Cluster clustering and positioning method and device based on multi-view fusion, equipment and medium

Abstract

The application relates to a cluster clustering and positioning method and device based on multi-view fusion, equipment and medium. The method comprises the following steps: acquiring a sparse distance matrix among nodes in a cluster; based on the same, constructing multi-feature views such as an original distance matrix, a Gaussian similarity, node degree centrality and a Laplace feature vector; constructing a self-representation matrix according to the node similarity of each view and stacking the same into a three-order tensor; performing low-rank approximation to construct a fusion affinity matrix, and dividing the cluster into multiple subnets through spectral clustering; extracting a distance submatrix from each subnet, obtaining local relative coordinates through multidimensional scaling transformation; identifying a shared node between subnets as an anchor point, splicing each local coordinate to a global coordinate system through Procrustes analysis, and obtaining a global positioning result. By using the method, the clustering criterion and the positioning geometric configuration requirement can be kept consistent under the condition of non-full-connection sparse distance observation, so that error transmission is inhibited and the global positioning accuracy is improved.

Description

Technical Field

[0001] This application relates to the field of cluster collaborative navigation and positioning technology, and in particular to a clustering and positioning method, apparatus, device and medium based on multi-view fusion. Background Technology

[0002] With the rapid development of large-scale dynamic networks such as wireless sensor networks and unmanned intelligent swarms, high-precision spatial positioning of nodes has become a key technology supporting collaborative computing and data fusion. In disaster relief and collaborative operations by unmanned aerial vehicle (UAV) swarms, collaborative navigation capabilities directly determine whether tasks such as formation keeping can be accomplished. In electromagnetically polluted environments such as indoors and canyons, GNSS signals are often unavailable, and inertial navigation systems suffer from severe drift. Therefore, relative distance measurement between nodes becomes the core, and even the sole, source of information for collaborative positioning. How to efficiently reconstruct the global geometry of the swarm using only local, noisy, and sparse distance observations is a fundamental challenge.

[0003] When the cluster size is small, centralized optimization can be used to solve the problem; however, as the number of nodes increases to hundreds, the computational complexity increases cubically, and fully connected distance measurements become almost impossible to obtain. Under resource constraints, the communication and sensing topology is highly sparse, resulting in significant gaps in the Euclidean distance matrix; local topological changes trigger perturbations and recalculations of the global matrix, leading to insufficient stability and scalability. The sparse topology makes the observation matrix highly incomplete, severely limiting positioning accuracy.

[0004] Existing methods mainly fall into two categories: The first is distance imputation based on shortest paths, which estimates missing values ​​using algorithms such as the Floyd algorithm and then obtains the relative positions through multidimensional scaling transformations. However, there is a deviation between path distance and Euclidean distance, and this deviation increases dramatically with increasing sparsity, introducing system deformation errors. The second is low-rank matrix completion, which utilizes the low-rank property of the distance matrix to recover missing elements from finite sampling. However, under highly sparse conditions, completion inevitably introduces new distance estimation errors and distorts the original topology; moreover, this method often requires global matrix decomposition and iterative optimization, and the computational complexity increases sharply with the cluster size, making it difficult to meet real-time requirements.

[0005] To address these challenges, the clustered localization strategy divides the cluster into several sub-clusters. Within each sub-cluster, multi-dimensional scale transformations are performed independently using relatively complete local distances, and then the coordinates are stitched together using shared nodes to form global coordinates. This approach reduces the scale of a single solution and adapts to dynamic topologies.

[0006] However, existing clustering methods are mostly geared towards communication efficiency or energy balance, which is inconsistent with the goal of positioning accuracy. Communication-stable subclusters may have ill-conditioned geometric configurations, making it difficult to obtain accurate local coordinates; while deliberately creating ideal geometric subclusters would increase the communication burden. The inconsistency between clustering and positioning goals renders the traditional sequential process of "clustering first, then positioning, then stitching" significantly flawed: the clustering criteria and the distance information required for positioning are dissimilar, making it difficult to avoid ill-conditioned subnets; during stitching, local positioning errors are easily accumulated through shared nodes, severely limiting the upper limit of global coordinate accuracy. Summary of the Invention

[0007] Therefore, it is necessary to provide a clustering and positioning method, device, equipment, and medium based on multi-view fusion that can keep the clustering criteria consistent with the positioning geometry requirements under non-fully connected sparse distance observation conditions, thereby suppressing error propagation and improving global positioning accuracy.

[0008] A clustering and localization method based on multi-view fusion, the method comprising: Obtain the sparse distance matrix between nodes in a cluster consisting of multiple nodes; Based on the sparse distance matrix, construct multiple feature views including the original distance matrix view, the Gaussian similarity matrix view, the node degree centrality matrix view, and the Laplacian eigenvector matrix view; Based on the similarity between the feature vectors of nodes in each feature view, a corresponding self-representation matrix is ​​constructed, and all self-representation matrices are stacked into a third-order tensor. The third-order tensor is approximated by a low-rank method. A fusion affinity matrix is ​​constructed based on the feature views after the low-rank approximation. Spectral clustering is then performed based on the fusion affinity matrix to divide the cluster into multiple subnets. For each subnet, extract its internal distance submatrix, and obtain the local relative coordinates of each subnet through multidimensional scaling transformation; The shared nodes among the multiple subnets are identified, and using the shared nodes as anchor points, the local relative coordinates of each subnet are stitched together to the same global coordinate system using Protodyakonov analysis to obtain the global positioning result of the cluster.

[0009] In one embodiment, low-rank approximation of the third-order tensor includes: Each feature view slice of the third-order tensor is subjected to singular value decomposition to obtain the corresponding singular value. For each feature view slice, calculate the cumulative energy percentage of the corresponding singular values, and determine the number of singular values ​​corresponding to the first time the cumulative energy percentage reaches the preset energy retention threshold as the truncation rank of the corresponding feature view slice. For each feature view slice, a low-rank approximation matrix is ​​obtained by performing low-rank truncation based on the corresponding truncation rank. Stack the low-rank approximation matrices of all feature view slices to reconstruct a low-rank tensor.

[0010] In one embodiment, the energy retention threshold is when the cumulative energy percentage reaches 90%.

[0011] In one embodiment, when constructing the fusion affinity matrix based on each feature view after low-rank approximation, the fusion affinity matrix is ​​obtained by weighted averaging of all feature views after low-rank approximation.

[0012] In one embodiment, spectral clustering is performed based on the fusion affinity matrix to divide the cluster into multiple subnets, including: Construct a Laplacian matrix based on the fusion affinity matrix, solve for the eigenvalues ​​of the Laplacian matrix, and sort the solved eigenvalues ​​in ascending order. Calculate the difference between each adjacent feature value after sorting the feature values ​​in ascending order, and determine the smaller index of the adjacent feature value pair with the largest difference as the number of clusters k; Take the eigenvectors corresponding to the k smallest eigenvalues, arrange them in columns to form an embedding matrix, take each row of the embedding matrix as a data point, perform K-means clustering, and obtain the subnet label to which each node belongs.

[0013] In one embodiment, identifying shared nodes among the plurality of subnets includes: For each node in all subnets, construct the corresponding set of neighboring nodes and extract the subnet label to which each node belongs, obtained from spectral clustering. For each node, iterate through the set of its neighboring nodes, count the number of types of subnet labels to which the neighboring nodes belong, and mark the node as a candidate shared node if the number of types is greater than 1. For any two different subnets, obtain the candidate shared nodes that belong to both subnets and form a subset of shared nodes for the corresponding subnet pair; The final set of shared nodes is obtained by taking the union of the shared node subsets of all subnet pairs.

[0014] In one embodiment, the cluster is a drone cluster, an unmanned vehicle cluster, or a wireless sensor network node cluster.

[0015] A clustering and positioning device based on multi-view fusion, the device comprising: The sparse distance matrix acquisition module is used to obtain the sparse distance matrix between nodes in a cluster consisting of multiple nodes. A multi-feature view construction module is used to construct multiple feature views based on the sparse distance matrix, including the original distance matrix view, the Gaussian similarity matrix view, the node degree centrality matrix view, and the Laplacian eigenvector matrix view. The third-order tensor construction module is used to construct the corresponding self-representation matrix based on the similarity between the node feature vectors in each feature view, and stack all the self-representation matrices into a third-order tensor. The subnetting module is used to perform low-rank approximation on the third-order tensor, construct a fusion affinity matrix based on each feature view after low-rank approximation, and perform spectral clustering based on the fusion affinity matrix to divide the cluster into multiple subnets. The local relative coordinates acquisition module is used to extract the internal distance submatrix of each subnet and obtain the local relative coordinates of each subnet through multidimensional scaling transformation; The global positioning module is used to identify shared nodes among the multiple subnets, and using the shared nodes as anchor points, uses Protodyakonov analysis to stitch the local relative coordinates of each subnet to the same global coordinate system to obtain the global positioning result of the cluster.

[0016] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps in the above-described clustering and localization method based on multi-view fusion.

[0017] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the above-described clustering and localization method based on multi-view fusion.

[0018] The aforementioned clustering and localization method, apparatus, device, and medium based on multi-view fusion construct multiple feature views based on the sparse distance matrix between nodes in a cluster composed of multiple nodes. These feature views include the original distance matrix view, Gaussian similarity matrix view, node degree centrality matrix view, and Laplacian eigenvector matrix view. According to the similarity between the eigenvectors of nodes in each feature view, corresponding self-representation matrices are constructed. All self-representation matrices are stacked into a third-order tensor. Low-rank approximation is performed on the third-order tensor. A fusion affinity matrix is ​​constructed based on each feature view after low-rank approximation. Spectral clustering is then performed based on the fusion affinity matrix to divide the cluster into multiple subnets. The internal distance submatrix of each subnet is extracted. Local relative coordinates of each subnet are obtained through multi-dimensional scaling transformation. Shared nodes between multiple subnets are identified. Using shared nodes as anchor points, Protodyakonov analysis is used to stitch the local relative coordinates of each subnet to the same global coordinate system, resulting in the global localization result of the cluster.

[0019] Beneficial effects: This method constructs complementary multi-view features from a single sparse distance matrix, and then performs spectral clustering after fusion via tensor low-rank approximation. This ensures that the clustering results highly match the geometric configuration required for localization, avoiding the ill-conditioned localization subnets introduced by traditional clustering methods. Furthermore, each subnet independently performs multi-dimensional scale localization and is rigidly spliced ​​together using shared nodes as anchor points, effectively suppressing the propagation and accumulation of local errors in the global coordinate system. The entire technical solution does not require global distance completion; it relies only on a small number of local distance observations to achieve high-precision global relative localization of large-scale clusters, significantly reducing computational complexity and enhancing scalability and robustness under dynamic sparse topologies. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating a clustering and localization method based on multi-view fusion in one embodiment; Figure 2 This is a schematic diagram of a sparse topology of a cluster in an experiment; Figure 3 This is a schematic diagram of the clustering results in an experiment. Figure 4 This is a schematic diagram showing the cluster node location estimation results under the proposed method in an experiment. Figure 5 This is a structural block diagram of a clustering and positioning device based on multi-view fusion in one embodiment; Figure 6 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0022] To address the problems in existing technologies, such as the disconnect between clustering criteria and positioning geometry requirements, and the tendency for local positioning errors to accumulate and propagate during stitching, which limits global positioning accuracy under non-fully connected sparse distance observation conditions, this application addresses these issues. Figure 1 As shown, a clustering and localization method based on multi-view fusion is provided, which specifically includes the following steps: Step S100: Obtain the sparse distance matrix between nodes in a cluster consisting of multiple nodes.

[0023] Step S110: Construct multiple feature views based on the sparse distance matrix, including the original distance matrix view, the Gaussian similarity matrix view, the node degree centrality matrix view, and the Laplacian eigenvector matrix view.

[0024] Step S120: Based on the similarity between the feature vectors of nodes in each feature view, construct the corresponding self-representation matrix respectively, and stack all the self-representation matrices into a third-order tensor.

[0025] Step S130: Perform low-rank approximation on the third-order tensor, construct a fusion affinity matrix based on each feature view after low-rank approximation, and perform spectral clustering based on the fusion affinity matrix to divide the cluster into multiple subnets.

[0026] Step S140: Extract the internal distance submatrix for each subnet and obtain the local relative coordinates of each subnet through multidimensional scaling transformation.

[0027] Step S150: Identify shared nodes among multiple subnets, and using the shared nodes as anchor points, use Protodyakonov analysis to stitch the local relative coordinates of each subnet to the same global coordinate system to obtain the global positioning result of the cluster.

[0028] This application proposes a cooperative navigation method that uses only the distance matrix as the sole input, adaptively clusters, and completes global localization. The overall design follows the framework of "clustering first, then localization, and then stitching together," but its unique feature is that the affinity matrix on which clustering depends is homologous and isomorphic with the distance information used for subsequent subnet localization, and shared nodes are used simultaneously for cluster boundary confirmation and coordinate stitching and anchoring.

[0029] Before detailing the specific steps of this method, we first formally model the cluster cooperative localization problem under sparse topology.

[0030] Consider by A dynamic cluster consisting of nodes has a true global relative coordinate matrix as follows: ,in In terms of spatial dimension, under resource-constrained or highly adversarial environments, the communication and perception topology of a cluster exhibits sparsity, meaning that only the true distances between a subset of node pairs can be obtained.

[0031] Furthermore, based on the connectivity relationships between nodes, the connectivity matrix is ​​defined as follows: Its elements are defined as having a value of 1 when connected and a value of 0 when disconnected. The expression can be written as: (1) Let the sparsity be... ,when At that time, that is This is a highly incomplete sparse EDM. The sparse distance matrix observed between nodes is defined as follows: Its elements are defined as Simultaneously satisfying: (2) In formula (2), For a node pair connectivity matrix to have valid observations, To observe noise. The objective of this application is based on this sparse and noisy... (The sparse distance matrix in step S100) accurately reconstructs the global relative coordinates of all nodes. .

[0032] The aforementioned problem model faces two major challenges: First, when the sparsity is low, the Euclidean distance matrix is ​​highly incomplete, making it impossible to solve directly using the classical Multidimensional Scaling (MDS) method due to the incomplete EDM. Second, existing completion methods (such as shortest path filling or low-rank matrix completion) introduce additional estimation errors, which amplify rapidly with increasing sparsity, causing deformation of the original topology and severely affecting global positioning accuracy. To address these challenges, this application proposes a "clustering-local positioning-stitching" strategy: by constructing multi-view features and utilizing tensor low-rank approximation to obtain robust cluster partitioning, each cluster is approximately fully connected and possesses a good geometric configuration, thereby achieving high-precision MDS positioning within each subnet; finally, robust stitching of global coordinates is achieved through Procrustes analysis (i.e., Procrustes) of shared nodes.

[0033] In step S100, in the cluster cooperative navigation scenario, the cluster is composed of... The system consists of several nodes, which acquire distance information from each other using relative ranging sensors such as ultra-wideband (UWB) and lidar. However, in real-world large-scale cluster deployments, limitations such as communication bandwidth, node power consumption, obstacle obstruction, and electromagnetic interference prevent effective distance measurements from being obtained between all node pairs. Consequently, the resulting distance matrix exhibits a highly sparse characteristic, meaning it contains a large number of unknown or missing elements.

[0034] Specifically, each node in the cluster is equipped with an ultra-wideband ranging module. Periodically send messages to neighboring nodes within communication range Initiate a ranging request and obtain the relative distance measurement between the two by calculating the signal's time of flight. Due to obstacle obstruction, node power consumption limitations, and communication bandwidth constraints, only some node pairs can successfully complete distance measurement, while the remaining node pairs cannot obtain effective distance data.

[0035] All successfully obtained distance measurements are aggregated to the cluster head node or ground aggregation center via multi-hop routing. The aggregation center initializes a... An empty matrix is ​​generated by filling the corresponding positions of the matrix with the distance values ​​reported by each node according to the source and target node indices, setting the diagonal elements of the matrix to 0, and leaving the remaining elements that were not measured as unknown. This results in a sparse Euclidean distance matrix with a large number of missing elements.

[0036] Furthermore, in order to extract rich topological and geometric information from a single sparse distance matrix, four complementary feature views are constructed in step S110: the original distance matrix, the Gaussian similarity matrix, the node degree centrality matrix, and the Laplacian eigenvector matrix.

[0037] In this embodiment, when analyzing the cluster cooperative ranging and navigation problem, discrete time intervals are defined. The three-dimensional coordinates of each node are as follows Then the entire set of positions can be defined as , ,in This indicates transpose. The relative distance between nodes is calculated based on the Euclidean distance formula using the position coordinates of each node itself and its observable neighboring nodes. This is applicable to a number of nodes... The set of cluster nodes, defined as the sparse distance matrix observed between nodes. Its elements are defined as When the cluster is not fully connected or when some nodes cannot perform relative observations due to external interference or loss, the internal measurement matrix will be used when some elements are missing. , indicating that the distance between nodes is unknown or unobservable. Considering observation noise and node loss, the sparse distance matrix... The elements in the middle satisfy: (3) At this point, the original distance matrix is ​​the sparse distance matrix. That is, denoted as a feature view. .

[0038] In this embodiment, to convert distance into a similarity metric for easier subsequent clustering analysis, a Gaussian kernel function is used and unconnected edges are masked. Similarity is defined as follows: (4) In formula (4), Take the mean of all non-zero distances to adaptively adjust the kernel width. This represents the mean effective observation distance in the distance matrix. The resulting Gaussian similarity matrix is ​​denoted as the feature view. Gaussian similarity assigns high similarity to nearby nodes and near-zero similarity to distant nodes, naturally reflecting the local neighborhood structure.

[0039] In this embodiment, to reflect the global distance centrality of nodes in the network, a node degree centrality vector is constructed, thereby forming a matrix view. The global influence of each node is defined as the sum of the shortest path distances to all other reachable nodes. Since the original distance matrix may be disconnected, the distances between all pairs of nodes are first calculated using either Floyd's algorithm or Dijkstra's algorithm. Then the view can be written as: (5) In this embodiment, in order to capture the global structural information of the graph and provide a classical embedding for subsequent spectral clustering, a method based on the distance matrix is ​​used. Perform threshold determination and obtain the adjacency logical index matrix. Construct the Laplacian eigenvector matrix: (6) In formula (6), Represented by the adjacency matrix The diagonal matrix is ​​composed of rows and elements. Eigendecomposition is performed on formula (6), and the smallest value is taken. Eigenvectors corresponding to the non-zero eigenvalues: (7) but This view contains global segmentation information of the graph and serves as a natural input for spectral clustering.

[0040] After obtaining multiple feature views through step S110, each view characterizes the topological and geometric properties of the cluster nodes from different perspectives. However, these feature views differ significantly in their physical dimensions and mathematical properties: for example, the elements of the original distance matrix view are Euclidean distance values ​​(with the dimension of length), the elements of the Gaussian similarity matrix view are dimensionless values ​​in the [0,1] interval, the node degree centrality matrix view reflects the sum of shortest path distances, and the elements of the Laplacian eigenvector matrix view are the eigenvector components obtained from spectral decomposition. These heterogeneous features cannot be directly fused and analyzed within the same mathematical framework.

[0041] Therefore, it is necessary to uniformly convert each feature view into an isomorphic representation that can characterize the similarity relationship between node pairs. This conversion is achieved in step S120 by constructing a self-representation matrix. Specifically, for each feature view, the feature vector describing the "attribute of a single node" is mapped to a relation matrix describing the "similarity of node pairs" through a similarity metric. After this conversion, regardless of the physical meaning of the original view, the resulting self-representation matrix uses a uniform value in the range [0,1] to characterize the similarity between node pairs: the closer the value is to 1, the more similar the two nodes are in that view; the closer the value is to 0, the less similar they are.

[0042] In this embodiment, a view is defined. self-representation matrix Its elements are compute nodes. and In view Cosine similarity between feature vectors: (8) In formula (8), Indicates the first The similarity matrix of feature views, where a value closer to 1 indicates more similar nodes, and a value closer to 0 indicates less similar nodes. , Representing views respectively At the node and The self-representation matrix below.

[0043] Furthermore, the views are unified into a third-order tensor using a self-representation matrix, as follows: (9) In formula (9), Represents a view The third-order tensor components under equation (9) encode the similarity relationship of all node pairs under multiple perspectives, which is the basis for subsequent low-rank modeling.

[0044] In step S130, in order to remove noise from each view and extract the common low-rank structure, the tensor is... We perform low-rank approximation by adopting an energy-preserving adaptive truncation strategy and estimating the effective rank for each mode using the idea of ​​Tucker decomposition.

[0045] Specifically, to remove noise from each view and extract the common low-rank structure, the third-order tensor is... Singular value decomposition is performed on each feature view slice to obtain the corresponding singular values. For each feature view slice, calculate the cumulative energy percentage of the corresponding singular values. The number of singular values ​​corresponding to the first time the cumulative energy percentage reaches a preset threshold is determined as the truncation rank of the corresponding feature view slice. Specifically, calculate the minimum number of singular values ​​required for the cumulative energy to reach the energy retention threshold. (10) In formula (10), take Slice each feature view By using SVD decomposition to truncate the matrix, we can achieve a low-rank approximation: (11) In formula (11), and They represent the preceding Left and right singular vector matrices composed of singular components For the front A diagonal matrix composed of singular values. The low-rank approximation matrices of all feature view slices are stacked to reconstruct the low-rank tensor. And remember This step effectively suppresses noise and compresses redundant information.

[0046] In this embodiment, the energy retention threshold is when the cumulative energy percentage reaches 90%.

[0047] Furthermore, when constructing the fusion affinity matrix based on the feature views after low-rank approximation, a weighted average of all feature views after low-rank approximation is performed to obtain the fusion affinity matrix, which is expressed as: (12) Because small numerical perturbations may be introduced during the low-rank approximation process, a small number of negative or asymmetric elements may appear in the affinity matrix. To address this, the absolute value of the fused matrix is ​​taken in formula (12) to eliminate the aforementioned numerical errors and ensure the non-negativity of the matrix elements. After this processing, the resulting affinity matrix has symmetry and positive definiteness, and its elements uniformly represent the comprehensive similarity of node pairs under different perspectives. It can serve as a reliable input for spectral clustering, effectively improving the stability and accuracy of subsequent subnet partitioning.

[0048] In this embodiment, spectral clustering is performed based on the fusion affinity matrix to divide the cluster into multiple subnets. This includes: First, constructing a Laplacian matrix based on the fusion affinity matrix and solving for the eigenvalues ​​of the Laplacian matrix. The solved eigenvalues ​​are then arranged in ascending order. Next, the difference between adjacent eigenvalues ​​in the ascending order is calculated. Among the adjacent eigenvalue pairs with the largest difference, the smaller index is determined as the cluster number k. The eigenvectors corresponding to the k smallest eigenvalues ​​are taken and arranged in columns to form an embedding matrix. Each row of the embedding matrix is ​​taken as a data point, and K-means clustering is performed to obtain the subnet label to which each node belongs.

[0049] Specifically, using the unnormalized Laplace matrix Perform spectral embedding and construct the Laplacian matrix: (13) (14) In formulas (12) and (13), Represented as an intermediate variable, it refers to the diagonal matrix formed by summing the elements column-wise from the fusion affinity matrix. The fusion affinity matrix represents the first... OK Column elements.

[0050] Furthermore, solving the generalized eigenvalue problem , to obtain eigenvalues and their corresponding eigenvectors Sort the eigenvalues ​​in ascending order and select the top [values]. The embedding matrix is ​​composed of the smallest non-zero eigenvectors. ,in It can be derived from the eigenvalue gap, i.e., the first and The difference between the eigenvalues ​​is automatically determined, or if the number of clusters is known in the actual application scenario, it can be set directly. value.

[0051] Next, the embedding matrix Each row is considered as the corresponding node in Coordinate vectors in 3D space, for this K-means clustering is performed on each row vector. Preferably, to enhance stability, the process can be repeated 10 times, and the optimal clustering result is selected to obtain the node clustering labels. This leads to the set of node clusters, represented as: (15) The above spectral clustering process embeds the original complex graph structure into a low-dimensional Euclidean space through Laplacian eigenmaps, so that closely connected nodes are close to each other in the embedding space, thereby enabling K-means to effectively identify clusters of non-convex and nonlinear structures and obtain subnet partitioning results that match the localized geometric configuration.

[0052] In step S140, the internal distance submatrix of each subnet is extracted, and the local relative coordinates of each subnet are obtained through multidimensional scaling transformation.

[0053] In this embodiment, for each cluster From the original distance matrix Extracting the corresponding submatrix is ​​a process described as follows: (16) Furthermore, for the number of nodes... Cluster node subset The corresponding distance matrix Should meet: The aforementioned clustered subnets can be directly solved using classical MDS to obtain local relative coordinates.

[0054] In step S150, identifying shared nodes among multiple subnets includes: constructing a corresponding set of neighboring nodes for each node in all subnets, and extracting the subnet labels to which each node belongs obtained by spectral clustering; for each node, traversing the corresponding set of neighboring nodes, counting the number of types of subnet labels to which the neighboring nodes belong; if the number of types is greater than 1, marking the node as a candidate shared node; for any two different subnets, obtaining candidate shared nodes that belong to both subnets simultaneously, forming a subset of shared nodes for that subnet pair; and taking the union of the subsets of shared nodes for all subnet pairs to obtain the final set of shared nodes.

[0055] In this embodiment, a shared node is defined as a node that connects multiple different clusters. For each node... Count the number of its neighbors that belong to different clusters. If it is greater than 1, then the node... These are considered candidate shared nodes. The final set of shared nodes is then determined by the intersection of the common node sets among clusters, and is used for subsequent subnet splitting.

[0056] Specifically, set , , The set of cluster nodes, and the set of shared nodes are: (17) In formula (16), Cluster The set of neighbors.

[0057] Furthermore, the subnet with the most shared nodes is selected as the reference frame, that is: (18) Furthermore, using shared nodes as control points, the local coordinates of each subnet are sequentially registered to the global frame through Protodyakonov analysis. For shared nodes that participate in registration multiple times, a weighted average is used to integrate their coordinate estimates. If there are still uncovered nodes after all subnets are stitched together (common in extremely sparse topology cases), then least-squares polygonal localization is performed using the already located nodes as a reference, combined with distance observations.

[0058] In this embodiment, after calculating the global coordinates of all nodes, the positioning results are distributed to each node in the cluster one by one through the downlink.

[0059] In this embodiment, the method provided herein is applicable to various types of autonomous unmanned swarm systems and distributed sensor networks. Specifically, the nodes of the swarm can be any one or a combination of unmanned aerial vehicle (UAV) nodes, unmanned vehicle (UAV) nodes, unmanned surface vessel (USV) nodes, underwater autonomous vehicle (UAV) nodes, mobile robot nodes, or wireless sensor network nodes.

[0060] The common characteristic of the above-mentioned cluster nodes is that each node has the ability to measure relative distances with at least some of its neighboring nodes. However, due to practical factors such as communication bandwidth limitations, node energy constraints, obstacle obstruction, or electromagnetic interference, only some node pairs in the cluster can obtain effective distance measurements, resulting in a highly sparse distance matrix. Therefore, this method has universal applicability to the above-mentioned cluster types.

[0061] To evaluate the performance of the proposed method, the following simulation environment was built. The total number of cluster nodes was set to 28, and the real two-dimensional coordinates were generated from a set of preset points distributed in... , Within the planar region. Three non-overlapping subnets are preset, with node sizes of 12, 10, and 6 respectively. The actual subnet labels are only used for performance evaluation, and the algorithm itself does not utilize this information. Figure 2 This is a schematic diagram of the cluster subnet topology. The solid light blue circles represent nodes shared between cluster subnets, while the nodes of other colors belong to different subnets.

[0062] Considering the topological connectivity constraints in the real-world scenario, the topological observation sparsity of this cluster is approximately 45%, exhibiting a typical "dense within clusters, sparse between clusters" network structure. The observation distance matrix topology is constructed based on the given adjacency topology, and the distance observation values ​​are directly given by the Euclidean distance of the true coordinates. By adding additional measurement noise, the algorithm's geometric reconstruction capability under sparse noise observations is examined. Specifically, the industry-standard distance noise model is used as the distance error function between two nodes, with the specific expression as follows: (19) In formula (19), Representing distance measurement bias, it is a distance-independent deterministic modeling term; Representing the proportional distance error, it is a probabilistic modeling term related to distance. Observation noise. and parameters The unit of measurement is meters. This is a dimensionless parameter. In this experiment, the simulation selects... , .

[0063] Figure 3 This shows the clustering results under the proposed method. Figure 3 It can be seen that the global cluster topology is effectively divided into three subnets, and the number of nodes in each subnet is consistent with the simulation settings, demonstrating the effectiveness and accuracy of the algorithm in adaptive clustering under large-scale sparse topology.

[0064] Based on the extraction of the topological distance observation matrix under effective clustering, the algorithm ultimately achieves coordinate estimation of cluster nodes. The results are shown in [reference needed]. Figure 4As shown in the figure, the solid black circles represent the actual locations of the cluster nodes, the red triangles represent the estimated node locations, and the green arrows represent the deviations between the estimated and actual node locations. Under the coupling of distance observation errors and sparse topology constraints, the estimated node locations are largely consistent with the actual topology, with a maximum node estimation error of approximately 2.02 m and a global root mean square error of approximately 0.92 m. This demonstrates that the proposed algorithm can achieve effective location estimation for large-scale sparse topologies and can provide support for subsequent cluster tasks.

[0065] The aforementioned clustering and localization method based on multi-view fusion proposes a clustering method that constructs multi-view features from a single distance matrix and fuses them using a third-order tensor low-rank approximation. This introduces multi-view clustering theory into cluster network analysis. Adaptive rank estimation preserves structural information under different modalities, achieving robust clustering even under sparse and noisy distance matrices. Furthermore, a subnet automatic identification and rigid splicing mechanism based on shared nodes is designed. This mechanism automatically divides subnets using cluster labels output by spectral clustering and uses shared nodes as natural anchor points in MDS localization. Only a few common nodes are needed to complete cross-subnet coordinate alignment, significantly reducing the complexity of subnet splicing. Simultaneously, this method constructs a tightly coupled integrated framework for clustering and localization. The affinity matrix generated by clustering in this framework maintains the same origin as the input for subnet localization. Shared nodes simultaneously serve cluster confirmation and coordinate transformation calibration, breaking the problem of insufficient information utilization in the traditional "clustering first, then localization" serial mode. This achieves the collaborative navigation goal of "clear clustering, accurate localization, and seamless connection" of clusters.

[0066] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0067] In one embodiment, such as Figure 5 As shown, a clustering and localization device based on multi-view fusion is provided, including: a sparse distance matrix acquisition module 200, a multi-feature view construction module 210, a third-order tensor construction module 220, a subnetting module 230, a local relative coordinate acquisition module 240, and a global localization acquisition module 250, wherein: The sparse distance matrix acquisition module 200 is used to acquire the sparse distance matrix between nodes in a cluster consisting of multiple nodes. Multiple feature view construction module 210 is used to construct multiple feature views based on the sparse distance matrix, including the original distance matrix view, Gaussian similarity matrix view, node degree centrality matrix view and Laplacian eigenvector matrix view; The third-order tensor construction module 220 is used to construct corresponding self-representation matrices based on the similarity between the node feature vectors in each feature view, and stack all self-representation matrices into a third-order tensor; The subnetting module 230 is used to perform low-rank approximation on the third-order tensor, construct a fusion affinity matrix based on each feature view after low-rank approximation, and perform spectral clustering based on the fusion affinity matrix to divide the cluster into multiple subnets. The local relative coordinates acquisition module 240 is used to extract the internal distance submatrix of each subnet and obtain the local relative coordinates of each subnet through multidimensional scaling transformation; The global positioning module 250 is used to identify shared nodes among the multiple subnets, and using the shared nodes as anchor points, uses Protodyakonov analysis to stitch the local relative coordinates of each subnet to the same global coordinate system to obtain the global positioning result of the cluster.

[0068] Specific limitations regarding the clustering and positioning device based on multi-view fusion can be found in the limitations of the clustering and positioning method based on multi-view fusion described above, and will not be repeated here. Each module in the aforementioned clustering and positioning device based on multi-view fusion can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0069] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 6As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a clustering and positioning method based on multi-view fusion. The display screen can be an LCD screen or an e-ink display screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0070] Those skilled in the art will understand that Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0071] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps: Obtain the sparse distance matrix between nodes in a cluster consisting of multiple nodes; Based on the sparse distance matrix, construct multiple feature views including the original distance matrix view, the Gaussian similarity matrix view, the node degree centrality matrix view, and the Laplacian eigenvector matrix view; Based on the similarity between the feature vectors of nodes in each feature view, construct the corresponding self-representation matrix, and stack all the self-representation matrices into a third-order tensor. The third-order tensor is approximated by a low-rank method. A fusion affinity matrix is ​​constructed based on the feature views after the low-rank approximation. Spectral clustering is then performed based on the fusion affinity matrix to divide the cluster into multiple subnets. For each subnet, extract its internal distance submatrix, and obtain the local relative coordinates of each subnet through multidimensional scaling transformation; The shared nodes among the multiple subnets are identified, and using the shared nodes as anchor points, the local relative coordinates of each subnet are stitched together to the same global coordinate system using Protodyakonov analysis to obtain the global positioning result of the cluster.

[0072] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor: Obtain the sparse distance matrix between nodes in a cluster consisting of multiple nodes; Based on the sparse distance matrix, construct multiple feature views including the original distance matrix view, the Gaussian similarity matrix view, the node degree centrality matrix view, and the Laplacian eigenvector matrix view; Based on the similarity between the feature vectors of nodes in each feature view, construct the corresponding self-representation matrix, and stack all the self-representation matrices into a third-order tensor. The third-order tensor is approximated by a low-rank method. A fusion affinity matrix is ​​constructed based on the feature views after the low-rank approximation. Spectral clustering is then performed based on the fusion affinity matrix to divide the cluster into multiple subnets. For each subnet, extract its internal distance submatrix, and obtain the local relative coordinates of each subnet through multidimensional scaling transformation; The shared nodes among the multiple subnets are identified, and using the shared nodes as anchor points, the local relative coordinates of each subnet are stitched together to the same global coordinate system using Protodyakonov analysis to obtain the global positioning result of the cluster.

[0073] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0074] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0075] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A clustering and localization method based on multi-view fusion, characterized in that, The method includes: Obtain the sparse distance matrix between nodes in a cluster consisting of multiple nodes; Based on the sparse distance matrix, multiple feature views are constructed, including an original distance matrix view, a Gaussian similarity matrix view, a node degree centrality matrix view, and a Laplacian eigenvector matrix view. The original distance matrix view is the sparse distance matrix itself; the Gaussian similarity matrix view is a matrix obtained by converting distances into similarity metrics using a Gaussian kernel function on the sparse distance matrix; the node degree centrality matrix view is a matrix view constructed based on the sum of the shortest path distances from each node to all other reachable nodes; and the Laplacian eigenvector matrix view is a matrix view constructed based on the sparse distance matrix using a Laplacian matrix, performing eigenvalue decomposition on the Laplacian matrix, and selecting the eigenvectors corresponding to the smallest non-zero eigenvalues. Based on the similarity between the feature vectors of nodes in each feature view, a corresponding self-representation matrix is ​​constructed, and all self-representation matrices are stacked into a third-order tensor. The third-order tensor is approximated by a low-rank method. A fusion affinity matrix is ​​constructed based on the feature views after the low-rank approximation. Spectral clustering is then performed based on the fusion affinity matrix to divide the cluster into multiple subnets. For each subnet, extract its internal distance submatrix and obtain the local relative coordinates of each subnet through multidimensional scaling transformation; The shared nodes among the multiple subnets are identified, and using the shared nodes as anchor points, the local relative coordinates of each subnet are stitched together to the same global coordinate system using Protodyakonov analysis to obtain the global positioning result of the cluster.

2. The clustering and localization method based on multi-view fusion according to claim 1, characterized in that, The low-rank approximation of the third-order tensor includes: Each feature view slice of the third-order tensor is subjected to singular value decomposition to obtain the corresponding singular value. For each feature view slice, calculate the cumulative energy percentage of the corresponding singular values, and determine the number of singular values ​​corresponding to the first time the cumulative energy percentage reaches the preset energy retention threshold as the truncation rank of the corresponding feature view slice. For each feature view slice, a low-rank approximation matrix is ​​obtained by performing low-rank truncation based on the corresponding truncation rank. Stack the low-rank approximation matrices of all feature view slices to reconstruct a low-rank tensor.

3. The clustering and localization method based on multi-view fusion according to claim 2, characterized in that, The energy retention threshold is when the cumulative energy percentage reaches 90%.

4. The clustering and localization method based on multi-view fusion according to claim 1, characterized in that, When constructing the fusion affinity matrix based on the feature views after low-rank approximation, the weighted average of all feature views after low-rank approximation is performed to obtain the fusion affinity matrix.

5. The clustering and localization method based on multi-view fusion according to claim 1, characterized in that, Based on the fusion affinity matrix, spectral clustering is performed to divide the cluster into multiple subnets, including: Construct a Laplacian matrix based on the fusion affinity matrix, solve for the eigenvalues ​​of the Laplacian matrix, and sort the solved eigenvalues ​​in ascending order. Calculate the difference between each adjacent feature value after sorting the feature values ​​in ascending order, and determine the smaller index of the adjacent feature value pair with the largest difference as the number of clusters k; Take the eigenvectors corresponding to the k smallest eigenvalues, arrange them in columns to form an embedding matrix, take each row of the embedding matrix as a data point, perform K-means clustering, and obtain the subnet label to which each node belongs.

6. The clustering and localization method based on multi-view fusion according to claim 1, characterized in that, Identifying shared nodes among the multiple subnets includes: For each node in all subnets, construct the corresponding set of neighboring nodes and extract the subnet label to which each node belongs, obtained from spectral clustering. For each node, iterate through the set of its neighboring nodes, count the number of types of subnet labels to which the neighboring nodes belong, and mark the node as a candidate shared node if the number of types is greater than 1. For any two different subnets, obtain the candidate shared nodes that belong to both subnets and form a subset of shared nodes for the corresponding subnet pair; The final set of shared nodes is obtained by taking the union of the shared node subsets of all subnet pairs.

7. The clustering and localization method based on multi-view fusion according to any one of claims 1 to 6, characterized in that, The cluster can be a drone cluster, an unmanned vehicle cluster, or a wireless sensor network node cluster.

8. A clustering and positioning device based on multi-view fusion, characterized in that, The device implements the clustering and localization method based on multi-view fusion as described in any one of claims 1-7, including: The sparse distance matrix acquisition module is used to obtain the sparse distance matrix between nodes in a cluster consisting of multiple nodes. A multi-feature view construction module is used to construct multiple feature views based on the sparse distance matrix, including the original distance matrix view, the Gaussian similarity matrix view, the node degree centrality matrix view, and the Laplacian eigenvector matrix view. The third-order tensor construction module is used to construct the corresponding self-representation matrix based on the similarity between the node feature vectors in each feature view, and stack all the self-representation matrices into a third-order tensor; The subnetting module is used to perform low-rank approximation on the third-order tensor, construct a fusion affinity matrix based on each feature view after low-rank approximation, and perform spectral clustering based on the fusion affinity matrix to divide the cluster into multiple subnets. The local relative coordinates acquisition module is used to extract the internal distance submatrix of each subnet and obtain the local relative coordinates of each subnet through multidimensional scaling transformation; The global positioning module is used to identify shared nodes among the multiple subnets, and using the shared nodes as anchor points, uses Protodyakonov analysis to stitch the local relative coordinates of each subnet to the same global coordinate system to obtain the global positioning result of the cluster.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

Images