Overlapping clustering method, system, and medium based on hypergraph cover

Abstract

The application provides an overlapping clustering method and system based on hypergraph covering and a medium, relates to the technical field of complex networks, and the method comprises the following steps: acquiring a sample set, constructing at least two types of relation view hypergraphs, the hypergraphs comprising a semantic neighborhood hypergraph and a factor-induced hypergraph; representing the samples to a concept space shared by the semantic neighborhood hypergraph and the factor-induced hypergraph, obtaining a concept covering representation of the samples; determining an adaptive overlapping budget interval of each sample according to the local density of each sample and the cross-relation divergence in different views; constructing a joint optimization objective function, alternatingly and iteratively optimizing the joint optimization objective function; determining a final concept set to which each sample belongs according to the concept covering representation and the adaptive overlapping budget interval of each sample after optimization, and outputting an overlapping clustering result. The application solves the problems of sample overlapping attribution description, high-order relation fusion utilization and high-dimensional sparse data processing efficiency.

Description

Technical Field

[0001] This invention relates to the field of complex network technology, and in particular to an overlapping clustering method, system, and medium based on hypergraph covering. Background Technology

[0002] Cluster analysis is an important unsupervised learning method that aims to automatically discover the potential organizational structure of data based on the similarity between samples in the absence of human annotation.

[0003] To meet the representation needs of overlapping data, existing techniques have proposed fuzzy clustering, overlapping clustering, and nonnegative decomposition methods, allowing samples to be associated with multiple clusters simultaneously. While these methods overcome the single-attribution limitation to some extent, most still rely primarily on pairwise similarity relationships between samples or on global low-rank decomposition results, and are insufficient for characterizing the high-order group relationships prevalent in complex data. When multiple samples jointly form stable local groups, semantic groups, or functional groups, edges in ordinary graph models can only connect two nodes, making it difficult to directly express the holistic nature of multi-dimensional relationships. In contrast, a hyperedge in a hypergraph can connect multiple samples simultaneously, making it more suitable for describing local clusters, co-occurrence structures, cooperative relationships, and nonlinear high-order neighborhoods, and is therefore increasingly used in clustering modeling.

[0004] Existing hypergraph clustering methods typically construct hyperedges using nearest neighbor relationships, mutual nearest neighbor relationships, representative point relationships, sparse representations, or matrix factorization results, and then combine these with hypergraph Laplacian regularization, splitting criteria, label propagation, or embedding learning to achieve cluster optimization. While these methods have advantages in representing higher-order relationships, they still have shortcomings when handling complex overlapping data. Firstly, most of the higher-order relationships used in existing methods are fixed and participate in subsequent learning after the hypergraph is constructed. Different relationship construction methods and the resulting structures often differ in reliability and are easily affected by noise, outliers, local density unevenness, and parameter settings. Without an effective differentiation mechanism, low-quality relationships may be continuously propagated during the optimization process, thus interfering with the clustering results. Secondly, existing hypergraph construction methods usually emphasize one type of relationship information, such as local neighborhood relationships, representative point attraction relationships, or decomposition response relationships, making it difficult to simultaneously consider the cluster core structure, inter-cluster transition regions, and global reference relationships. For boundary samples located at the intersection of different potential clusters, there is also a lack of more detailed higher-order relationship representation, thus failing to fully reflect their overlapping characteristics.

[0005] Furthermore, many overlapping clustering methods use uniform thresholds, uniform sparsity constraints, or uniform coverage upper limits to control the degree to which samples participate in multiple clusters. While these methods are relatively simple to implement, they ignore the differences in the local structure of samples. In real-world data, core cluster samples usually have a clear single-cluster affiliation, while samples located in sparse regions, boundary regions, or semantic transition regions are more likely to be associated with multiple clusters simultaneously. Applying uniform overlapping constraints to all samples makes it difficult to accurately reflect the true coverage requirements of different samples. Meanwhile, existing techniques often use binary sample-hyperedge association matrices as high-order structure inputs, only characterizing whether a sample is connected to a hyperedge, making it difficult to further characterize the strength of a sample's participation in the potential group structure and the uncertainty of its boundaries. In high-dimensional sparse data scenarios such as text, image semantics, and medical coding, the relationship between samples and local groups often exhibits both continuity and uncertainty; simple binary representations easily lose important structural information.

[0006] In multi-relation or multi-view fusion scenarios, existing methods typically integrate multi-source information through fixed weighting, shared low-dimensional representations, or joint decomposition. However, different relation construction methods do not consistently represent the sample structure. Without an effective characterization of the differences in contributions from different relations, low-quality relations can easily interfere with the final clustering results. Some methods directly perform joint optimization on the sample-level representation space. Under conditions of high-dimensional sparse data or large-scale samples, the variable size and computational cost increase rapidly with the number of samples, thus limiting the algorithm's computational efficiency and scalability. Even when using shared representations or joint decomposition, existing multi-view methods often focus on the consistency of the representation layer, lacking consistency calibration for the interpretation results of potential concepts under different relation views. This can easily lead to different views forming offset representations of the same overlapping structure. Therefore, for overlapping clustering tasks with complex high-dimensional sparse data, existing overlapping clustering, hypergraph clustering, and multi-view clustering methods still have shortcomings in characterizing sample overlap attribution, utilizing higher-order relations, and improving the efficiency of high-dimensional sparse data processing. These technical problems still need further resolution. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides an overlapping clustering method, system, and medium based on hypergraph covering, which overcomes the shortcomings of existing overlapping clustering, hypergraph clustering, and multi-view clustering in characterizing sample overlap, utilizing high-order relationships, and improving the efficiency of high-dimensional sparse data processing.

[0008] In a first aspect, embodiments of the present invention provide an overlapping clustering method based on hypergraph covering, comprising: Obtain a sample set and construct a hypergraph with at least two types of relational views, including a semantic neighborhood hypergraph and a factor-induced hypergraph; By representing samples onto a concept space shared by a semantic neighborhood hypergraph and a factor-induced hypergraph, a concept-covered representation of the samples is obtained. The adaptive overlap budget interval for each sample is determined based on the local density of each sample and the degree of cross-relation divergence in different views. Construct a joint optimization objective function and iteratively optimize the joint optimization objective function alternately. Based on the optimized concept coverage representation and adaptive overlap budget interval for each sample, the final concept set to which each sample belongs is determined, and the overlap clustering results are output.

[0009] Optional, the construction of the semantic neighborhood hypergraph includes: Perform semantic embedding on the samples; Determine the representative center in the embedded space; A hyperedge is formed by selecting samples that are semantically close to the representative center.

[0010] Optional, the construction of factor-induced hypergraphs includes: Matrix decomposition is performed on the sample set to obtain the response intensity of the sample on multiple latent factors; Select the samples with the highest latent factor response intensity to form a hyperedge; Remove invalid out-of-bounds edges.

[0011] Optionally, the process of obtaining the concept coverage representation of the sample includes: The local weighted mapping from the sample to the representative point is calculated based on the distance between the sample and the representative point in the embedding space; the sample is associated with multiple representative points that are closest to it.

[0012] Optional, the construction of adaptive overlapping budget intervals includes: The base budget value is calculated based on the local density and cross-relational divergence of the sample; the local density of the sample is calculated based on the average distance between the sample and its neighboring samples in the embedding space; the cross-relational divergence is calculated based on the degree of difference in the number of edges the sample participates in in the semantic neighborhood hypergraph and the factor-induced hypergraph. The baseline budget value is truncated globally and constrained by the minimum interval. The baseline budget value is negatively correlated with local density and positively correlated with the degree of difference in participation.

[0013] Optionally, the construction of the reconstruction loss includes: Based on the concept coverage representation of samples and the concept routing representation of hyperedges, the association probability between samples and hyperedges is calculated. Sample-hyperedge pairs that actually belong to the hyperedge are taken as positive samples. Unconnected samples are selected as hard negative samples based on the concept coverage similarity or embedding space distance between the sample and the samples within the hyperedge. A loss that distinguishes between positive and negative samples is constructed.

[0014] Optional, cross-view Figure 1 Consistency constraints include: The conceptual evidence is normalized based on the degree of participation of the samples in the semantic neighborhood hypergraph and the factor-induced hypergraph, as well as the view size, to obtain the normalized conceptual evidence of the semantic neighborhood hypergraph and the factor-induced hypergraph. We obtain global consensus evidence by weighted fusion of normalized conceptual evidence from semantic neighborhood hypergraphs and factor-induced hypergraphs; and constrain the differences between normalized conceptual evidence from each view and global consensus evidence.

[0015] Optionally, when determining the final concept set to which each sample belongs, the elements in the concept coverage vector of the sample are sorted by intensity, the number of selected concepts is determined according to the adaptive overlap budget interval of the sample, and the corresponding number of concepts with the highest intensity are taken as the overlap clustering result of the sample.

[0016] Secondly, embodiments of the present invention also provide an overlapping clustering system based on hypergraph covering, comprising: The acquisition unit is used to acquire a sample set and construct a hypergraph with at least two types of relational views, including a semantic neighborhood hypergraph and a factor-induced hypergraph. The first determining unit is used to represent the sample into a concept space shared by the semantic neighborhood hypergraph and the factor-induced hypergraph, so as to obtain the concept-covered representation of the sample. The second determining unit is used to determine the adaptive overlap budget interval for each sample based on the local density of each sample and the consistency of participation in different hypergraphs. The optimization unit is used to construct the joint optimization objective function and iteratively optimize the joint optimization objective function alternately. The output unit is used to determine the final concept set to which each sample belongs based on the optimized concept coverage representation and adaptive overlap budget interval, and outputs the overlap clustering results.

[0017] Thirdly, embodiments of the present invention also provide a computer-readable storage medium storing computer instructions that cause a computer to perform an overlapping clustering method based on hypergraph covering as described in the first aspect or any embodiment of the first aspect.

[0018] The embodiments of the present invention bring the following beneficial effects: The hypergraph-based overlapping clustering method provided in this invention is designed for data objects with multiple semantic, attribute, label, or multi-functional attribution features. It constructs two complementary views—a semantic neighborhood hypergraph and a factor-induced hypergraph—and combines a sample adaptive overlap budget mechanism with cross-viewing under a shared concept space. Figure 1The consistency constraint and the two-layer mapping structure from samples to representative points and concepts enable joint modeling of local and global high-order relationships in complex data. It can flexibly control the degree of overlap based on the sample density and cross-view participation differences, and suppress low-quality view interference through dynamic view weights. It has significant beneficial effects on improving clustering accuracy, multi-view fusion robustness, computational efficiency and output stability.

[0019] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0021] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0022] Figure 1 A flowchart illustrating the overlapping clustering method based on hypergraph covering provided in an embodiment of the present invention; Figure 2 A flowchart illustrating an overlapping clustering method based on hypergraph covering, provided in another embodiment of the present invention; Figure 3 This is a detailed framework diagram of the overlapping clustering process in another embodiment of the present invention; Figure 4 This is a structural block diagram of an overlapping clustering system based on hypergraph covering provided in an embodiment of this application. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] In multi-relation or multi-view fusion scenarios, existing methods typically integrate multi-source information through fixed weighting, shared low-dimensional representations, or joint decomposition. However, different relation construction methods do not consistently represent the sample structure. Without an effective characterization of the differences in contributions from different relations, low-quality relations can easily interfere with the final clustering results. Some methods directly perform joint optimization on the sample-level representation space. Under conditions of high-dimensional sparse data or large-scale samples, the variable size and computational cost increase rapidly with the number of samples, thus limiting the algorithm's computational efficiency and scalability. Even when using shared representations or joint decomposition, existing multi-view methods often focus on the consistency of the representation layer, lacking consistency calibration for the interpretation results of potential concepts under different relation views. This can easily lead to different views forming offset representations of the same overlapping structure. Therefore, for overlapping clustering tasks with complex high-dimensional sparse data, existing overlapping clustering, hypergraph clustering, and multi-view clustering methods still have shortcomings in characterizing sample overlap attribution, utilizing higher-order relations, and improving the efficiency of high-dimensional sparse data processing. These technical problems still need further resolution.

[0025] To facilitate understanding of this embodiment, a detailed description of an overlapping clustering method based on hypergraph covering disclosed in this embodiment of the invention will be provided first.

[0026] The embodiments of this invention are applicable to data analysis scenarios where samples have multiple semantic, multiple attribute, multiple label, or multiple functional attribution features. They can be used for multi-label learning, overlapping community discovery in social networks, multifunctional gene clustering in bioinformatics, multi-interest group identification in recommendation systems, and overlapping clustering analysis of multi-source heterogeneous data such as text, images, and logs.

[0027] Figure 1 This is a flowchart illustrating an overlapping clustering method based on hypergraph covering provided in an embodiment of the present invention. Figure 1 As shown, the method may include: S102: Obtain a sample set and construct a hypergraph of at least two types of relation views, including a semantic neighborhood hypergraph and a factor-induced hypergraph.

[0028] To facilitate the description of the embodiments of this application, the concepts and symbols used in this application are defined.

[0029] In this embodiment of the application, given a high-dimensional sparse dataset arriving in chronological order... in, For the sample size, denoted as the feature dimension. It should be noted that in the embodiments of this application, each sample can simultaneously belong to multiple latent concepts, and the clustering results of the samples are represented in an overlapping manner.

[0030] Let the set of common nodes be Build on this set of nodes A hypergraph with relational views. The hypergraph representation corresponding to each relational view is:

[0031] in, For the first A set of superedges in a relational view. The number of super edges of this view:

[0032] This is the sample-hyperedge correlation matrix. When the sample... Belongs to superedge hour, ,otherwise To reduce the computational scale of direct optimization on the sample-level concept coverage matrix, a method is introduced... Let there be _n_ representative points, and denote the set of representative points as:

[0033] Define the sample-representative point transfer matrix as follows:

[0034] in, Indicates sample To the representative point Local transitive weights. The representative point-concept basis matrix is ​​defined as:

[0035] in, For the number of potential concepts, Indicates representative point On the concept The contribution strength. Based on this, a sample-concept coverage matrix is ​​constructed:

[0036] in, Indicates sample Concept Coverage strength. For each relationship view. Define the hyperedge-concept routing matrix:

[0037] in, Indicates the first In the first relation view Superedge and Concept The correlation strength. To ensure concept scale stability, the representative point-concept basis matrix is... Apply normalization constraints to each column:

[0038] Further define the sample The total coverage is:

[0039] An adaptive overlap budget interval is set for each sample. ,in and Representing samples respectively The minimum coverage requirement and maximum coverage tolerance are determined. A mutual nearest neighbor graph is constructed in the semantic embedding space, and its graph Laplacian matrix is ​​denoted as:

[0040] in, The graph weight matrix, This is the degree matrix. This term is used to constrain similar samples to have similar concept coverage representations.

[0041] In the sample set After input, first in the same node set Two complementary high-order relation hypergraphs are constructed: a semantic neighborhood hypergraph to describe local semantic neighborhood relations, and a factor-induced hypergraph to describe factor collaborative response relations.

[0042] First, a semantic neighborhood hypergraph is constructed, which can represent the local clustering patterns between a sample and its semantically most similar neighboring samples. It reflects the local manifold structure of the data, captures the local adjacency and short-range correlation of samples, but the hyperedges allow for the simultaneous modeling of higher-order interactions between multiple samples.

[0043] For raw data Perform low-dimensional semantic embedding to obtain

[0044] in, It is a low-dimensional semantic embedding matrix. For embedding mapping, In the embedding space, calculate the k-nearest neighbors of the sample to obtain... Representative centers:

[0045] For each center Take its position in the embedded space The nearest neighbor samples form a semantic hyperedge, that is:

[0046] The semantic neighborhood hypergraph, composed of all semantic hyperedges, has its correlation matrix denoted as:

[0047] Then, a factor-induced hypergraph is constructed based on the response strength of samples to several latent factors, such as those obtained through matrix factorization, topic modeling, prototype clustering, or the hidden layers of an autoencoder. If a group of samples exhibits high responses to the same factor or the same set of factors—for example, if they jointly activate a topic, share a latent feature dimension, or belong to the same cluster—then these samples form a hyperedge. The factor-induced hypergraph expresses the collaborative response relationship between samples due to the sharing of latent driving factors. This relationship may span local neighborhoods, connecting samples that are geographically distant but have similar factor patterns in the feature space.

[0048] For the original data matrix Performing nonnegative matrix decomposition, we obtain:

[0049] in, The number of factors. For For each column, select the column with the largest activation value. Each sample is used as a factor-induced hyperedge, that is:

[0050] After filtering out excessively small, excessively large, and duplicate hyperedges, the factor-induced hypergraph is obtained, and its correlation matrix is ​​denoted as:

[0051] Therefore, embodiments of the present invention obtain two types of relation views on the same set of nodes:

[0052] Here, sem is a semantic neighborhood hypergraph, and fac is a factor-induced hypergraph, which provides complementary high-order relation inputs for subsequent overlapping clustering.

[0053] S104: Represent the sample in the shared concept space of the semantic neighborhood hypergraph and the factor-induced hypergraph to obtain the concept-covered representation of the sample.

[0054] To avoid large-scale optimization directly on the sample-level coverage matrix, this embodiment of the invention introduces a representative point transfer mechanism, decomposing the sample coverage representation into two parts: local transfer from sample to representative point and global base representation from representative point to concept. First, in the embedding space... Selected from Representative points:

[0055] Representative points can be generated from cluster centers, density peaks, or representative samples. For each sample... Only the most recent one is retained. Let there be _n_ representative points, and denote their index set as _n_{i=1}_{i Define the sample-representative point transfer weight as follows:

[0056] in, For the sample Representation in the embedding space, Let be the scale parameter. For a sparse and row-normalized matrix, satisfying

[0057] In one implementation of this invention, the matrix Once determined by the aforementioned local distance relationships, they can be kept fixed, requiring only optimization. and In another implementation, while keeping the support of the nearest representative point unchanged, [the following can be done]: Local fine-tuning is performed, and the model is reprojected onto the probabilistic simplex after each iteration. Preferably, the model is... It is a fixed matrix.

[0058] Furthermore, initialize the representative point-concept basis matrix:

[0059] This constructs the sample-concept coverage matrix. :

[0060] Among them, the OK Indicates sample exist A latent conceptual distribution of coverage intensity. This representation preserves the local structure of the samples while significantly reducing the size of the variable to be optimized.

[0061] S106: Determine the adaptive overlap budget interval for each sample based on the local density of each sample and the cross-relational divergence in different hypergraphs.

[0062] In this embodiment, to overcome the bias caused by applying uniform overlap constraints to all samples in existing methods, this embodiment generates an adaptive overlap budget interval for each sample based on the sample's local density and the cross-relationship divergence degree in different hypergraphs.

[0063] First, the samples are computed in the embedding space. Local density:

[0064] in, Indicates sample of nearest neighbor set Let be the density scale parameter. Secondly, to eliminate the influence of differences in hyperedge scale between different relational views, define the sample at the _________. The normalized participation in each relational view is:

[0065] Let its average participation rate across relationships be:

[0066] Then the sample Cross-relationship divergence is defined as:

[0067] in, This is a stable term. Further normalization is performed on the local density and divergence:

[0068] Then define the sample The minimum coverage budget and the maximum coverage budget are respectively:

[0069] in, Indicates will Cut off to interval Inside, To control parameters, and to ensure the validity of the budget interval, a minimum interval constraint is further applied:

[0070] in, This is the preset minimum budget interval. Therefore, for samples with high local density and small cross-relational discrepancies in the cluster core region, the coverage budget tends to be tighter; while for samples in boundary regions, sparse regions, or with inconsistent cross-relational expressions, a wider overlap coverage is allowed, which is more in line with the actual data structure.

[0071] After obtaining the sample-concept coverage matrix Then, for each relationship view Further study of the hyperedge-concept routing matrix, represented as:

[0072] To establish a continuous association path between sample, concept, and hyperedge. For the ... Any sample in a relation view With super-edge The probability of continuous association is defined as:

[0073] in, for The OK, For the first The bias term corresponding to each superedge, For temperature parameters, For the Sigmoid function. This is achieved by introducing a bias term. This allows the association probability to cover The entire interval is considered to avoid the prediction result being limited to above 0.5 due to the non-negative inner product. Let the set of positive correlations be:

[0074] To enhance the model's ability to distinguish similar but unconnected samples, for each hyperedge... Select the most easily confused samples from those not yet entered by the edge. These samples constitute the difficult negative sample set. Among them, difficult negative samples can be screened based on the distance between the sample and the hyperedge center, the similarity of representative point representation, or the similarity of concept coverage. Therefore, the first The reconstruction loss of a relational view is defined as:

[0075] in, This is used to assign weights to difficult negative samples. This term can simultaneously enhance the ability to preserve true high-order relations and suppress spurious relations.

[0076] To avoid interference with the final clustering results when different relation views have inconsistent quality, this embodiment of the invention introduces a relation contribution adjustment mechanism and further imposes consistency constraints on conceptual evidence under different relations. To eliminate the direct impact of node degree and view size on conceptual evidence, the first... Samples in a relational view On the concept The normalization evidence is as follows:

[0077] Therefore, we obtain the first... Normalized conceptual evidence matrix of relational views:

[0078] Define the globally weighted consensus evidence matrix as follows:

[0079] in, For the first The contribution weights of each relational view satisfy:

[0080] Cross-relationship concept consistency loss is defined as:

[0081] Simultaneously, based on the current reconstruction quality and consistency deviation of each relation view, the relation contribution weights are adaptively updated. Define the... The quality metrics for each relational view are:

[0082] in, Let be the balancing coefficient. Then the relation weights are updated as follows:

[0083] in, For temperature parameters. Therefore, a higher-quality relationship view that is more consistent with the global conceptual interpretation will receive a greater contribution weight.

[0084] S108: Construct a joint optimization objective function and iteratively optimize the joint optimization objective function alternately.

[0085] Based on the above, this embodiment of the invention constructs a joint optimization objective. The overall objective function is: The graph smoothing term is:

[0086] The constraint term used to constrain neighboring samples in the embedding space to have similar concept coverage representations is: The sample adaptive overlap budget constraint term is:

[0087] in, This is used to ensure that the total sample coverage is within its adaptive budget interval; the representative point-concept decorrelation term is:

[0088] in , This represents the off-diagonal portion after setting the diagonal elements to zero. This item is used to suppress redundant correlations between different concepts.

[0089] The objective function satisfies the following constraints:

[0090] This embodiment of the invention employs an alternating iterative method to solve the above objective function. Initialization , , and Then, repeat the following steps until convergence.

[0091] First, update the sample coverage matrix based on the current... and ,calculate:

[0092] Next, update the hyperedge-concept routing matrix and bias terms, and fix them. , and For each relation view and Update using gradient descent, and denote the intermediate variable as...

[0093] Then perform nonnegative projection and line truncation to obtain

[0094] in, and Step size, This indicates that the first line of each row should be retained. Set the largest element, and set the rest of the elements to zero.

[0095] Update the representative point-concept basis matrix again, and fix it. , and Update by gradient descent :

[0096] And perform nonnegative projection, column normalization, and sparse truncation: in, This indicates column-based normalization. This indicates that the first line of each row should be retained. The largest element.

[0097] Then fine-tune the optional sample-representative point transfer matrix, the matrix Keep it fixed and do not participate in subsequent optimizations. After fixing the nearest representative point mask, it can be optimized using the following formula. Make local fine-tuning:

[0098] And perform nonnegative projection and probabilistic simplex projection under the constraint of local representative point mask:

[0099] in, This is the nearest representative point mask matrix. This represents the Hadamard product. This indicates that the projection is done row by row onto the probability simplex.

[0100] Finally, update the relationship contribution weights based on the current quality metrics of each relationship view. Update contribution weights as follows:

[0101] When the change in the objective function between two consecutive iterations is less than a preset threshold Or reach the maximum number of iterations Stop iterating when the time is right.

[0102] S110: Based on the optimized concept coverage representation and adaptive overlap budget interval of each sample, determine the final concept set to which each sample belongs and output the overlap clustering results.

[0103] After optimization, output the sample-concept coverage matrix:

[0104] For the sample First, cover the vector Sort the values ​​from largest to smallest, and record the sorted values ​​as:

[0105] Based on the total coverage of the sample and the budget range, the final number of output concepts is determined as follows:

[0106] Then select the front with the highest coverage intensity. One concept as a sample The overlapping clustering results are as follows:

[0107] This output method ensures that the final number of labels remains consistent with the adaptive budget range for the samples, while avoiding output instability caused by relying solely on a single fixed threshold. The final output includes a sample-concept coverage matrix. Hyperedge-Concept Routing Matrix of Each Relationship View Relationship contribution weight and the overlapping cluster affiliation set of each sample. .

[0108] This invention employs a collaborative modeling approach using semantic neighborhood hypergraphs and factor-induced hypergraphs, combined with a misplaced point transitive covering representation, adaptive overlap budgeting, and cross-relational concept consistency constraints. This approach enhances the stability, robustness, and interpretability of overlap clustering while maintaining the expressive power of high-order relations. The method constructs a covering representation using a sample-representative point transitive matrix and a representative point-concept basis matrix, avoiding sample-level dense optimization and making it suitable for high-dimensional sparse scenarios. The time complexity of a single iteration is approximately [missing value]. The space complexity is approximately .

[0109] As an optional implementation, the construction of a semantic neighborhood hypergraph includes: Perform semantic embedding on the samples; Determine the representative center in the embedded space; A hyperedge is formed by selecting samples that are semantically close to the representative center.

[0110] As an optional implementation method, the construction of factor-induced hypergraphs includes: Matrix decomposition is performed on the sample set to obtain the response intensity of the sample on multiple latent factors; Select the samples with the highest latent factor response intensity to form a hyperedge; Remove invalid out-of-bounds edges.

[0111] As an optional implementation, the process of obtaining the concept coverage representation of the sample includes: The local weighted mapping from the sample to the representative point is calculated based on the distance between the sample and the representative point in the embedding space; the sample is associated with multiple representative points that are closest to it.

[0112] As an optional implementation, the construction of the adaptive overlapping budget interval includes: The base budget value is calculated based on the local density and cross-relational divergence of the sample; the local density of the sample is calculated based on the average distance between the sample and its neighboring samples in the embedding space; the cross-relational divergence is calculated based on the degree of difference in the number of edges the sample participates in in the semantic neighborhood hypergraph and the factor-induced hypergraph. The baseline budget value is truncated globally and constrained by the minimum interval. The baseline budget value is negatively correlated with local density and positively correlated with the degree of difference in participation.

[0113] As an optional implementation, the construction of the reconstruction loss includes: Based on the concept coverage representation of samples and the concept routing representation of hyperedges, the association probability between samples and hyperedges is calculated. Sample-hyperedge pairs that actually belong to the hyperedge are taken as positive samples. Unconnected samples are selected as hard negative samples based on the concept coverage similarity or embedding space distance between the sample and the samples within the hyperedge. A loss that distinguishes between positive and negative samples is constructed.

[0114] As an optional implementation method, cross-view Figure 1 Consistency constraints include: The conceptual evidence is normalized based on the degree of participation of the samples in the semantic neighborhood hypergraph and the factor-induced hypergraph, as well as the view size, to obtain the normalized conceptual evidence of the semantic neighborhood hypergraph and the factor-induced hypergraph. We obtain global consensus evidence by weighted fusion of normalized conceptual evidence from semantic neighborhood hypergraphs and factor-induced hypergraphs; and constrain the differences between normalized conceptual evidence from each view and global consensus evidence.

[0115] As an optional implementation, when determining the final concept set to which each sample belongs, the elements in the concept coverage vector of the sample are sorted by intensity, the number of selected concepts is determined according to the adaptive overlap budget interval of the sample, and the corresponding number of concepts with the highest intensity are taken as the overlap clustering result of the sample.

[0116] Figure 2 A flowchart of an overlapping clustering method based on hypergraph covering provided in another embodiment of the present invention. Figure 3 This is a detailed framework diagram of the overlapping clustering process in another embodiment of the present invention.

[0117] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The present invention includes, but is not limited to, the following embodiments. Figure 2 As shown, taking bioinformatics applications as an example, the specific implementation process is as follows: In bioinformatics analysis, the same gene or protein often participates in multiple biological processes or signaling pathways simultaneously. For example, some proteins are involved in both immune responses and cell proliferation regulation, thus exhibiting overlapping affiliation characteristics across multiple clusters. Furthermore, transcriptome sequencing, proteome detection, and multi-omics joint analysis typically generate new samples continuously in batches. Re-clustering all historical samples each time would incur high computational costs and potentially disrupt existing stable cluster structures. Therefore, this invention is particularly suitable for constructing multifunctional overlapping clusters under dynamic incremental sample conditions in bioinformatics.

[0118] This embodiment uses gene functional overlap identification in bioinformatics as an example. It assumes that the objects to be analyzed are several candidate genes, each gene sample is represented by a 4-dimensional feature vector, corresponding to normalized expression response intensity, co-expression correlation, protein-protein interaction local connectivity, and functional annotation similarity score. For ease of explanation, six gene samples are selected from the sample set for illustrative demonstration, denoted as... In practical applications, the sample size can be much larger than this, and the feature dimension can also be extended to higher-dimensional transcriptome features, interaction network features, domain features, or multi-omics fusion features.

[0119] The main parameter in this embodiment can be set as: the number of nearest neighbors in the semantic neighborhood hypergraph. The number of samples retained by each hyperedge in the factor-induced hypergraph , representing the number of points number of latent concepts The number of nearest neighbor representative points retained for each sample The number of difficult negative samples selected for each superedge Sigmoid temperature parameter Difficult negative sample weights Graph smoothing weights Overlapping budget constraint weights Conceptual consistency weight Remove relevant weights Sparse regularized weights The global upper and lower bound parameters for the adaptive budget of the samples can be set. , The above parameters can be adjusted in practical applications according to the data size, sparsity, and overlap strength.

[0120] (1) Sample input and construction of the dual-relation hypergraph In this embodiment, the 4-dimensional feature vectors of the 6 gene samples are illustrated as follows:

[0121] Among them, samples and A higher response in the first two dimensions indicates that it is closer to the same potential functional group; the sample and The closer proximity in the latter two dimensions indicates that it is closer to another potential functional group; the sample and Samples that simultaneously exhibit a certain response to two types of patterns in terms of multidimensional features can be considered as potentially overlapping samples.

[0122] First, low-dimensional semantic embedding is performed on the original samples to obtain the embedding representation. A semantic neighborhood hypergraph is constructed in the embedding space based on nearest neighbor relationships. For ease of explanation, this embodiment yields three semantic hyperedges, denoted as follows:

[0123] This constitutes the association matrix of the semantic neighborhood hypergraph. .

[0124] The original data matrix is ​​then nonnegatively decomposed, and a factor-induced hypergraph is constructed based on the factor activation results. Three factor-induced hyperedges can be schematically obtained:

[0125] This constitutes the correlation matrix of the factor-induced hypergraph. It can be seen that the semantic neighborhood hypergraph is more biased towards local proximity structures, while the factor-induced hypergraph is more biased towards the collaborative response of samples on latent factors. The two provide complementary high-order relational expressions for the same set of samples.

[0126] (2) Construction of representative point transitive coverage representation Three representative points are selected in the embedding space, denoted as follows: , , In this embodiment, for ease of explanation, it can be understood as being related to the sample. , , The closest representative location. Construct a sample-representative point transfer matrix based on the distance relationship between the sample and the representative point. After normalization, we can schematically obtain:

[0127] matrix Each row of the matrix sums to 1, and each sample maintains a non-zero association with only two nearest neighbor representative points. Further initialization of the representative point-concept basis matrix is ​​then performed. And normalize them column-wise. This can be schematically written as:

[0128] The three columns correspond to the concepts respectively. , and And satisfy:

[0129] This yields the sample-concept coverage matrix:

[0130] After calculation, the coverage result in this embodiment can be approximated as follows:

[0131] The first and second rows indicate the samples. , Mainly composed of concepts Coverage; lines 3 and 4 indicate the sample , Mainly composed of concepts The lines 5 and 6 show a clear dual-concept response, indicating that they have potential overlapping properties.

[0132] (3) Sample adaptive overlap budget generation After obtaining the coverage representation Then, based on the local density of the sample Cross-relationship divergence Calculate the adaptive overlap budget interval for each sample. In this embodiment, the cluster core samples have high local density and small cross-relationship divergence, while the boundary samples... and The cross-relational discrepancies are relatively larger. After normalization and interval truncation, the following budget results can be obtained: At the same time, based on the coverage matrix Calculate the total coverage for each sample:

[0133] available:

[0134] This shows that, despite and Its total coverage is on the same order of magnitude as other samples, but its budget interval has a higher lower bound, thus allowing and requiring it to retain multiple concept attributions in the final output stage, which is consistent with its structural state in the transition region with more obvious overlapping features.

[0135] (4) Node-hyperedge continuous association modeling and relation contribution adjustment After obtaining the covering matrix Subsequently, hyperedge-concept routing matrices are learned for the semantic neighborhood view and the factor-induced view, respectively. and And introduce a bias term for each superedge. For ease of explanation, after several rounds of optimization, the routing matrix corresponding to the three hyperedges in the semantic view can be approximated as:

[0136] The corresponding bias vector can be approximated as:

[0137] The routing matrix in the factor-induced view can be approximated as:

[0138] The corresponding bias vector can be approximated as:

[0139] Therefore, according to Calculate the probability of continuous association between the sample and each hyperedge. The calculation results show that the sample and The probability of association with the first type of hyperedge is relatively high, and the sample and The probability of association with the second type of hyperedge is relatively high, while the sample and High correlations were maintained on both the third type of hyperedge and some cross-cluster hyperedges, indicating that both samples were in the potential functional crossover region under both relational views. Further based on...

[0140] A normalized conceptual evidence matrix is ​​constructed, and the relation contribution weights are updated based on the reconstruction quality and consistency deviation of each relation view. After optimization, the weights of the two relation views in this embodiment can be approximated as follows:

[0141] This indicates that the semantic neighborhood view contributes slightly more to the final clustering result in this embodiment, but the factor-induced view still provides important supplementary evidence.

[0142] (5) Final output After completing sample coverage optimization, relation routing update, budget constraint adjustment, and concept consistency calibration, according to

[0143] Determine the number of output concepts for each sample. In this embodiment,

[0144] Then, for each sample, select the one with the highest coverage intensity. This concept serves as the final result. Therefore, we obtain:

[0145] The corresponding overlapping label matrix can be written as:

[0146] Among them, the 5th line Indicates sample Simultaneously belongs to the concept and concept ; Line 6 Indicates sample Simultaneously belongs to the concept and concept .

[0147] Therefore, in this embodiment, the present invention can not only identify relatively stable core functional groups, but also retain overlapping samples located at the boundaries of different functional modules, avoiding forcibly classifying them into a single cluster, which is more in line with the characteristics of actual biological functional objects that may participate in multiple processes at the same time.

[0148] (6) Parameter settings The main parameters involved in this embodiment include: semantic nearest neighbor size. Factor super-edge size , representing the number of points Conceptual Number The number of representative points retained for each sample Difficult negative sample number Temperature parameters Difficult negative sample weights Graph smoothing weights Overlapping budget constraint weights Conceptual consistency weight Remove relevant weights and sparse regularization weights wait.

[0149] in, and It mainly affects the local extent and group size of higher-order relations in the hypergraph; larger ones It is beneficial to preserve a wider semantic neighborhood information, but if it is too large, it may introduce noisy connections; a larger It facilitates the formation of a more complete factor response group, but may also weaken the ability to distinguish boundary samples. Parameters and The main influences are the degree of compression and local preservation of the representative point representation; smaller ones. It helps reduce computational complexity, and larger This helps to enhance the smoothness of the covering representation. Parameters and The discriminant boundary that jointly determines the probability of continuous association between nodes and hyperedges; smaller It helps to differentiate between positive and negative correlations, but if the value is too small, it may result in an overly sharp numerical value. Parameter The strength of the determination of the total sample coverage following the budget interval. Determine the degree of consistency in the interpretation of concepts under different relational views. Used to suppress conceptual redundancy Used to enhance the smoothness of coverage of neighboring samples.

[0150] This embodiment illustrates the complete process of the present invention in the context of gene functional overlap identification. Specifically, it achieves stable output of sample overlap clustering results through dual-relationship hypergraph construction, representative point transitive coverage representation, adaptive overlap budget generation, node-hyperedge continuous association modeling, relation contribution adjustment, and cross-relationship concept consistency constraints. It should be noted that although the above embodiment provides a relatively detailed description of the present invention, the present invention is not limited to the specific implementation methods described above. Equivalent substitutions, parameter adjustments, changes in relation construction methods, or expansions of application scenarios made based on the technical concept of the present invention should all fall within the protection scope of the present invention.

[0151] This embodiment illustrates how, in a bioinformatics application scenario, the present invention achieves dynamic overlapping clustering construction and updating of gene functional modules through a complete process: candidate new cluster initialization, competitive collaborative allocation, dynamic bipartite graph construction, local reversible cutting, key node identification, and overlapping evidence propagation and fusion. It should be noted that although most details of the present invention have been described in detail using the above examples, this does not limit the present invention to the specific embodiments described. Furthermore, adjustments or modifications can still be made to the above technical solutions based on the content of this specification. Any modifications or equivalent substitutions made based on the technical solutions of this invention should fall within the scope of protection claimed by the present invention.

[0152] Figure 4 This is a structural block diagram of an overlapping clustering system based on hypergraph covering provided in an embodiment of this application. Figure 4 As shown, the system includes: The acquisition unit 401 is used to acquire a sample set and construct a hypergraph of at least two types of relation views, including a semantic neighborhood hypergraph and a factor-induced hypergraph. The first determining unit 403 is used to represent the sample to the concept space shared by the semantic neighborhood hypergraph and the factor-induced hypergraph, so as to obtain the concept coverage representation of the sample; The second determining unit 405 is used to determine the adaptive overlap budget interval for each sample based on the local density of each sample and the cross-relation divergence degree in different hypergraphs. Optimization unit 407 is used to construct the joint optimization objective function and iteratively optimize the joint optimization objective function alternately. Output unit 409 is used to determine the final concept set to which each sample belongs based on the optimized concept coverage representation and adaptive overlap budget interval, and outputs the overlap clustering results.

[0153] The system provided in this application embodiment has the same implementation principle and technical effects as the aforementioned method embodiment. For the sake of brevity, any parts not mentioned in the system embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0154] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0155] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0156] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0157] This application provides a computer-readable storage medium that stores computer instructions, which cause the computer to execute embodiments of this application. Figure 1 The method provided in the illustrated embodiment.

[0158] The aforementioned computer-readable storage medium may be any combination of one or more computer-readable media. A computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium may be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), or flash memory, optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium may be any tangible medium that contains or stores a program that may be used by or in connection with an instruction execution system, apparatus, or device.

[0159] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including—but not limited to—electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0160] The program code contained on a computer-readable medium may be transmitted using any suitable medium, including—but not limited to—wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0161] Computer program code for performing the operations of the embodiments of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0162] The foregoing has described specific embodiments of this application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps described in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0163] In the description of the embodiments of this application, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the embodiments of this application. In the embodiments of this application, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in the embodiments of this application, as well as the features of different embodiments or examples.

[0164] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of embodiments of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0165] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order according to the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0166] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0167] It should be noted that the terminals involved in the embodiments of this application may include, but are not limited to, personal computers (PCs), personal digital assistants (PDAs), wireless handheld devices, tablet computers, mobile phones, MP3 players, MP4 players, etc.

[0168] In the embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0169] Furthermore, the functional units in the various embodiments of this application can be integrated into a single processor, or each unit can exist physically separately, or two or more units can be integrated into a single unit. The integrated units described above can be implemented in hardware or in a combination of hardware and software functional units.

[0170] The integrated units implemented as software functional units described above can be stored in a computer-readable storage medium. These software functional units, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0171] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present application should be included within the scope of protection of the present application.

Claims

1. An overlapping clustering method based on hypergraph covering, characterized in that, include: Obtain a sample set and construct a hypergraph with at least two types of relation views, the hypergraph including a semantic neighborhood hypergraph and a factor-induced hypergraph; The sample is represented in the concept space shared by the semantic neighborhood hypergraph and the factor-induced hypergraph to obtain the concept coverage representation of the sample; The adaptive overlap budget interval for each sample is determined based on the local density of each sample and the degree of cross-relation divergence in different views. Construct a joint optimization objective function, and iteratively optimize the joint optimization objective function alternately. Based on the optimized concept coverage representation of each sample and the adaptive overlap budget interval, the final concept set to which each sample belongs is determined, and the overlap clustering result is output.

2. The overlapping clustering method based on hypergraph covering according to claim 1, characterized in that, The construction of the semantic neighborhood hypergraph includes: Perform semantic embedding on the samples; Determine the representative center in the embedded space; A hyperedge is formed by selecting samples that are semantically close to the representative center.

3. The overlapping clustering method based on hypergraph covering according to claim 1, characterized in that, The construction of the factor-induced hypergraph includes: Perform matrix factorization on the sample set to obtain the response intensity of the sample on multiple latent factors; A hyperedge is formed by selecting multiple samples with the highest response intensity of the latent factor. Remove invalid out-of-bounds edges.

4. The overlapping clustering method based on hypergraph covering according to claim 1, characterized in that, The process of obtaining the concept coverage representation of the sample includes: The local weighted mapping from the sample to the representative point is calculated based on the distance between the sample and the representative point in the embedding space; the sample is associated with multiple representative points that are closest to it.

5. The overlapping clustering method based on hypergraph covering according to claim 1, characterized in that, The construction of the adaptive overlapping budget interval includes: The base budget value is calculated based on the local density and cross-relation divergence of the sample; the local density of the sample is calculated based on the average distance between the sample and its neighboring samples in the embedding space; the cross-relation divergence is calculated based on the degree of difference in the number of edges the sample participates in in the semantic neighborhood hypergraph and the factor-induced hypergraph. The basic budget value is truncated globally and constrained by a minimum interval, wherein the basic budget value is negatively correlated with the local density and positively correlated with the degree of difference in participation.

6. The overlapping clustering method based on hypergraph covering according to claim 1, characterized in that, The construction of the reconstruction loss includes: The association probability between a sample and a hyperedge is calculated based on the concept coverage representation of the sample and the concept routing representation of the hyperedge. Sample-hyperedge pairs that actually belong to the hyperedge are taken as positive samples. Unconnected samples are selected as hard negative samples based on the concept coverage similarity or embedding space distance between the sample and the samples within the hyperedge. A loss that distinguishes between positive and negative samples is constructed.

7. The overlapping clustering method based on hypergraph covering according to claim 1, characterized in that, The cross-view consistency constraints include: Based on the degree of participation of the sample in the semantic neighborhood hypergraph and the factor-induced hypergraph and the view size, the conceptual evidence is normalized to obtain the normalized conceptual evidence of the semantic neighborhood hypergraph and the factor-induced hypergraph. The normalized conceptual evidence of the semantic neighborhood hypergraph and the factor-induced hypergraph is weighted and fused to obtain global consensus evidence; the difference between the normalized conceptual evidence of each view and the global consensus evidence is constrained.

8. The overlapping clustering method based on hypergraph covering according to claim 1, characterized in that, When determining the final concept set to which each sample belongs, the elements in the concept coverage vector of the sample are sorted by intensity. The number of selected concepts is determined according to the adaptive overlap budget interval of the sample, and the corresponding number of concepts with the highest intensity is taken as the overlap clustering result of the sample.

9. An overlapping clustering system based on hypergraph covering, characterized in that, include: An acquisition unit is used to acquire a sample set and construct a hypergraph of at least two types of relation views, wherein the hypergraph includes a semantic neighborhood hypergraph and a factor-induced hypergraph; The first determining unit is used to represent the sample into the concept space shared by the semantic neighborhood hypergraph and the factor-induced hypergraph to obtain the concept coverage representation of the sample; The second determining unit is used to determine the adaptive overlap budget interval for each sample based on the local density of each sample and the cross-relation divergence degree in different hypergraphs. An optimization unit is used to construct a joint optimization objective function and iteratively optimize the joint optimization objective function alternately. The output unit is used to determine the final concept set to which each sample belongs based on the optimized concept coverage representation of each sample and the adaptive overlap budget interval, and outputs the overlap clustering results.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause the computer to perform the hypergraph-cover-based overlapping clustering method as described in any one of claims 1 to 9.

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