Graph clustering has been widely applied in exploring regularities emerging in relational data.Recently,the rapid development of network theory correlates graph clustering with the detection of community structure,a c...Graph clustering has been widely applied in exploring regularities emerging in relational data.Recently,the rapid development of network theory correlates graph clustering with the detection of community structure,a common and important topological characteristic of networks.Most existing methods investigate the community structure at a single topological scale.However,as shown by empirical studies,the community structure of real world networks often exhibits multiple topological descriptions,corresponding to the clustering at different resolutions.Furthermore,the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree.It is very challenging to detect multiscale community structure in heterogeneous networks.In this paper,we propose a novel,unified framework for detecting community structure from the perspective of dimensionality reduction.Based on the framework,we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction.We then propose a novel method to detect communities at multiple topological scales within our framework.We further show that existing algorithms fail to deal with heterogeneous node degrees.We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework.Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks.展开更多
A model-free adaptive control method is proposed for the spacecrafts whose dynamical parameters change over time and cannot be acquired accurately. The algorithm is based on full form dynamic linearization.A dimension...A model-free adaptive control method is proposed for the spacecrafts whose dynamical parameters change over time and cannot be acquired accurately. The algorithm is based on full form dynamic linearization.A dimension reduction matrix is introduced to construct an augmented system with the same dimension input and output. The design of the controller depends on the system input and output data rather than the knowledge of the controlled plant. The numerical simulation results show that the improved controller can deal with different models with the same set of controller parameters,and the controller performance is better than that of PD controller for the time-varying system with disturbance.展开更多
The compressive sensing (CS) theory allows people to obtain signal in the frequency much lower than the requested one of sampling theorem. Because the theory is based on the assumption of that the location of sparse...The compressive sensing (CS) theory allows people to obtain signal in the frequency much lower than the requested one of sampling theorem. Because the theory is based on the assumption of that the location of sparse values is unknown, it has many constraints in practical applications. In fact, in many cases such as image processing, the location of sparse values is knowable, and CS can degrade to a linear process. In order to take full advantage of the visual information of images, this paper proposes the concept of dimensionality reduction transform matrix and then se- lects sparse values by constructing an accuracy control matrix, so on this basis, a degradation algorithm is designed that the signal can be obtained by the measurements as many as sparse values and reconstructed through a linear process. In comparison with similar methods, the degradation algorithm is effective in reducing the number of sensors and improving operational efficiency. The algorithm is also used to achieve the CS process with the same amount of data as joint photographic exports group (JPEG) compression and acquires the same display effect.展开更多
基金funded by the National Natural Science Foundation of China under Grant Nos. 60873245,60933005,60873243,60903139 and 60803123funded by the National High Technology Research and Development 863 Programof China under Grant No. 2010AA012503the Beijing Natural Science Foundation under Grant No. 4122077
文摘Graph clustering has been widely applied in exploring regularities emerging in relational data.Recently,the rapid development of network theory correlates graph clustering with the detection of community structure,a common and important topological characteristic of networks.Most existing methods investigate the community structure at a single topological scale.However,as shown by empirical studies,the community structure of real world networks often exhibits multiple topological descriptions,corresponding to the clustering at different resolutions.Furthermore,the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree.It is very challenging to detect multiscale community structure in heterogeneous networks.In this paper,we propose a novel,unified framework for detecting community structure from the perspective of dimensionality reduction.Based on the framework,we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction.We then propose a novel method to detect communities at multiple topological scales within our framework.We further show that existing algorithms fail to deal with heterogeneous node degrees.We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework.Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11102007)the Fundamental Research Fund for the Central Universities(Grant No.YWF-14-YHXY-012)
文摘A model-free adaptive control method is proposed for the spacecrafts whose dynamical parameters change over time and cannot be acquired accurately. The algorithm is based on full form dynamic linearization.A dimension reduction matrix is introduced to construct an augmented system with the same dimension input and output. The design of the controller depends on the system input and output data rather than the knowledge of the controlled plant. The numerical simulation results show that the improved controller can deal with different models with the same set of controller parameters,and the controller performance is better than that of PD controller for the time-varying system with disturbance.
基金supported by the National Natural Science Foundation of China (61077079)the Specialized Research Fund for the Doctoral Program of Higher Education (20102304110013)the Program Ex-cellent Academic Leaders of Harbin (2009RFXXG034)
文摘The compressive sensing (CS) theory allows people to obtain signal in the frequency much lower than the requested one of sampling theorem. Because the theory is based on the assumption of that the location of sparse values is unknown, it has many constraints in practical applications. In fact, in many cases such as image processing, the location of sparse values is knowable, and CS can degrade to a linear process. In order to take full advantage of the visual information of images, this paper proposes the concept of dimensionality reduction transform matrix and then se- lects sparse values by constructing an accuracy control matrix, so on this basis, a degradation algorithm is designed that the signal can be obtained by the measurements as many as sparse values and reconstructed through a linear process. In comparison with similar methods, the degradation algorithm is effective in reducing the number of sensors and improving operational efficiency. The algorithm is also used to achieve the CS process with the same amount of data as joint photographic exports group (JPEG) compression and acquires the same display effect.