39.43 32.56 206.63 seeds 0.70 1.56 <![CDATA[ 0.95 ]]> 1.24 2.67 2.98 7.99 Synchronous 0.77 0.67 <![CDATA[ 0.69 ]]> 1.15 1.15 0.94 9.50 wine 7.56 19.41 <![CDATA[ 8.61 ]]> 31.70 21.69 22.64 102.57

Claims

1. A label propagation algorithm based on triple integration similarity, characterized in that, Includes the following steps: Step 1. Based on distance, correlation coefficient and density, the original dataset is represented as similarity graphs from three different perspectives, and all known label information in the dataset is represented as a label matrix using one-hot encoding; Step 2. Based on the similarity graphs obtained in Step 1 from the three different perspectives, solve for the corresponding three natural kernel matrices. Based on the similarity graphs obtained in Step 1 from the three different perspectives and the K-nearest neighbor method, solve for the corresponding three local similarity graphs and three local kernel matrices respectively. Step 3. Based on the natural kernel matrix and local kernel matrix obtained in Step 2, set the initialization state matrix, the maximum number of iterations and the iteration termination condition, and solve the final triple integrated similarity graph by iterative method. Any off-diagonal element in the triple integrated similarity graph simultaneously contains sample pair information based on distance, correlation coefficient and density. Step 4. Based on the topological properties of the Hessian matrix, transform the off-diagonal and diagonal elements of the triple integrated similarity graph obtained in Step 3 to obtain the standard propagation matrix, which fully preserves the distance, correlation coefficient, and density information of any sample pair while meeting the requirements of label propagation. Step 5. Based on the label matrix represented by the one-hot encoding obtained in Step 1 and the propagation matrix obtained in Step 4, the label information is propagated from labeled samples to unlabeled samples through an iterative process using the propagation rule assisted by Fick's law. The iteration terminates when the maximum number of iterations is reached or the convergence condition is met. At this time, the maximum value index corresponding to each sample in the label matrix is ​​the category to which the sample is classified.

2. The label propagation algorithm based on triple integration similarity as described in claim 1, characterized in that: Step 1 specifically includes step 1.1: All data in the dataset... The samples were divided into labeled sample sets based on whether they were labeled or unlabeled. and unlabeled sample set ,in , , , and All include dimensional features, and Total number of categories; Step 1.2: From a distance perspective, plot all samples using an undirected weighted graph. It means that among them ,and Adjacency matrix any element in Calculated using the following Gaussian kernel function: ； in and All Any element in , , The bandwidth of the Gaussian kernel function is set to the median of the Euclidean distances between all sample pairs, resulting in the adjacency matrix. As the first layer of initial similarity graph; Step 1.3: From the perspective of correlation coefficient, plot all samples using an undirected weighted graph. It means that among them ,and Adjacency matrix any element in The Pearson correlation coefficient is obtained from the following formula: ； in and All Any element in , , for The variance of the adjacency matrix obtained As a second initial similarity graph; Step 1.4: From a density perspective, plot all samples using an undirected weighted graph. It means that among them , Adjacency matrix any element in It is calculated using the following Gaussian kernel function based on local distance: ； in and All Any element in , , The bandwidth of the Gaussian kernel function based on local distance is set to the median of the local distances between all sample pairs, resulting in the adjacency matrix. As a third initial similarity graph; For the sample The local distance is given by the following formula: ； Where positive integers It is a user-defined hyperparameter representing the size of the local neighborhood, while Indicates sample Divorce No. The Euclidean distance between the nearest samples; Step 1.5: Convert the label values ​​of all labeled samples to... Unique thermal coding Store the samples, setting the label value for all unlabeled samples to [value]. Zero-dimensional matrix ,Will and The one-hot encoded representation is obtained by concatenating the components. Tag matrix .

3. The label propagation algorithm based on triple integration similarity as described in claim 2, characterized in that: Step 2 specifically includes step 2.1: based on the three initial similarity maps obtained in step 1. Calculate the corresponding natural kernel matrix respectively , where any element is given by the following formula: ； Make ; Step 2.2: Based on the three adjacency matrices obtained in Step 1 The K-nearest neighbor method is used to calculate the corresponding local similarity graphs. any element Given by the following formula: ； Step 2.3: Based on the local similarity map obtained in Step 2.2 Calculate the corresponding local kernel matrix respectively , where any element Given by the following formula: 。 4. The label propagation algorithm based on triple integration similarity as described in claim 3, characterized in that: Step 3 specifically includes step 3.1: Based on the three natural kernel matrices obtained in step 2.1, for any Set the initial state matrix Set the maximum number of iterations. Set the iteration termination condition Among them, positive numbers Hyperparameters provided by the user; Step 3.2: Based on the three natural kernel matrices obtained in Step 2.1 and the three local kernel matrices obtained in Step 2.3, use an iterative approach for any... Solve for any time interval. state matrix The iteration method is given by the following formula: ； Step 3.3: According to the iteration method in Step 3.2, when Or the iteration termination condition is met. When the iteration terminates, for any The state matrix is ​​fixed or converges to The final triple integration similarity graph is then calculated using the following formula. : 。 5. The label propagation algorithm based on triple integration similarity as described in claim 4, characterized in that: Step 4 specifically includes step 4.1: based on the triple-integrated similarity graph obtained in step 3.

3. Set hyperparameters The triple-integrated similarity graph any off-diagonal element Transform into ; Step 4.2: To satisfy the topological properties of the Hessian matrix, let the triple integrated similarity graph... any diagonal element And hyperparameters Must meet ; Step 4.3: Based on the transformation rules in Steps 4.1 and 4.2, obtain the propagation matrix that satisfies the topological properties of the Hessian matrix. As shown below: 。 6. The label propagation algorithm based on triple integration similarity according to claim 5, characterized in that: Step 5 specifically includes step 5.1: representing the unique-hot encoding obtained in step 1. Tag matrix and the propagation matrix obtained in step 4.3 Based on the propagation rules aided by Fick's law, a learning rate is set. The following iterative formula can be used to calculate any time step. soft label vector at time : ； Step 5.2: Set the maximum number of iterations Termination threshold Set the iteration termination condition When the number of iterations Or the iteration termination condition is met. When the iteration terminates, the soft tag vector is recorded. Predicted category for any sample It can be given by the following formula: ； in soft label vector The OK.

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