Network user classification method based on adaptive clustering center clustering

Abstract

The application discloses a network user classification method based on adaptive clustering center clustering. The method is based on the idea of DPC clustering algorithm, and attribute division is performed according to user behavior data features. According to the distance between data points and other data points, the combined density value of each user behavior is calculated, and noise points, boundary points and normal points are divided. The noise points are discarded, the normal points are first divided into sub-clusters, then the representative points of the sub-clusters are subjected to distance transformation by calculating shared neighbors, the final clustering center, i.e. the user attribute label, is selected from the representative points of the sub-clusters. Finally, according to the similarity between the sub-clusters, the boundary points are divided into the category in which the nearest normal point is located. The method has few required parameters, strong adaptive capacity and high automation degree of the clustering process, can automatically determine the classification category according to the data distribution characteristics, does not need manual determination of attribute features or quantity, and can effectively distinguish users with different attributes.

Description

Technical Field

[0001] This invention belongs to the field of big data processing technology, specifically relating to a network user classification method based on adaptive clustering center clustering. Background Technology

[0002] Big data analytics extracts features from users' past behavioral data, categorizes users based on attributes, and assigns different tags. This allows for personalized content delivery to each user in later services. Clustering exemplifies the principle of "birds of a feather flock together," grouping different objects based on similarity to achieve high similarity within clusters and low similarity between clusters. As a core component of unsupervised learning, clustering analysis can function as a standalone process for identifying the inherent distribution structure of data, or it can serve as a foundation for other learning methods such as classification, data mining, and machine learning. Therefore, clustering algorithms are well-suited for analyzing massive amounts of user behavior data to achieve user attribute classification tasks.

[0003] Existing clustering algorithms can be categorized into partitioning clustering methods, density-based clustering methods, hierarchical clustering methods, model clustering methods, and spectral clustering. In 2014, Rodriguez and Laio proposed a density-based peak density clustering algorithm (DPC, Clustering by fast search and find of density peaks) in Science. The DPC algorithm is based on two assumptions: (1) cluster centers are surrounded by their nearest neighbor data points, highlighting the high density of the cluster centers; (2) any cluster center is far from points with higher density. The DPC algorithm has advantages such as fewer parameter requirements and non-iterative nature, and can effectively detect clusters of arbitrary shapes from large-scale datasets with low computational complexity. However, the selection of the cutoff distance dc parameter in the DPC algorithm depends on human subjective experience. When using the DPC algorithm to classify user attributes, it is necessary to manually determine the number of categories and category labels, which cannot be adaptively selected according to data characteristics, resulting in insufficient classification precision. Especially when the number of users with different attributes varies greatly, the density of behavioral data is uneven, and the classification effect of the DPC algorithm is not good. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a network user classification method based on adaptive clustering center clustering. According to the distribution characteristics of user behavior data, it automatically determines the attribute categories and the number of categories, thereby automating the classification process without manual intervention and improving the accuracy and reliability of the classification results.

[0005] The network user classification method based on adaptive clustering center clustering includes the following steps:

[0006] Step 1: Obtain user behavior data from online platforms, extract features from the user behavior data, and construct a feature dataset D. The online platform can be an e-commerce platform, a social platform, or a multimedia video platform.

[0007] Step 2: In the feature dataset D, each data point represents a user's behavioral characteristic. Calculate the parameters that reflect the distribution of user characteristics within the dataset:

[0008] S2.1 Calculate the distance d(a,b) between data point a and other data points in the feature dataset D in sequence:

[0009] d(a,b)=||x a -x b ||

[0010] Where, x a Indicates the position of data point a, x b This indicates the positions of the other data points. Then, the other data points are sorted from smallest to largest based on the calculation results.

[0011] S2.2. Based on the calculation results of s1.1, select the r data points closest to data point p and put them into set NN. r In {p}:

[0012] NN r {p}={x∈D|d(p,x)≤d(p,p r )}

[0013] Where p and x are points in dataset D, p r Let r represent the r-th nearest neighbor of data point p. Then, calculate the reverse nearest neighbor (RNN) of data point p and put it into the set RNN. r In {p}:

[0014] RNN r (p)={x∈D|p∈NN r (x)}

[0015] Statistical set RNN r The number of points in {p}. Starting with 2, the step size is r, up to the set RNN. r {p} and set RNN r-1 The number of points in {p} is equal, or the set is an RNN. r If {p} is not an empty set, then the value of r at this point is recorded as the optimal value of K:

[0016]

[0017] Set RNN rThe number of points in the {p} denoted as the reverse nearest neighbor weights of data point p in an RNN. K _weight(p). The maximum reverse nearest neighbor weight of all data points is denoted as the maximum mutual neighbor value Mmn of the dataset.

[0018] S2.3 Calculate the ratio of the reverse nearest neighbor weight of data point p to the sum of the Euclidean distances between its optimal_K nearest neighbors, and use this ratio as the initial density Initial_ρ(p) of data point p:

[0019]

[0020] Where K = optimal_K.

[0021] Calculate the sum of the initial densities of data point p and its optimal_K nearest neighbors, which is taken as the resultant density ρ(p) of data point p:

[0022]

[0023] Step 3: Based on the calculation results of Step 2, determine the noise points and boundary points in dataset D:

[0024] S3.1. Traverse each data point in dataset D, and discard data points with an initial density of zero as noise points. This prevents inactive users or users with excessively random behavior from affecting the overall classification.

[0025] S3.2 Calculate the local distance ratio ω(p) of the maximum mutual neighbors of data point p:

[0026]

[0027] The set NN Mmn {p} represents the set of the Mmn nearest data points to data point p, and d(q,q) Mmn ) represents the relationship between data point q and its nearest Mmn-th data point q. Mmn The remaining points in dataset D are sorted from largest to smallest based on the ratio of local distances between their largest mutual neighbors and their combined density. The last θ×100% of the data points are placed into sets Set1 and Set2, respectively. The points in set bp are considered as boundary points.

[0028] bp={p∈Set1∩Set2}

[0029] Boundary points indicate that the corresponding user behavior characteristics are relatively ambiguous.

[0030] Step 4: Based on the sum density of the data points, find the parent node for each data point using the density peak clustering assignment rule:

[0031]

[0032] Data points without parent nodes are used as representative points of the sub-clusters, rep(Sc). i ):

[0033]

[0034] Sc i ={p1, p2, p3, ..., rep(Sc i )}

[0035] The representative point rep(Sc) of the sub-cluster i ) and its child nodes are grouped into a sub-cluster.

[0036] Step 5: Calculate the sub-cluster Sc respectively i For each data point, the K nearest neighbors set is used as the union of the subclusters Sc. i extended subclusters extend_Sc i :

[0037]

[0038] Then calculate the intersection of the extended subclusters between different subclusters:

[0039] SN(Sc i ,Sc j ) = extend_Sc i ∩extend_Sc j

[0040] Set SN(Sc) i ,Sc j The data points in ) are called subclusters Sc i With sub-clusters Sc j Shared neighbors.

[0041] Step 6: Calculate the distance between the variable spatial transformations of the representative points of different subclusters:

[0042] S6.1 Calculate the Euclidean distance d(rep(Sc) between representative points of different subclusters. i ),rep(Sc j )):

[0043] d(rep(Sc i ),rep(Sc j ))=||rep(Sc i ),rep(Sc j )||

[0044] S6.2. Calculate the variable spatial transformation distance between representative points of each sub-cluster according to the association relationship between them:

[0045] (1) If the sub-cluster Sc i With sub-clusters Sc j There are shared neighbors, i.e., |SN(Sc) i ,Sc j If |≠0, then the subcluster Sc i With sub-clusters Sc j The direct association represents the variable spatial transformation distance between its representative points as follows:

[0046]

[0047] (2) If the sub-cluster Sc i With sub-clusters Sc j There are no shared neighbors between them, but there are other subclusters such that subcluster Sc i Able to reach sub-cluster Sc through shared neighbors with other sub-clusters j Then the sub-cluster Sc i With sub-clusters Sc j Indirect association, representing the variable spatial transformation distance between points, is:

[0048]

[0049] Where o and l are the preceding and following nodes on the path Path(i,j), and Path(i,j) represents the subcluster Sc i Reaching subcluster Sc via shared neighbors with other subclusters j The path.

[0050] (3) If sub-cluster Sc i With sub-clusters Sc j If they are neither directly nor indirectly related, then the variable spatial transformation distance between their representative points is:

[0051] SNS(rep(Sc i ),rep(Sc j ))=MaxD×(1+d(rep(Sc i ),rep(Sc j )))

[0052] Where MaxD is the maximum distance between all representative points of the subclusters.

[0053] Step 7: Based on the transformed distance obtained in Step 6, and combined with the resultant density, calculate the upward distance δ of the representative point of the sub-cluster. rep(Sci) :

[0054]

[0055] Representative points whose upward distance is greater than the threshold MaxD are retained as cluster centers. The number of retained cluster centers is the number of clusters.

[0056] Step 8: Assign subclusters and boundary points whose upward distance from the representative point is less than the threshold, complete the behavioral feature classification of all users, and assign the same attribute label to users in the same cluster:

[0057] S8.1 Calculate the similarity SIM(Sc) between subclusters i ,Sc j ):

[0058]

[0059] Where Θ(Sc i ,Sc j The ) represents the average combination density difference between subclusters:

[0060]

[0061] The average combination density of subclusters:

[0062]

[0063] S8.2 For subclusters whose upward distance from the representative point is less than the threshold, assign them to the cluster class with the highest similarity to them.

[0064] S8.3 For a boundary point, find the nearest non-boundary point and assign it to the cluster in which the non-boundary point is located.

[0065] The present invention has the following beneficial effects:

[0066] This method is based on the idea of ​​DPC clustering algorithm, which divides attributes according to user behavior data characteristics. Compared with deep learning-based classification methods, it does not require prior category labeling and extensive training. Compared with directly using DPC clustering, this method requires fewer parameters, has strong adaptability, and a high degree of automation in the clustering process. It can automatically determine the classification categories based on the characteristics of data distribution, without the need for manual determination of attribute features or quantities. It performs particularly well when the density of user feature distribution is uneven, effectively distinguishing users. Attached Figure Description

[0067] Figure 1 This shows the data point distribution of the input data in Example 1;

[0068] Figure 2 This is a schematic diagram of the boundary points and subclusters in Example 1;

[0069] Figure 3This is a schematic diagram of direct association between subclusters;

[0070] Figure 4 This is a schematic diagram of indirect association between subclusters;

[0071] Figure 5 This is a schematic diagram showing the lack of association between subclusters.

[0072] Figure 6 This is a schematic diagram of cluster center decision-making in Example 1;

[0073] Figure 7 This is a schematic diagram of the clustering structure in Example 1. Detailed Implementation

[0074] The following section, in conjunction with the accompanying diagram, provides a further explanation of the network user classification method based on adaptive clustering center clustering;

[0075] Example 1

[0076] Step 1, targeting Figure 1 For the dataset shown, calculate the parameters of the data distribution within the reaction set:

[0077] s1.1 Calculate the distance d(a,b) between data point a and other data points in the feature dataset D in sequence:

[0078] d(a,b)=||x a -x b ||

[0079] Where, x a Indicates the position of data point a, x b This indicates the positions of the other data points. Then, the other data points are sorted from smallest to largest based on the calculation results.

[0080] s1.2. Based on the calculation results of s1.1, select the r data points closest to data point p and put them into set NN. r In {p}:

[0081] NN r {p}={x∈D|d(p,x)≤d(p,p r )}

[0082] Where p and x are points in dataset D, p r Let r represent the r-th nearest neighbor of data point p. Then, calculate the reverse nearest neighbor (RNN) of data point p and put it into the set RNN. r In {p}:

[0083] RNN r (p)={x∈D|p∈NN r (x)}

[0084] Statistical set RNN r The number of points in {p}. Starting with 2, the step size is r, up to the set RNN. r {p} and set RNN r-1 The number of points in {p} is equal, or the set is an RNN. r If {p} is not an empty set, then the value of r at this point is recorded as the optimal value of K:

[0085]

[0086] Set RNN r The number of points in the {p} denoted as the reverse nearest neighbor weights of data point p in an RNN. K _weight(p). The maximum reverse nearest neighbor weight of all data points is denoted as the maximum mutual neighbor value Mmn of the dataset.

[0087] s1.3 Calculate the ratio of the reverse nearest neighbor weight of data point p to the sum of the Euclidean distances between its optimal_K nearest neighbors, and use this ratio as the initial density Initial_ρ(p) of data point p:

[0088]

[0089] Where K = optimal_K.

[0090] Calculate the sum of the initial densities of data point p and its optimal_K nearest neighbors, which is taken as the resultant density ρ(p) of data point p:

[0091]

[0092] Step 2: Based on the calculation results of Step 1, determine the noise points and boundary points in the dataset:

[0093] s2.1. Traverse each data point in dataset D, and discard data points with an initial density of zero as noise points. s2.2. Calculate the local distance ratio ω(p) of the maximum mutual neighbors of data point p:

[0094]

[0095] The set NN Mmn {p} represents the set of the Mmn nearest data points to data point p, and d(q,q) Mmn ) represents the relationship between data point q and its nearest Mmn-th data point q. MmnThe remaining points in dataset D are sorted from largest to smallest based on the ratio of local distances between their largest mutual neighbors and their combined density. The last θ×100% of the data points are placed into sets Set1 and Set2, respectively. The points in set bp are considered as boundary points.

[0096] bp={p∈Set1∩Set2}

[0097] Step 3: Based on the sum density of the data points, find the parent node for each data point using the density peak clustering assignment rule:

[0098]

[0099] Data points without parent nodes are used as representative points of the sub-clusters, rep(Sc). i ):

[0100]

[0101] Sc i ={p1,p 2, p3,…rep(Sc i )}

[0102] The representative point rep(Sc) of the sub-cluster i ) and its child nodes are grouped into a sub-cluster. For example Figure 2 As shown, each point is connected to its parent node by dashed lines. The data points connected by intersecting dashed lines form a sub-cluster, and the intersection of the dashed lines is the representative point of the sub-cluster. Figure 2 Points not connected by dashed lines are boundary points.

[0103] Step 4: Calculate the sub-clusters Sc respectively i For each data point, the K nearest neighbors set is used as the union of the subclusters Sc. i extended subclusters extend_Sc i :

[0104]

[0105] Then calculate the intersection of the extended subclusters between different subclusters:

[0106] SN(Sc i ,Sc j ) = extend_Sc i ∩extend_Sc j

[0107] Set SN(Sc) i ,Sc j The data points in ) are called subclusters Sc i With sub-clusters Scj Shared neighbors.

[0108] Step 5: Calculate the distance between the variable spatial transformations of the representative points of different subclusters:

[0109] s5.1 Calculate the Euclidean distance d(rep(Sc) between representative points of different subclusters. i ),rep(Sc j )):

[0110] d(rep(Sc i ),rep(Sc j ))=||rep(Sc i ),rep(Sc j )||

[0111] s5.2. Enclose all data points in a subcluster using a closed curve. Use solid circles to represent representative points of the subcluster, dashed hollow circles to represent shared neighbors between subclusters, and solid hollow circles to represent other data points. Calculate the variable spatial transformation distance between representative points of each subcluster according to their inter-subcluster relationships:

[0112] (1) As Figure 3 As shown, sub-cluster Sc i With sub-clusters Sc j There are shared neighbors, i.e., |SN(Sc) i ,Sc j If |≠0, then the subcluster Sc i With sub-clusters Sc j The direct association represents the variable spatial transformation distance between its representative points as follows:

[0113]

[0114] (2) Figure 4 As shown, sub-cluster Sc i With sub-clusters Sc j There are no shared neighbors, but there are subclusters Sc. o ,Sc l , where sub-clusters Sc o With Sc i There are shared neighbors, subclusters Sc l With Sc j There are shared neighbors, and the sub-cluster Sc o With Sc l There are also shared neighbors between subclusters. Therefore, by utilizing the shared neighbors between each pair of subclusters, the subcluster Sc can be improved. i Reaching the subcluster Sc via path Path(i,j)={i,o,l,j} j Then the sub-cluster Sc i With sub-clusters Sc jIndirect association, representing the variable spatial transformation distance between points, is:

[0115]

[0116] (3) Figure 5 As shown, sub-cluster Sc i with sub-clusters Sc j If they are neither directly nor indirectly related, then the variable spatial transformation distance between their representative points is:

[0117] SNS(rep(Sc i ),rep(Sc j ))=MaxD×(1+d(rep(Sc i ),rep(Sc j )))

[0118] Where MaxD is the maximum distance between all representative points of the subclusters.

[0119] Step 6: Based on the transformed distance obtained in Step 5, and combined with the resultant density, calculate the upward distance of the representative point of the sub-cluster.

[0120]

[0121] Representative points of subclusters whose upward distance is greater than the threshold MaxD are retained as cluster centers, such as... Figure 6 As shown, the number of cluster centers retained is the number of clusters, which is 2 in this embodiment.

[0122] Step 7: Assign subclusters and boundary points whose upward distance from the representative point is less than the threshold:

[0123] s7.1 Calculate the similarity SIM(Sc) between subclusters i ,Sc j ):

[0124]

[0125] Where Θ(Sc i ,Sc j The ) represents the average density difference between subclusters:

[0126]

[0127] The average combination density of subclusters:

[0128]

[0129] s7.2 For subclusters whose upward distance from the representative point is less than the threshold, assign them to the cluster class with the highest similarity to them.

[0130] s7.3 For a boundary point, find the nearest non-boundary point and assign it to the cluster containing that non-boundary point. The result is as follows: Figure 7 As shown, Figure 1 The data points were divided into two categories: data points represented by solid circles were clustered with solid asterisks, and data points represented by hollow circles were clustered with hollow asterisks.

[0131] Example 2

[0132] Clustering was performed on the dataset shown in Table 1 using the method proposed in this application and commonly used methods in the prior art.

[0133]

[0134] Table 1

[0135] To demonstrate the effectiveness of this method, commonly used clustering performance evaluation metrics in the art, such as the F-value, Normalized Mutual Information (NMI), and Adjusted Rand Index (ARI), were selected to evaluate the clustering results in the examples.

[0136] The F-value is between [0,1]. The closer the value is to 1, the more accurate the clustering result is.

[0137] The NMI value ranges from 0 to 1. The closer the value is to 1, the better the clustering performance.

[0138] The ARI value is between -1 and 1. The closer the value is to 1, the more accurate the clustering result is.

[0139] The comparison results of F-values, NMI values, and ARI values ​​of different clustering methods on different datasets are shown in Tables 2, 3, and 4:

[0140]

[0141]

[0142] Table 2

[0143]

[0144] Table 3

[0145]

[0146] Table 4.

Claims

1. A network user classification method based on adaptive clustering center clustering, characterized in that: Specifically, the following steps are included: Step 1: Obtain user behavior data from the online platform, extract features from the user behavior data, and construct a feature dataset D; Step 2: For each data point in the feature dataset D, calculate its distance to other data points, then sort them by distance to obtain the r-nearest neighbor set and the reverse r-nearest neighbor set for each data point. Continuously increase the value of r until the reverse r-nearest neighbor set is not empty, or the size of the reverse r-nearest neighbor set remains unchanged before and after increasing the value of r. Record this value of r as the optimal K value (optimal_K), and the size of the reverse r-nearest neighbor set as the reverse nearest neighbor weight RNN for that data point. K _weight(p) defines the initial density of the data point as the ratio of the reverse nearest neighbor weight of the data point to the sum of the distances between its optimal_K nearest neighbors, and the combined density as the sum of the initial densities of the data point and its optimal_K nearest neighbors; calculate the reverse nearest neighbor weights of all data points, and record the maximum value as the maximum mutual neighbor value Mmn of the dataset D. Step 3: Traverse each data point in dataset D, discarding data points with an initial density of zero as noise points; for the remaining data points, calculate the local distance ratio ω(p) of the maximum mutual neighbors in sequence: The set NN Mmn {p} represents the set of the Mmn nearest data points to data point p, and d(q,q) Mmn ) represents the relationship between data point q and its nearest Mmn-th data point q. Mmn The remaining points in dataset D are sorted in descending order of the ratio of local distances between their largest mutual neighbors and the sum density value. The last θ×100% of the data points are placed into sets Set1 and Set2 respectively, and the points in set bp are regarded as boundary points. bp={p∈Set1∩Set2} Step 4: Based on the sum density of the data points, find the parent node for each data point using the density peak clustering assignment rule: Data points without parent nodes are used as representative points of the sub-clusters, rep(Sc). i ): Sc i ={p1,p2,p3,…rep(Sc i )} The representative point rep(Sc) of the sub-cluster i ) and its child nodes are grouped into a sub-cluster; Step 5: Calculate the sub-cluster Sc respectively i For each data point, the K nearest neighbors set is used as the union of the subclusters Sc. i extended subclusters extend_Sc i : Then calculate the intersection of the extended subclusters between different subclusters: SN(Sc i ,Sc j )=extend_Sc i ∩extend_Sc j Set SN(Sc) i ,Sc j The data points in ) are called subclusters Sc i With sub-clusters Sc j Shared neighbors; Step 6: Calculate the distance d(rep(Sc) between representative points of different subclusters. i ),rep(Sc j Determine the correlation and perform a variable spatial distance transformation: S6.1, Subcluster Sc i With sub-clusters Sc j There are shared neighbors, i.e., |SN(Sc) i ,Sc j If |≠0, then the subcluster Sc i With sub-clusters Sc j The direct association represents the variable spatial transformation distance between its representative points as follows: S6.2, If subclusters Sc i With sub-clusters Sc j There are no shared neighbors between them, but there are other subclusters such that subcluster Sc i Able to reach sub-cluster Sc through shared neighbors with other sub-clusters j Then the sub-cluster Sc i With sub-clusters Sc j Indirect association, representing the variable spatial transformation distance between points, is: Where o and l are the preceding and following nodes on the path Path(i,j), and Path(i,j) represents the subcluster Sc i Reaching subcluster Sc via shared neighbors with other subclusters j The path; S6.3, Subcluster Sc i With sub-clusters Sc j If they are neither directly nor indirectly related, then the variable spatial transformation distance between their representative points is: SNS(rep(Sc i ),rep(Sc j ))=MaxD×(1+d(rep(Sc i ),rep(Sc j ))) Where MaxD is the maximum distance between all sub-cluster representative points; Step 7: Based on the transformed distance obtained in Step 6, and combined with the resultant density, calculate the upward distance of the representative point of the sub-cluster. Representative points whose upward distance is greater than the threshold MaxD are retained as cluster centers; the number of retained cluster centers is the number of clusters. Step 8: Calculate the similarity SIM(Sc) between subclusters. i ,Sc j For subclusters whose upward distance from the representative point is less than the threshold, they are assigned to the cluster with the highest similarity. For boundary points, the nearest non-boundary point is found and assigned to the cluster in which the non-boundary point is located. Users in the same cluster are assigned the same attribute label to complete the classification of behavioral features of all users.

2. The network user classification method based on adaptive clustering center clustering as described in claim 1, characterized in that: The online platform mentioned is an e-commerce platform, a social platform, or a multimedia video platform.

3. The network user classification method based on adaptive clustering center clustering as described in claim 1, characterized in that: The specific process of step 2 is as follows: S2.1 Calculate the distance d(a,b) between data point a and other data points in the feature dataset D in sequence: d(a,b)=||x a -x b || Where, x a Indicates the position of data point a, x b Indicate the positions of other data points; then sort the other data points from smallest to largest according to the calculation results; S2.

2. Based on the calculation results of s1.1, select the r data points closest to data point p and put them into set NN. r In {p}: NN r {p}={x∈D|d(p,x)≤d(p,p r )} Where p and x are points in dataset D, p r Let r represent the r-th nearest neighbor of data point p; then calculate the reverse nearest neighbor (RNN) of data point p and put it into the set RNN. r In {p}: RNN r (p)={x∈D|p∈NN r (x)} Statistical set RNN r The number of points in {p}; starting with 2, stepping r, until the set RNN is reached. r {p} and set RNN r-1 The number of points in {p} is equal, or the set is an RNN. r If {p} is not an empty set, then the value of r at this point is recorded as the optimal value of K: Set RNN r The number of points in the {p} denoted as the reverse nearest neighbor weights of data point p in an RNN. K _weight(p); The maximum reverse nearest neighbor weight of all data points is denoted as the maximum mutual neighbor value Mmn of the dataset; S2.3 Calculate the ratio of the reverse nearest neighbor weight of data point p to the sum of the Euclidean distances between its optimal_K nearest neighbors, and use this ratio as the initial density Initial_ρ(p) of data point p: Where K = optimal_K; Calculate the sum of the initial densities of data point p and its optimal_K nearest neighbors, which is taken as the resultant density ρ(p) of data point p:

4. The network user classification method based on adaptive clustering center clustering as described in claim 1, characterized in that: Define the similarity between subclusters SIM(Sc) i ,Sc j )for: Where Θ(Sc i ,Sc j The ) represents the average density difference between subclusters: The average combination density of subclusters:

Images