Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks,solved by approaches based on multiple attribute decision that suffer from ignoring the correlat...Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks,solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.展开更多
Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully...Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.展开更多
Real-world data can often be represented in multiple forms and views,and analyzing data from different perspectives allows for more comprehensive learning of the data,resulting in better data clustering results.Non-ne...Real-world data can often be represented in multiple forms and views,and analyzing data from different perspectives allows for more comprehensive learning of the data,resulting in better data clustering results.Non-negative matrix factorization(NMF)is used to solve the clustering problem to extract uniform discriminative low-dimensional features from multi-view data.Many clustering methods based on graph regularization have been proposed and proven to be effective,but ordinary graphs only consider pairwise relationships between samples.In order to learn the higher-order relationships that exist in the sample manifold and feature manifold of multi-view data,we propose a new semi-supervised multi-view clustering method called dual hypergraph regularized partially shared non-negative matrix factorization(DHPS-NMF).The complex manifold structure of samples and features is learned by constructing samples and feature hypergraphs.To improve the discrimination power of the obtained lowdimensional features,semi-supervised regression terms are incorporated into the model to effectively use the label information when capturing the complex manifold structure of the data.Ultimately,we conduct experiments on six real data sets and the results show that our algorithm achieves encouraging results in comparison with some methods.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62162040 and 11861045)。
文摘Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks,solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.
基金Supported by the National Natural Science Foundation of China （ No. 60872083 ） and the National High Technology Research and Development Program of China （No. 2007AA12Z149）.
基金supported by the National Natural Science Foundation of China(Nos.11661141019 and 61621003)the National Ten Thousand Talent Program for Young Topnotch Talents+1 种基金Chinese Academy Science(CAS)Frontier Science Research Key Project for Top Young Scientist(No.QYZDB-SSW-SYS008)the Key Laboratory of Random Complex Structures and Data Science,CAS(No.2008DP173182).
文摘Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.
基金supported by the National Natural Science Foundation of China (Grant Nos.62073087,U1911401,62071132,and 61973090)the Guangdong Key R&D Project of China (Grant No.2019B010121001)。
文摘Real-world data can often be represented in multiple forms and views,and analyzing data from different perspectives allows for more comprehensive learning of the data,resulting in better data clustering results.Non-negative matrix factorization(NMF)is used to solve the clustering problem to extract uniform discriminative low-dimensional features from multi-view data.Many clustering methods based on graph regularization have been proposed and proven to be effective,but ordinary graphs only consider pairwise relationships between samples.In order to learn the higher-order relationships that exist in the sample manifold and feature manifold of multi-view data,we propose a new semi-supervised multi-view clustering method called dual hypergraph regularized partially shared non-negative matrix factorization(DHPS-NMF).The complex manifold structure of samples and features is learned by constructing samples and feature hypergraphs.To improve the discrimination power of the obtained lowdimensional features,semi-supervised regression terms are incorporated into the model to effectively use the label information when capturing the complex manifold structure of the data.Ultimately,we conduct experiments on six real data sets and the results show that our algorithm achieves encouraging results in comparison with some methods.
