Graph clustering method

Abstract

The application discloses a graph clustering method, comprising the following steps: extracting multiple image features of all images, reducing the multiple image features to a low-dimensional space and splicing, dividing all images into internal points and boundary points; calculating a distance matrix of all internal points and converting the distance matrix into a weight matrix; constructing a maximum spanning tree of all internal points and constructing a path similarity matrix according to the maximum spanning tree; calculating a degree matrix and a Laplace matrix according to the similarity matrix; arranging all internal points in descending order according to the degree, adding points not assigned with a cluster label into a cluster one by one and calculating a MeanCut value of the point; if the MeanCut value is lower than before, traversing the next point; otherwise, rejecting the current point from being added into the cluster; traversing the points not assigned with a cluster label from the beginning, generating the next cluster and until all internal points are assigned with a cluster label; for each boundary point, assigning a nearest internal point label to it to generate a final clustering result. The application can improve the image clustering precision and efficiency.

Description

Technical Field

[0001] This invention belongs to the technical field of unsupervised classification, specifically relating to a graph clustering method. Background Technology

[0002] Clustering is a powerful unsupervised classification method for exploring similar patterns and is widely used in many fields such as computer science, earth science, biology, and economics. To address the various challenges in cluster analysis, a variety of clustering algorithms have been proposed or improved, broadly categorized into partition-based, density-based, grid-based, prototype-based, orientation-based, hierarchical, and graph-based methods. Among these, graph clustering best aligns with the fundamental idea of ​​clustering: maximizing intra-cluster similarity and minimizing inter-cluster similarity. Specifically, it establishes connections between points using the graph structure and divides the graph into multiple disconnected subgraphs according to graph partitioning rules, with each connected subgraph corresponding to a cluster.

[0003] Spectral clustering, as the most typical graph clustering method, has attracted widespread attention due to its excellent performance, ease of implementation, and strong robustness. Classical spectral clustering algorithms use Euclidean distance to measure the edge weights of the graph and relax the constraints of the index matrix, solving for the optimal partitioning of the graph through eigenvalue decomposition of the Laplacian matrix. However, when dealing with non-spherical data distributions, Euclidean similarity-based methods may lead to unbalanced graph partitioning, while relaxation operations can cause information loss in the index matrix, resulting in clustering errors. Furthermore, since users often lack prior knowledge, the preset clustering number parameter required by mainstream spectral clustering methods is difficult to determine manually. Therefore, a new graph clustering method needs to be developed to eliminate the problem of information loss in the index matrix and improve clustering accuracy. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a graph clustering method that can improve the accuracy of face recognition and reduce the computational complexity of the face recognition process.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A graph clustering method includes the following steps:

[0007] Step 1: Input all images to be identified and classified, extract multiple image features for each image, reduce each high-dimensional image feature to a low-dimensional space of the same dimension, and stitch them together to obtain the low-dimensional image features of all images. Search for the K nearest neighbors of all images in the feature space, and calculate the density gradient factor of each image to its K nearest neighbors. According to the set density gradient factor threshold, divide all images into internal points and boundary points.

[0008] Step 2: Calculate the distance matrix of all interior points to obtain the side length matrix between all images, and then calculate the side weight matrix between all images based on the side length matrix.

[0009] Step 3: Construct the maximum spanning tree of all internal points, and calculate the similarity matrix of all images based on the maximum spanning tree and the edge weight matrix between all images.

[0010] Step 4: Based on the similarity matrix obtained in Step 3, construct the degree matrix and Laplacian matrix of the similarity between each image and other images;

[0011] Step 5: Sort all internal points in descending order of degree. Add each unlabeled point to a cluster and calculate the MeanCut value of the point based on the degree matrix and Laplacian matrix. If the MeanCut value is lower than before, proceed to the next point. Otherwise, reject the current point from being added to the cluster and complete the extraction of the current cluster. Then, start traversing the unlabeled points from the beginning to generate the next cluster, until all internal points are labeled.

[0012] Step 6: For each boundary point, assign the label of the nearest interior point to it to generate the final clustering result, thereby realizing the recognition and classification of different face images.

[0013] Furthermore, step 1 specifically includes:

[0014] S11. Construct the KD index for all images, and search for the K nearest neighbor object for each image based on the KD index;

[0015] S12. Calculate the average distance of each image to its K nearest neighbor and use it as its density, then calculate its density gradient factor based on the density;

[0016] S13. Sort the density gradient factors of all images in descending order, select the data sample points before the percentage threshold as internal points, and the remaining points as boundary points.

[0017] Furthermore, step 2 specifically includes:

[0018] S21. Calculate the Euclidean distance between any two pairs of internal points, use the Euclidean distance as the length of the side between the images, and then construct the side length matrix between all images based on the Euclidean distance.

[0019] S22. The Laplacian kernel function is used to transform the Euclidean distance into weights between point pairs, thereby transforming the side length matrix into the edge weight matrix between all images in the fully connected graph.

[0020] Furthermore, step 3 specifically includes:

[0021] S31. For all internal points, calculate the search neighborhood radius Eps based on the set ratio;

[0022] S32. Based on the calculated Eps, the DBSCAN algorithm is used to perform preliminary clustering of all internal points, generating several connected subgraphs of all internal points.

[0023] S33. For each subgraph, the edges retained by DBSCAN are used to generate the corresponding sub-maximum spanning tree using the Kruskal algorithm. In each sub-maximum spanning tree, the minimum edge weight in the path between two internal points is taken as the path similarity based on the edge weight matrix in step 2.

[0024] S34. Treat each sub-maximum spanning tree as a point, and then use the Kruskal algorithm to generate the global maximum spanning tree. Calculate the path similarity between different sub-maximum spanning trees according to the method in step S33, and then obtain the similarity matrix used to characterize the similarity between images.

[0025] Furthermore, the specific method for step 4 is as follows:

[0026] Calculate the degree matrix and Laplacian matrix of the interior points based on the similarity matrix:

[0027]

[0028] D = diag(d1, d2, ..., d...) n );

[0029] L = DW;

[0030] Among them, w ij Indicates the interior point v i and interior point v j The similarity between them, d i Indicates the interior point v i The degree, D, W, and L represent the degree matrix, similarity matrix, and Laplace matrix, respectively.

[0031] Furthermore, the specific method for step 5 is as follows:

[0032] S51. Sort all interior points in descending order of degree {v1, v2, ..., v...} n};

[0033] S52. Initialize the indicator vector of the first cluster of all internal points as follows:

[0034] x1 T =[x i1 x i2 , ..., x in ] = [0, 0, ..., 0];

[0035] S53, among all internal points, the first point v that has not been assigned a cluster label. j Join to the current cluster, i.e., x ij =1, and calculate the objective function value at this time. Where D and L represent the degree matrix and Laplacian matrix of the interior points, respectively;

[0036] S54, Move the next point v that has not been assigned a cluster label. k Join to the current cluster, i.e., x lk =1, recalculate the objective function value to MeanCut(x) i If MeanCut(x)′, i )′≤MeanCut(x i ), where MeanCut(x i (a) is a point v k If the MeanCut value from the previous family is added, then the next unlabeled sample point is added; otherwise, the point v is removed. k Remove the current cluster, and then continue traversing the next unlabeled point;

[0037] S55. After traversing all internal points, complete the extraction of the first cluster, and re-traverse the internal points that have not been assigned cluster labels until all internal points are assigned labels, then end the iteration.

[0038] Furthermore, the specific method for step 6 is as follows:

[0039] Search for the nearest internal point of each boundary point and assign the cluster ID information of that internal point to the boundary point.

[0040] Compared with existing technologies, the beneficial effects of this invention are as follows: When the graph clustering method proposed in this invention is applied to face recognition, the clustering accuracy is high, reaching 98.2% on the Yale standard dataset. Furthermore, it has low computational complexity, demonstrating significant performance advantages over traditional and cutting-edge spectral clustering algorithms, greatly saving time for different face recognition methods (see...). Figure 7 );

[0041] The method of this invention effectively enhances the correlation of points within a cluster and weakens the association between different clusters by constructing path similarity to characterize the similarity between images. Compared with the traditional Ncut method based on Euclidean metric, it can more effectively extract cluster structures of arbitrary shapes. Greedy optimization of the objective function based on degree descent order can eliminate the loss of information in the indicator matrix. This algorithm can identify clusters of arbitrary shapes and has strong robustness to noise. In addition, by introducing a density gradient factor, this invention can effectively separate weakly connected clusters. Furthermore, the FastMST algorithm designed in this invention has significantly improved the running efficiency compared with traditional spanning tree methods, thus improving computational efficiency.

[0042] In addition, this invention has broad application prospects. It can be applied not only to facial recognition but also to voice data. By extracting voice features, it can identify different speakers. This invention can also be applied to datasets with spatial location information to analyze their spatial aggregation patterns and spatiotemporal evolution. At the same time, it can identify cell types based on the gene expression levels of different cells. Attached Figure Description

[0043] Figure 1 This is a flowchart of the graph clustering method of the present invention;

[0044] Figure 2 This is a flowchart illustrating the application of the present invention in a face recognition scenario.

[0045] Figure 3 This is a flowchart of the FastMatchingTree (FastMST) algorithm in an embodiment of the present invention;

[0046] Figure 4 This is a comparison of the time efficiency of FastMST with three maximum spanning tree algorithms in the embodiments of the present invention;

[0047] Figure 5 This is the clustering result of MeanCut on an artificial dataset with noisy and weakly connected clusters in the embodiments of the present invention;

[0048] Figure 6 This is the result of using density gradient factor to identify weakly connected clusters in an embodiment of the present invention; where (a) is a three-dimensional plot of density gradient factor of artificial dataset, and (b)-(e) are the clustering results of MeanCut on four artificial datasets with weakly connected clusters;

[0049] Figure 7 This is a comparison of the time efficiency of the embodiments of the present invention with various spectral clustering algorithms;

[0050] Figure 8 This is a comparison of the accuracy of the embodiments of the present invention with various clustering methods. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0052] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0053] The present invention will be further described below with reference to specific embodiments, but these are not intended to limit the scope of the invention.

[0054] like Figure 1 As shown, this invention discloses a graph clustering method, comprising the following steps:

[0055] Step 1: Input all images to be identified and classified, extract multiple image features from each image, reduce each high-dimensional image feature to a low-dimensional space of the same dimension, and stitch them together to obtain the low-dimensional image features of all images. Search for the K nearest neighbors of all images in the feature space, and calculate the density gradient factor from each image to its K nearest neighbors. Based on the set density gradient factor threshold, divide all images into interior points and boundary points. This step specifically includes:

[0056] S11. Construct the KD index for all images, and search for the K nearest neighbor object for each image based on the KD index;

[0057] S12. Calculate the average distance of each image to its K nearest neighbors and use it as its density. Then, calculate its density gradient factor based on the density.

[0058]

[0059]

[0060] In the formula, v i Let v represent the i-th sample point. j Let j represent the j-th sample point, and k represent the number of nearest neighbors in KNN;

[0061] S13. Sort the density gradient factors of all images in descending order, select the data sample points before the percentage threshold as internal points, and the remaining points as boundary points.

[0062] Step 2: Calculate the distance matrix of all interior points to obtain the edge length matrix between all images, and then calculate the edge weight matrix between all images based on the edge length matrix; this step specifically includes:

[0063] S21. Calculate the Euclidean distance between any two pairs of internal points, use the Euclidean distance as the length of the side between the images, and then construct the side length matrix between all images based on the Euclidean distance.

[0064] S22. Use the Laplace kernel function to transform the Euclidean distance into weights between point pairs. That is, the edge weight of the graph, where v i Let v represent the i-th interior point. j Let represent the j-th interior point, and σ represent the smoothing parameter of the Gaussian kernel function, thus transforming the edge length matrix into an edge weight matrix between all images in the fully connected graph.

[0065] Step 3: Construct the maximum spanning tree of all internal points, and calculate the similarity matrix representing the similarity between all images based on the maximum spanning tree and the edge weight matrix between all images; specifically, this step includes the following sub-steps:

[0066] S31. For interior points in d-dimensional space definition:

[0067] min Y=[min y1, min y2,..., min y d ];

[0068] max Y=[max y1, max y2,..., max y d ];

[0069] Then, calculate the search neighborhood radius Eps based on the set ratio:

[0070]

[0071] S32. Based on the calculated Eps, the DBSCAN algorithm is used to perform preliminary clustering of all internal points to generate several connected subgraphs.

[0072] S33. For each subgraph, the edges retained by DBSCAN are used to generate the corresponding sub-maximum spanning tree using the Kruskal algorithm. In the maximum spanning tree of each subgraph, there is one and only one path between any two points. Based on the edge weight matrix in step 2, the minimum edge weight in the path between two internal points is taken as their path similarity.

[0073] S34. Treat each sub-maximum spanning tree as a point, and then use the Kruskal algorithm to generate the global maximum spanning tree. Calculate the path similarity between points in different maximum spanning trees according to step S33, and then generate a path similarity matrix to represent the similarity between images.

[0074] Step 4: Calculate the degree matrix and Laplacian matrix based on the path similarity matrix obtained in Step 3; specifically:

[0075] The degree matrix and Laplacian matrix of the interior points are calculated based on the similarity matrix as follows:

[0076]

[0077] D = diag(d1, d2, ..., d...) n );

[0078] L = DW;

[0079] Among them, w ij Indicates the interior point v i and interior point v j The similarity between them, d i Indicates the interior point v i The degree, D, W, and L represent the degree matrix, similarity matrix, and Laplacian matrix, respectively.

[0080] Step 5: Sort all internal points in descending order of degree. Add each unlabeled point to a cluster and calculate its MeanCut value based on the degree matrix and Laplacian matrix. If the MeanCut value is lower than before, proceed to the next point; otherwise, reject the current point from joining the cluster and complete the extraction of the current cluster. Then, iterate through the unlabeled points from the beginning to generate the next cluster, until all internal points are labeled. This step is specifically as follows:

[0081] S51. Sort all interior points in descending order of degree {v1, v2, ..., v...} n};

[0082] S52. Initialize the indicator vector of the first cluster as follows:

[0083] x1 T =[x i1 x i2 , ..., x in ] = [0, 0, ..., 0];

[0084] S53, assign the first unlabeled point v j Join to the current cluster, i.e., x ij =1, and calculate the objective function value at this time. Where D and L represent the degree matrix and the Laplacian matrix, respectively;

[0085] S54, Move the next point v that has not been assigned a cluster label. k Join to the current cluster, i.e., x 1k=1, recalculate the objective function value to MeanCut(x) i If MeanCut(x)′, i )′≤MeanCut(x i ), where MeanCut(x i (a) is a point v k If the MeanCut value from the previous family is added, then the next unlabeled sample point is added; otherwise, the point v is removed. k Remove the current cluster, and then continue traversing the next unlabeled sample point;

[0086] S55. After traversing all points, complete the extraction of the first cluster, and re-traverse the internal points that have not been assigned cluster labels until all internal points are assigned labels, then end the iteration.

[0087] Step 6: For each boundary point, assign the label of the nearest interior point to it to generate the final clustering result; specifically, search for the nearest interior point of each boundary point and assign the cluster ID information of that interior point to the boundary point.

[0088] The invention will be further illustrated below with specific examples.

[0089] The dataset used in this embodiment is the Yale face image dataset, which contains 165 64×64 face images from 15 individuals, with 11 images per person. Four image features were extracted in this embodiment: Gabor, Gist, LBP, and ResNet18. Gabor can capture multi-scale, multi-directional texture features and has good adaptability to lighting. Gist is a global feature used to simulate the shape of the scene, generating a 512-dimensional vector for each image. Local Binary Patterns (LBP) can encode small-scale texture information. ResNet18 is a pre-trained deep convolutional feature. The extracted features are then reduced to the same 22-dimensional low-dimensional space using PCA, concatenated, and input into the MeanCut clustering process. For the MeanCut method of this invention, this embodiment sets ratio = 0.2, k = 8, and percentile = 0.71. This embodiment was tested on a single machine with an 8-core Intel i7 processor and 64GB of memory, running Windows 10, and the algorithm was implemented using MATLAB.

[0090] The implementation process of this embodiment will now be described in detail with reference to the accompanying drawings. The specific steps are as follows:

[0091] 1) Input all face images and extract Gabor, Gist, LBP, and ResNet18 image features for each image; then, use PCA to reduce the dimensionality of the extracted high-dimensional features to a 22-dimensional space and concatenate them to obtain the low-dimensional image features of all images. Search for the K-nearest neighbor (KNN) for all images in the feature space. The technology roadmap for face recognition is as follows: Figure 2 As shown;

[0092] 2) Calculate the density gradient factor of each image in the feature space based on the KNN nearest neighbor method, temporarily remove external points, and retain internal points as objects for subsequent MeanCut clustering;

[0093] 2) Construct the maximum spanning tree of all interior points in the feature space using the FastMST algorithm; based on the calculated Eps, perform preliminary clustering of all interior points intV using the DBSCAN algorithm to generate several connected subgraphs; for each subgraph, use the Kruskal algorithm to generate the corresponding sub-maximum spanning tree; finally, treat each sub-maximum spanning subtree as a point, and then use the Kruskal algorithm to generate the global maximum spanning tree. The FastMST algorithm flow is as follows: Figure 3 As shown, its efficiency is significantly improved compared to traditional spanning tree methods, and it is 15 times faster than Prim's algorithm. Specifically, as shown... Figure 4 As shown;

[0094] 3) Construct a path similarity matrix to characterize the similarity between face images based on the maximum spanning tree, and calculate the degree matrix and Laplacian matrix based on the similarity matrix;

[0095] 4) Sort all internal points in descending order of degree, add them one by one to a cluster, and calculate the MeanCut value. If the MeanCut value is lower than before, proceed to the next point; otherwise, refuse to add the current point to the cluster and complete the extraction of the current cluster. Then, traverse the unlabeled points from the beginning to generate the next cluster, until all internal points are labeled.

[0096] 5) For each boundary point, the label of the nearest interior point is assigned to it to generate the final clustering result. According to the clustering result, MeanCut has a classification accuracy of up to 98.2%, and completely and accurately identified 10 out of 15 people.

[0097] In summary, this embodiment employs path similarity to effectively enhance the correlation between points within a cluster and weaken the association between different clusters. Compared to the traditional Ncut method based on Euclidean metric, it can more effectively extract cluster structures of arbitrary shapes, as shown in the following example. Figure 5As shown, MeanCut can effectively identify spherical clusters, strip-shaped clusters, and island-shaped clusters. Furthermore, by introducing a density gradient factor, this invention can effectively separate weakly connected clusters, specifically as follows... Figure 6 As shown, weak connections between spherical and square clusters are accurately separated. This invention has low computational complexity and significant performance advantages compared to traditional and cutting-edge spectral clustering algorithms, specifically as follows: Figure 7 Compared to other spectral clustering methods, this method has a lower runtime under the same computational environment, and the method in this embodiment has higher accuracy (see...). Figure 8 ).

[0098] In addition to the Yale dataset of facial images, this invention can also be applied to human voice data to identify different speakers by extracting voice features; it can also be applied to datasets with spatial location information to analyze their spatial clustering patterns and spatiotemporal evolution; it can also identify cell types based on the gene expression levels of different cells; furthermore, this method can be applied to other similar or related fields and has broad application prospects.

[0099] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made based on the content of this specification should be included within the protection scope of the present invention.

Claims

1. A graph clustering method, characterized in that, Includes the following steps: Step 1: Input all images to be identified and classified, extract multiple image features for each image, reduce each high-dimensional image feature to a low-dimensional space of the same dimension, and stitch them together to obtain the low-dimensional image features of all images. Search for the K nearest neighbors of all images in the feature space, and calculate the density gradient factor of each image to its K nearest neighbors. According to the set density gradient factor threshold, divide all images into internal points and boundary points. Step 2: Calculate the distance matrix of all interior points to obtain the side length matrix between all images, and then calculate the side weight matrix between all images based on the side length matrix. Step 3: Construct the maximum spanning tree of all internal points, and calculate the similarity matrix of all images based on the maximum spanning tree and the edge weight matrix between all images; Step 4: Based on the similarity matrix obtained in Step 3, construct the degree matrix and Laplacian matrix of the similarity between each image and other images; Step 5: Sort all internal points in descending order of degree. Add each unlabeled point to a cluster and calculate the MeanCut value of the point based on the degree matrix and Laplacian matrix. If the MeanCut value is lower than before, proceed to the next point. Otherwise, reject the current point from being added to the cluster and complete the extraction of the current cluster. Then, start traversing the unlabeled points from the beginning to generate the next cluster, until all internal points are labeled. Step 6: For each boundary point, assign the label of the nearest interior point to it to generate the final clustering result, thereby realizing the recognition and classification of different images.

2. The graph clustering method according to claim 1, characterized in that, Step 1 specifically includes: S11. Construct the KD index for all images, and search for the K nearest neighbor object for each image based on the KD index; S12. Calculate the average distance of each image to its K nearest neighbor objects and use it as its density. Then calculate its density gradient factor based on the density. S13. Sort the density gradient factors of all images in descending order, select the data sample points before the percentage threshold as internal points, and the remaining points as boundary points.

3. The graph clustering method according to claim 1, characterized in that, Step 2 specifically includes: S21. Calculate the Euclidean distance between any two pairs of internal points, use the Euclidean distance as the length of the side between the images, and then construct the side length matrix between all images based on the Euclidean distance. S22. The Laplacian kernel function is used to transform the Euclidean distance into weights between point pairs, thereby transforming the side length matrix into the edge weight matrix between all images in the fully connected graph.

4. The graph clustering method according to claim 1, characterized in that, Step 3 specifically includes: S31. For all internal points, calculate the search neighborhood radius Eps based on the set ratio; S32. Based on the calculated Eps, the DBSCAN algorithm is used to perform preliminary clustering of all internal points, generating several connected subgraphs of all internal points. S33. For each subgraph, the edges retained by DBSCAN are used to generate the corresponding sub-maximum spanning tree using the Kruskal algorithm. In each sub-maximum spanning tree, the minimum edge weight in the path between two internal points is taken as the path similarity based on the edge weight matrix in step 2. S34. Treat each sub-maximum spanning tree as a point, and then use the Kruskal algorithm to generate the global maximum spanning tree. Calculate the path similarity between different sub-maximum spanning trees according to the method in step S33, and then obtain a similarity matrix to represent the similarity between face images.

5. The graph clustering method according to claim 1, characterized in that, The specific method for step 4 is as follows: Calculate the degree matrix and Laplacian matrix of the interior points based on the similarity matrix: D=diag(d1,d2,...,d n ); L = DW; Among them, w ij Indicates the interior point v i and interior point v j The similarity between them, d i Indicates the interior point v i The degree, D, W, and L represent the degree matrix, similarity matrix, and Laplace matrix, respectively.

6. The graph clustering method according to claim 1, characterized in that, The specific method for step 5 is as follows: S51. Sort all interior points in descending order of degree {v1, v2, ..., v...} n }; S52. Initialize the indicator vector of the first cluster of all internal points as follows: x1 T =[x i1 ,x i2 ,...,x in ]=[0, 0,..., 0]; S53, among all internal points, the first point v that has not been assigned a cluster label. j Join to the current cluster, i.e., x ij =1, and calculate the objective function value at this time. Where D and L represent the degree matrix and Laplacian matrix of the interior points, respectively; S54, Move the next point v that has not been assigned a cluster label. k Join to the current cluster, i.e., x 1k =1, recalculate the objective function value to MeanCut(x) i If MeanCut(x)′, i )′≤MeanCut(x i ), where MeanCut(x i (a) is a point v k If the MeanCut value from the previous family is added, then the next unlabeled sample point is added; otherwise, the point v is removed. k Remove the current cluster, and then continue traversing the next unlabeled point; S55. After traversing all internal points, complete the extraction of the first cluster, and re-traverse the internal points that have not been assigned cluster labels until all internal points are assigned labels, then end the iteration.

7. The graph clustering method according to claim 1, characterized in that, The specific method for step 6 is as follows: Search for the nearest internal point of each boundary point and assign the cluster ID information of that internal point to the boundary point.

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