306 results about "Laplacian matrix" patented technology

The invention provides a method for learning and anomaly detection of trace modes by utilizing much feature information of a trace. Firstly, in the trace mode learning phase, similarities of motion directions and spatial positions between traces are considered at the same time, a typical trace motion mode is extracted by hierarchical agglomerative clustering, and is provided with high cluster accuracy; and the time efficiency is greatly improved through constructing a Laplacian matrix and reducing the dimensionality of the matrix. Then in the abnormity detection phase, a distribution area of scene starting points is learned through a GMM model, a moving window is used as a basic comparing element, differences of a trace to be detected and a typical trace in position and direction are measured by defining a position distance and a direction distance, and an on-line classifier based on the direction distance and the position distance is established. That the trace belongs to a starting point abnormity, a global abnormity or a local abnormity is determined online through a multi-feature abnormity detection algorithm; and due to the fact that starting point, direction and position feature differences are considered at the same time, and the global abnormity and the local child segment abnormity are considered, the learning and anomaly detection method based on multi-feature motion modes of the vehicle traces is higher in abnormity recognition rate when being compared to traditional methods.

In a method and system for matting a foreground object F having an opacity α constrained by associating a characteristic with selected pixels in an image having a background B, weights are determined for all edges of neighboring pixels for the image and used to build a Laplacian matrix L. The equation α is solved where α=arg min αT Lα s.t.αi=si, ∀i ∈ S, S is the group of selected pixels, and si is the value indicated by the associated characteristic. The equation Ii=αiFi+(1−αi)Bi is solved for F and B with additional smoothness assumptions on F and B; after which the foreground object F may be composited on a selected background B′ that may be the original background B or may be a different background, thus allowing foreground features to be extracted from the original image and copied to a different background.

The invention discloses a method for recognizing a human motion in the field of computer vision and pattern recognition. Firstly, a feature containing time and space information is used for expressing the motion status of a human body in a current frame, and a classifier is designed through a graph theory semi-supervised method so that the purpose of human motion recognition is achieved. In the process of extracting the human motion feature, outline and motion light stream information in the past, in the present time and in the future is simultaneously fused so that the motion posture of a human body can be more accurately described. In addition, in order to obtain a high recognition rate with a few samples, based on the graph theory semi-supervised method of the generalized Laplacian matrix, and the graph theory semi-supervised method is used for recognizing the human motion. Experiments prove that under the conditions that observation angles are different and the motion difference of different persons exists, the method can be used for obtaining the satisfactory recognition rate of common motions.

The invention provides an information search method and system based on interactive document clustering. The method comprises the following steps that a document set is horizontally partitioned and preprocessed; word frequency statistics is conducted, and high-frequency words constitute a characteristic word set; vector space representation of documents is generated, the distances between the documents are calculated, and a similarity matrix is generated; a Laplacian matrix is generated, the number of clusters and a representation matrix are determined according to intervals between proper values of the Laplacian matrix, secondary clustering is conducted, and initial distance results are obtained; users conduct interactive operation on the initial distance results, new characteristic words are mined through chi-square statistics, a vector space is reconstructed, and the clustering process is repeated; finally, clustering results are shown to the users, and therefore the users obtain different categories of search results. According to the information search method and system, a semi-supervised learning approach in which the users intervene is adopted, the documents are clustered and analyzed, and the users obtain the different categories of search results.

The invention discloses a local spline embedding-based orthogonal semi-monitoring subspace image classification method. The method comprises the following steps of: 1) selecting n samples serving as training sets and the balance serving as testing sets from image data sets, wherein the training sets comprise marked data and unmarked data; 2) building an extra-class divergence matrix and an intra-class divergence matrix by using the marked data; (3) training data characteristic space distribution by using a whole and building a Laplacian matrix in a local spline embedding mode; 4) according to a local spline, embedding an orthogonal semi-monitoring subspace model, and searching a projection matrix to perform dimensionality reduction on the original high dimension characteristic; 5) building a classifier for the training samples after the dimensionality reduction by using a support vector machine; and 6) performing the dimensionality reduction on the testing sets by using the projection matrix and classifying the testing sets after the dimensionality reduction by using the classifier. In the method, the information, such as image sample marking, characteristic space distribution and the like, is fully utilized; potential semantic relevance among image data can be found out; and image semantics can be analyzed and expressed better.

In a method and system for matting a foreground object F having an opacity α constrained by associating a characteristic with selected pixels in an image having a background B, weights are determined for all edges of neighboring pixels for the image and used to build a Laplacian matrix L. The equation α is solved where α=arg min αT Lα s.t.αi=si, ∀iεS, S is the group of selected pixels, and si is the value indicated by the associated characteristic. The equation Ii=αiFi+(1−αi)Bi is solved for F and B with additional smoothness assumptions on F and B; after which the foreground object F may be composited on a selected background B′ that may be the original background B or may be a different background, thus allowing foreground features to be extracted from the original image and copied to a different background.

The invention discloses an SAR (Synthetic Aperture Radar) image segmentation method based on parallel sparse spectral clustering, relating to the technical field of image processing and mainly solving the problem of limitation of segmentation application of large-scale SAR images in the traditional spectral clustering technology. The SAR image segmentation method comprises the steps of: 1, extracting features of an SAR image to be segmented; 2, configuring an MATLAB (matrix laboratory) parallel computing environment; 3, allocating tasks all to processor nodes and computing partitioned sparse similar matrixes; 4, collecting computing results by a parallel task dispatcher and merging into an integral sparse similar matrix; 5, resolving a Laplacian matrix and carrying out feature decomposition; 6, carrying out K-means clustering on a feature vector matrix subjected to normalization; and 7, outputting a segmentation result of the SAR image. The invention can effectively overcome the bottleneck problem in computation and storage space of the traditional spectral clustering technology, has remarkable segmentation effect on large-scale SAR images, and is suitable for SAR image target detection and target identification.

The invention discloses a finite time robust fault diagnosis design method for a leader-follower multi-agent system. The method includes the steps: firstly, building a multi-agent system connection diagram with a leader and showing the multi-agent system connection diagram by a directed graph to obtain a Laplacian matrix L of a follower and an adjacent matrix G of the leader; building a state equation and an output equation of each node flight control system and augmenting a state vector and a fault vector into new vectors; constructing a distributed error equation and a global error equation based on the directed graph for each node according to the built directed graph, constructing a finite time fault diagnosis observer of a flight control system based on finite time robust control, and performing finite time fault diagnosis for faults of a multi-agent executor based on the directed graph. Faults of an optional node of the control system or simultaneously occurring faults of a plurality of nodes are effectively and accurately diagnosed and estimated on line in finite time.

The invention relates to a method for image co-segmentation based on a hypergraph. The method comprises the following steps that two images with the similar or the same foregrounds are read in; segmentation process is conducted on the input images through the Mean-shift algorithm; statistical operation is conducted on a color histogram H of the images through a histogram statistical method; the similarity of adjacent sub blocks in one image and the similarity of similar sub blocks in the different images are calculated; a similarity matrix of nodes and a similarity matrix of hyperedges are calculated, the proper value and the proper vector of the Laplacian matrix of the hypergraph are calculated and the foregrounds and backgrounds are segmented. According to the method, calculating speed of segmentation is improved, the foregrounds are well related, the backgrounds are well related, more relative information of the sub blocks is kept, and the segmenting effect is improved.

The invention relates to an overlapping community discovering method based on spectral clustering and fuzzy sets. The overlapping community discovering method comprises the steps that 1, data sets ofa social network are read to generate a network structure graph, and the attribute information of nodes in the network is acquired; 2, the Jaccard coefficient and the attribute information of the nodes in the network are combined to calculate the similarity value among the nodes in the network; 3, a similarity matrix is built based on the similarity value among the nodes, and accordingly the normalized Laplacian matrix is built; 4, the feature vector and the feature value of each node are calculated, and a new feature vector is generated by utilizing methods of iteration and compression; 5, the new feature vector is orthogonalized, the membership grade is calculated, and the nodes with a plurality of high community membership grade values are subjected to division of overlapping communities; 6, the community division meeting the highest modularity requirement is selected according to the modularity divided each time; and 7, the final community division result is output. The overlappingcommunity discovering method can efficiently and accurately discover and divide the overlapping structures in the complex network.

The invention relates to a formation satellite configuration containment control method, in particular, a formation satellite finite-time configuration containment control method. The objective of the invention is to solve the problem of low robustness of an existing multiple-satellite system formation control method and the problem of incapability of completely adapting to a practical application environment which is caused by a situation that inter-satellite communication topology is an undirected graph in the existing multiple-satellite system formation control method. The formation satellite finite-time configuration containment control method includes the following steps that: a relative orbit dynamic model of formation satellites i of a satellite formation system and relative reference points is established according to an established relative motion dynamic equation of reference satellites and accompanying satellites, and is simplified as an expression described in the descriptions; a weighted adjacent matrix A and a Laplacian matrix in the graph theory of a directed graph in the satellite formation system are provided according to the formation types of the formation satellites i; and a distributed finite-time configuration containment control laws of the multi-dynamic-pilot-satellite satellite formation system are designed, and therefore, each following satellite can achieve at a configuration convex hull formed by pilot satellites in finite time, and formation satellite finite-time configuration containment control can be realized. The formation satellite finite-time configuration containment control method of the invention is applicable to the control field of formation satellite configuration.

The invention discloses a three-dimensional model search method based on mesh segmentation. The method comprises the following step of analyzing and constructing a segmentation field through a hierarchical spectrum, and particularly comprises the steps of judgment of concave vertexes, constructing of a Laplacian matrix, matrix decomposition, selection of low-frequency feature vectors, generation of sub feature vectors, weight calculation of the sub feature vectors, and constructing of an edge symbol matrix. Contour lines are sampled in the segmentation field and are grouped and merged through a grouping-merging algorithm to obtain a plurality of candidate contour sets, the final segmentation boundary is determined according to the weight of each contour line in the candidate contour sets, and three-dimensional models are automatically segmented. Three-dimensional model mixing feature description sub-matrixes are obtained by calculating the feature description sub-matrix of each segmentation block of the three-dimensional models, the similarity of the mixing feature description sub-matrixes of each three-dimensional model in a three-dimensional model database to be searched and a target three-dimensional model to be searched is calculated, the similarity values of the three-dimensional models are ranked and output from low to high, and the three-dimensional model searching is achieved.

The invention discloses an active formation fault-tolerant control method based on a fast adaptive technology. The active formation fault-tolerant control method comprises the steps that a laplacian matrix and a leader-following connection matrix of distributed multi-agent systems are achieved by constructing a connection diagram of multi-agent systems; according to a four-rotor aircraft model ofan existing nonlinear term, a corresponding observer and a fast adaptive fault estimator are constructed to predict the actual size of faults;alocal augmented system error dynamic equation and a wholeaugmented system error dynamic equation are constructed; Lyapunov function is constructed, the method that parameters in a computational controller and the fault estimator are calculated is derived and achieved through corresponding theories, and the requirements of formation control are finished under the action of actuator failure of the system and external interference. According to the activeformation fault-tolerant control method, adverse influence of the external interference on fault-tolerant control is completely eliminated at the theoretical level, performance of fault estimation isimproved, and the fault-tolerant control when the actuator fault occurs at any node of four-rotor aircraft formation or when the actuator fault occurs at multiple nodes at the same time is achieved.

Data points of input data are processed by first determining a Laplacian matrix for the data. A spectrum of the Laplacian matrix includes an attractive spectrum of positive eigenvalues, a repulsive spectrum of negative eigenvalues, and a neutral spectrum of zero eigenvalues. An operation for the processing is determined using the Laplacian matrix, using information about the attractive spectrum, the repulsive spectrum, and the neutral spectrum, wherein the information includes the spectra and properties derived from the Spectra. Then, the operation is performed to produce processed data.

The invention discloses a hyperspectral image classification method based on semi-supervised dictionary learning, mainly solving the problem of high dimension of hyperspectral image and low classification precision in small sample status. The hyperspectral image classification method includes: expressing the pixel dot of the hyperspectral image via the spectral feature vector; selecting mark sample set, no-mark sample set and the test sample set; forming class label matrix with mark sample; forming Laplacian matrix without mark sample; using the alternating optimization strategy and the gradient descent method for solving the semi-supervised dictionary learning model; using the learned dictionary for coding the mark sample, no-mark sample and test sample; using the learned sparse code as the characteristic for classifying the hyperspectral image. The hyperspectral image classification method based on semi-supervised dictionary learning adopts the semi-supervised thought to obtain higher classification accuracy compared with the supervised learning method and is applied to the field of precision agriculture, vegetation investigation and military reconnaissance.

The invention discloses a synthetic aperture radar image target identification method based on multi-parameter spectrum feature, aiming at solving the low SAR image target identification rate problem of the current method. The method comprises the steps of carrying out pretreatment on the selected image of the known category information and the image to be tested to obtain a training set and a testing set; respectively calculating the scale parameters of all the training sample points and the testing sample points; respectively calculating the multi-parameter affinity matrix of the training set and the testing set by using the obtained scale parameters; respectively constructing Laplacian matrixes of the training set and the testing set with the multi-parameter affinity matrix; carrying out feature decomposition on the Laplacian matrix of the training set to obtain a corresponding projection matrix; respectively projecting the training sample and the testing sample to the space stretched by the projection matrix to obtain a new training set and a new testing set; inputting the new training set and the testing set into a support vector machine for category identification to obtain the category information of the tested image. The invention has the advantage of high identification rate and can be used for identifying SAR images.

The present invention provides a multi-view clustering method based on non-negative matrix factorization and diversity-consistency. The technical problem is solved that the clustering precision and the normalization interaction information are low in a current multi-view clustering method. The method comprises the steps of: obtaining normalization non-negative multi-view data of an original imageset; constructing a base matrix, a coefficient matrix and a standard-similar indication matrix corresponding to the multi-view data; constructing a target function based on the non-negative matrix factorization and diversity-consistency multi-view clustering; obtaining an iteration updating expression of the base matrix, the coefficient matrix and the Laplacian matrix; obtaining the optimal valueof the standard-similar indication matrix; and performing K-mean clustering for the optimal value of the standard-similar indication matrix, and obtaining a clustering cluster corresponding to the multi-view data. The multi-view clustering method employs expression diversity and standard-similar consistency to learn the complementation and common information in the multi-view data so as to effectively improve the performances of the multi-view clustering, and can be applied to the field of biology information analysis and financial investment analysis, etc.

The invention proposes an adaptive multi-view clustering method based on paired synergetic regulation and NMF, and the method is designed to resolve the technical problem of a currently available multi-view clustering method that the precision is low and the normalized interactive information is also low. The method comprises the following steps: obtaining the normalized non-negative multi-view data of an original image set; calculating the Laplacian matrix for the multi-view data; constructing an objective function for adaptive multi-view clustering based on paired synergetic regularization and NMF; obtaining the iteratively updated expressions for the base matrix, the coefficient matrix and the weight parameters respectively; obtaining the updated base matrix, the coefficient matrix and weight parameters; and performing K-means clustering on the updated coefficient matrix to obtain the clustering result. According to the invention, through the use of a paired synergetic regulation method to keep the similarities of the views and through the use of the adaptive method to automatically learn the weight parameters for the similarity constraining items in the views, the multi-view clustering function is increased effectively so that the function can be applied for fields in user information analyzing, financial analyzing, medical science.

The invention discloses an SAR (Synthetic Aperture Radar) image target recognizing method based on nuclear scale tangent dimensionality reduction, which mainly solves the problem of low SAR image target recognizing rate of the traditional method. The method comprises the following steps of: preprocessing the selected image with the known class information and the image to be tested to acquire a training set and a testing set; mapping the training set to a higher dimensional space by the Gaussian kernel function, and respectively constructing an intra-class dissimilarity matrix and an extra-class dissimilarity matrix by using the mapped high dimensional feature as input, thereby acquiring a Laplacian matrix based on the nuclear scale tangent; carrying out feature decomposition on the matrix to acquire an optimal projection matrix; respectively projecting a training sample and a testing sample to a subspace formed by expansion of projection matrix vectors to acquire a new training set and a new testing set; and inputting the new training set and the new testing set into a support vector machine for classification and recognition to acquire the class information of the tested image. The method of the invention has the advantages of high recognition rate and good robustness and can be used for recognizing SAR images.

The invention discloses an image set unsupervised co-segmentation method based on deformable graph structure representation. The method is divided into the following four steps: firstly, superpixel segmentation is carried out on each graph in a graph set and a descriptor is extracted; secondly, an inner graph based on a Biharmonic distance is built for each picture, specifically, a two-dimensional image is stretched as a three-dimensional grid, and a Laplacian matrix is established on the three-dimensional grid according to a Riemann flow pattern space manner; thirdly, a deformable hypergraph which includes all superpixel in the graph set is established after the inner graph is established and the Biharmonic distance is calculated in a descriptor space(characteristic space); fourthly, clustering ideas considering connectivity are used, and an energy function which comprises the inner graph, the hypergraph and segmentation size constraints is established. Optimization is carried out by using the expectation maximization algorithm to obtain a final co-segmentation result. The algorithm partly uses CPU(Central Processor Unit) parallelism with CPU parallelism, the co-segmentation method has excellent segmentation accuracy and efficiency performance for the large-scale graph set.

The invention relates to a trajectory prediction method for multiple mobile robots, which comprises the steps of 1) building a multi-mobile-robot motion model in a complex plane; 2) building a topological graph of a multi-robot system; 3) solving a complex Laplacian matrix; 4) solving a stable matrix; 5) calculating a distributed discrete control signal; and 6) recording displacement information and calculating the final position. According to the invention, each robot can be enabled to predict a trajectory path thereof in the future within the shortest time, the method is completely distributed, and the utilized information is only the displacement information recorded by the robots by themselves. In addition, the robots can also work out the target position thereof by using the rotating speed of left and right wheels or displacement information recorded by other local coordinate systems if a global coordinate system is not available. The method helps the robots to calculate the target position thereof efficiently, and provides a feasible scheme for efficient formation of multiple mobile robots.

A system and method for segmenting an object in an image using an isoperimetric ratio in a graphics processing unit is disclosed. The object is identified by one or more selected pixels located within the object. The system includes a graphics processing unit and software loadable on the graphics processing unit. The software is operable to find weights for edges, to build a Laplacian matrix and a d vector, to eliminate the row and column corresponding to the one or more selected pixels to determine L0 and d0, to solve x0 in the equation L0x0=d0; and to threshold the potentials x at the value that selects the object having the lowest isoperimetric ratio.

The invention discloses an entropy sequencing-based semi-supervision spectral clustering method for determining a clustering number, and mainly solves the problem of selection of a characteristic vector of a Laplacian matrix in spectral clustering. The method comprises the following steps of: performing permutation on the characteristic vector by an entropy sequencing theory so as to acquire an array of the characteristic vector with the uppermost importance; for a k class problem, extracting the first k arrays of the characteristic vector and projecting the arrays into a k-dimensional space; clustering according to the distance of each point and 2k semiaxes in the k-dimensional space; recording the preserved clustering number as c except for a class without points in a 2k class or a clustering class with the point number less than one percent of that of input data; extracting the first c arrays of the characteristic vector and circulating the operation until the clustering number is stable, wherein corresponding class number is the optimal clustering number; and marking an input data point according to the coordinate of each input point so as to acquire a clustering result. The method has the advantages of high self-adaption performance and high clustering precision rate and can be used for self-adaptively determining an image category number.

The invention discloses a human body behavior identification method adopting non-supervision multiple-view feature selection. The method includes the steps that firstly, a plurality of types of visual feature expression are extracted from sets of video data, including different human body behavior types, collected in advance to acquire a multi-view feature data matrix; then, in terms of each view, a visual sense similarity graph and a geometric Laplacian matrix which are related to the corresponding view are built so as to build a target function for solving a multi-view feature selection matrix and solving a data clustering type matrix; the multi-view feature selection matrix is optimized and calculated through the iteration gradient descent method, and a two-value feature selection matrix is acquired according to the line sequencing result of W; finally, video data to be identified are converted into corresponding multi-view feature data, distances between data to be identified after feature selection and multi-view feature data collected in advance are compared, and a video to be identified is identified as the human body behavior type in the jth video data collected in advance, wherein j is the serial number of video data, corresponding to the minimum distance of each list of multi-view feature data, collected in advance. The method is high in calculation speed and has high identification accurate rate and noise and interference resistance ability.

Provided is a point cloud attribute compression method based on a KD tree and optimized graph transformation, wherein same, with regard to point cloud data, reduces the influence of a sub-graph issue on the graph transformation efficiency by means of a new transformation block division method, optimizes a graph transformation kernel parameter, and improves the compression performance of the graph transformation, and comprises: point cloud pre-processing, point cloud KD tree division, graph construction in the transformation block, graph transformation kernel parameter training, and a point cloud attribute compression process. The present invention optimizes the division method for a point cloud transformation block, and makes the number of points in the transformation block the same, and also realizes that the dimensionality of a transformation matrix is basically the same, so as to facilitate parallel processing of subsequent graph transformations; also optimizes the graph establishment in the transformation block, and avoids the sub-graph issue caused by the existing method; and at the same time optimizes, by training the kernel parameter of the graph transformation, the sparsity of a graph transformation Laplacian matrix, so as to achieve a better point cloud attribute compression performance.

The invention provides a hyperspectral remote sensing image dimension reduction and classification method based on spatial regularization manifold learning algorithm. The method comprises the following steps: the hyperspectral remote sensing image is divided into multiple sub blocks; partial data points are randomly selected to serve as connection data; the connection data and data of each sub block are combined to obtain enhanced sub block data; LLE algorithm and an image Laplacian matrix corresponding to regular spatial constraints are calculated respectively for each enhanced sub block, a composite Laplacian matrix is obtained, eigenvalue decomposition is carried out on the matrix, and a dimension reduction result is obtained; the dimension reductions are aligned, and a dimension reduction result for the overall image is obtained; and the dimension reduction data are classified finally. Data spatial information is effectively combined in a manifold learning algorithm framework, an image block and aligning strategy is adopted, and effects of regular spatial constraints can be achieved to the maximal degree. The algorithm is well adaptive to classification of multiple kinds of hyperspectral remote sensing data, and the classification precision of the hyperspectral remote sensing image can be improved obviously.

The invention discloses a multi-mobile-robot minimum step formation method, and the method comprises the following steps: 1), building a multi-mobile-robot motion model in a complex plane; 2), building a topological graph of a multi-mobile-robot system; 3), solving a complex Laplacian matrix; 4), configuring extreme points of the complex Laplacian matrix; 5), calculating distributed discrete control signals; 6), recording the displacement information and calculating the final position. The method can enable a robot to predict the final position of the robot in a formation in the shortest time, and is of a completely distributed type. The employed information is just the displacement information recorded by the robot, and there is no global coordinate system. The robot still can calculate the target position through the rotating speeds of the left and right wheels or the displacement information recorded by other local coordinate systems. The method efficiently helps the robot calculate the target position of the robot, and provides a feasible solution for the high-efficiency formation of multiple mobile robots.

The invention, which relates to the indoor scene classification field, provides a supergraph learning-based indoor scene classification method. The method comprises the following steps that: a target is extracted from an image by using nearly a hundred of target detectors and a super descriptor formed by the formed target descriptor is used as a feature descriptor of the image; a supergraph of the image descriptor is constructed by using a K neighbor method and a Laplacian matrix is calculated, thereby constructing a semi-supervised learning frame; a linear regression model is constructed and is added into the semi-supervised learning frame; according to the constructed semi-supervised learning frame, marking is carried out on the part of image descriptor by combining the extracted image feature descriptor, so that the semi-supervised learning frame can predetermine a label of an unmarked image automatically and iteratively and thus the image classification is completed; and meanwhile, the linear regression model is initialized during the automatic iteration process; and according to the linear regression model, image classification is carried out on data that are added newly directly by combining the extracted image feature descriptor, so that there is no need to construct a supergraph again.

The invention discloses a parallel community discovery method and device, and relates to the field of data mining. The method disclosed by the invention comprises the following steps: reading original social network data, converting the original social network data into an adjacency matrix way, and storing the original social network data on a HDFS (Hadoop distributed file system); calculating a stiffness matrix D and a Laplacian matrix of the adjacency matrix of a picture stored on the HDFS on a computing cluster configured with a Hadoop environment; carrying out the parallel Lanczos numerical value solving of a characteristic valve and a characteristic vector to the Laplacian matrix to obtain the characteristic vectors corresponding to the first K maximum characteristic values of the matrix; constructing a characteristic vector matrix for normalizing to obtain a standardized characteristic vector matrix and extract characteristics; taking each line as a point, and clustering the points into K types by a clustering method; according to the corresponding relationship of the points, equivalently dividing individuals in an original community into K types to finish the classification of the communities. The invention also discloses a parallel community discovery device. A technical scheme of the invention exhibits good adaptability to large-scale data.

A covariance-clustering algorithm for partitioning a graph into sub-graphs (clusters) using variations of the pseudo-inverse of the Laplacian matrix (A) associated with the graph. The algorithm does not require the number of clusters as an input parameter and, considering the covariance of the Markov field associated with the graph, algorithm finds sub-graphs characterized by a within-cluster covariance larger than an across-clusters covariance. The covariance-clustering algorithm is applied to a semantic graph representing the simulated evidence of multiple events.