Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds

Dong, Xiaowen; Frossard, Pascal; Vandergheynst, Pierre; Nefedov, Nikolai

doi:10.1109/tsp.2013.2295553

Cited by 173 publications

(25 citation statements)

References 41 publications

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“…Each point on G ( k , n ) represents a set of orthonormal bases Y that can span a dimensional space span ( Y ). Thus, the distance between the spaces span ( Y ) and can be defined as the sum of the principal angles for all the basis pairs: where is the principal angle between basis and basis [ 26 , 27 ].…”

Section: Methodsmentioning

confidence: 99%

Patient subgrouping with distinct survival rates via integration of multiomics data on a Grassmann manifold

Alfatemi

Peng

Rong

et al. 2022

BMC Med Inform Decis Mak

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Background Patient subgroups are important for easily understanding a disease and for providing precise yet personalized treatment through multiple omics dataset integration. Multiomics datasets are produced daily. Thus, the fusion of heterogeneous big data into intrinsic structures is an urgent problem. Novel mathematical methods are needed to process these data in a straightforward way. Results We developed a novel method for subgrouping patients with distinct survival rates via the integration of multiple omics datasets and by using principal component analysis to reduce the high data dimensionality. Then, we constructed similarity graphs for patients, merged the graphs in a subspace, and analyzed them on a Grassmann manifold. The proposed method could identify patient subgroups that had not been reported previously by selecting the most critical information during the merging at each level of the omics dataset. Our method was tested on empirical multiomics datasets from The Cancer Genome Atlas. Conclusion Through the integration of microRNA, gene expression, and DNA methylation data, our method accurately identified patient subgroups and achieved superior performance compared with popular methods.

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Section: Methodsmentioning

confidence: 99%

Patient subgrouping with distinct survival rates via integration of multiomics data on a Grassmann manifold

Alfatemi

Peng

Rong

et al. 2022

BMC Med Inform Decis Mak

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“…Therefore, information embedded in different spaces can be mapped into an unified space and the clustering algorithm can utilize the mapped information to derive islanding results. We summarize the key steps from [15] for finding a unified Laplacian matrix of a graph with M distinct information matrices as follows.…”

Section: Grassmann Manifoldmentioning

confidence: 99%

Spectral Graph Clustering for Intentional Islanding Operations in Resilient Hybrid Energy Systems

Chen

Badakhshan

et al. 2023

IEEE Trans. Ind. Inf.

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Establishing cleaner energy generation, therefore, improving the sustainability of the power system is a crucial task in this century, and one of the key strategies being pursued is to shift the dependence on fossil fuel to renewable technologies, such as wind, solar, and nuclear. However, with the increasing number of heterogeneous components included, the complexity of the hybrid energy system becomes more significant, and the complex system imposes a more stringent requirement of the contingency plan to enhance the overall system resilience. Among different strategies to ensure a reliable system, intentional islanding is commonly applied in practical applications for power systems and attracts abundant interest in the literature. In this study, we propose a hierarchical spectral clustering-based intentional islanding strategy at the transmission level with renewable generations. To incorporate the renewable generation that relies on the inverter technology, the frequency measurements are considered to represent the transient response, and it has been further used as embedded information in the clustering algorithm along with other important electrical information from the system to enrich the modeling capability of the proposed framework. To demonstrate the effectiveness of the islanding strategy, the modified IEEE 9-bus system coupled with wind farms is considered as the test case.

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“…Therefore, the principle angles {θ j } k j=1 between these subspaces can represent the distance between Y i and Y. Furthermore, this distance can be reformulated as follows [39].…”

Section: Commonality Loss Of Multiple Structuresmentioning

confidence: 99%

Structure Fusion Based on Graph Convolutional Networks for Node Classification in Citation Networks

et al. 2020

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Suffering from the multi-view data diversity and complexity, most of the existing graph convolutional networks focus on the networks’ architecture construction or the salient graph structure preservation for node classification in citation networks and usually ignore capturing the complete graph structure of nodes for enhancing classification performance. To mine the more complete distribution structure from multi-graph structures of multi-view data with the consideration of their specificity and the commonality, we propose structure fusion based on graph convolutional networks (SF-GCN) for improving the performance of node classification in a semi-supervised way. SF-GCN can not only exploit the special characteristic of each view datum by spectral embedding preserving multi-graph structures, but also explore the common style of multi-view data by the distance metric between multi-graph structures. Suppose the linear relationship between multi-graph structures; we can construct the optimization function of the structure fusion model by balancing the specificity loss and the commonality loss. By solving this function, we can simultaneously obtain the fusion spectral embedding from the multi-view data and the fusion structure as the adjacent matrix to input graph convolutional networks for node classification in a semi-supervised way. Furthermore, we generalize the structure fusion to structure diffusion propagation and present structure propagation fusion based on graph convolutional networks (SPF-GCN) for utilizing these structure interactions. Experiments demonstrate that the performance of SPF-GCN outperforms that of the state-of-the-art methods on three challenging datasets, which are Cora, Citeseer, and Pubmed in citation networks.

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Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds

Cited by 173 publications

References 41 publications

Patient subgrouping with distinct survival rates via integration of multiomics data on a Grassmann manifold

Patient subgrouping with distinct survival rates via integration of multiomics data on a Grassmann manifold

Spectral Graph Clustering for Intentional Islanding Operations in Resilient Hybrid Energy Systems

Structure Fusion Based on Graph Convolutional Networks for Node Classification in Citation Networks

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