On analyzing graphs with motif-paths

2021 ◽  
Vol 14 (6) ◽  
pp. 1111-1123
Author(s):  
Xiaodong Li ◽  
Reynold Cheng ◽  
Kevin Chen-Chuan Chang ◽  
Caihua Shan ◽  
Chenhao Ma ◽  
...  
Keyword(s):  
Link Prediction ◽  
Graph Clustering ◽  
Order Structure ◽  
Graph Analysis ◽  
High Order Structure ◽  
Node Ranking ◽  
Local Graph ◽  
Edge Based ◽  
Graph Motif ◽  
Better Than

Path-based solutions have been shown to be useful for various graph analysis tasks, such as link prediction and graph clustering. However, they are no longer adequate for handling complex and gigantic graphs. Recently, motif-based analysis has attracted a lot of attention. A motif, or a small graph with a few nodes, is often considered as a fundamental unit of a graph. Motif-based analysis captures high-order structure between nodes, and performs better than traditional "edge-based" solutions. In this paper, we study motif-path , which is conceptually a concatenation of one or more motif instances. We examine how motif-paths can be used in three path-based mining tasks, namely link prediction, local graph clustering and node ranking. We further address the situation when two graph nodes are not connected through a motif-path, and develop a novel defragmentation method to enhance it. Experimental results on real graph datasets demonstrate the use of motif-paths and defragmentation techniques improves graph analysis effectiveness.

scholarly journals Local hypergraph clustering using capacity releasing diffusion

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243485
Author(s):  
Rania Ibrahim ◽  
David F. Gleich
Keyword(s):  
Graph Clustering ◽  
Learning Task ◽  
Higher Order ◽  
Spectral Graph Theory ◽  
Clustering Technique ◽  
Clustering Quality ◽  
Connected Cluster ◽  
Local Graph ◽  
Synthetic Datasets ◽  
Better Than

Local graph clustering is an important machine learning task that aims to find a well-connected cluster near a set of seed nodes. Recent results have revealed that incorporating higher order information significantly enhances the results of graph clustering techniques. The majority of existing research in this area focuses on spectral graph theory-based techniques. However, an alternative perspective on local graph clustering arises from using max-flow and min-cut on the objectives, which offer distinctly different guarantees. For instance, a new method called capacity releasing diffusion (CRD) was recently proposed and shown to preserve local structure around the seeds better than spectral methods. The method was also the first local clustering technique that is not subject to the quadratic Cheeger inequality by assuming a good cluster near the seed nodes. In this paper, we propose a local hypergraph clustering technique called hypergraph CRD (HG-CRD) by extending the CRD process to cluster based on higher order patterns, encoded as hyperedges of a hypergraph. Moreover, we theoretically show that HG-CRD gives results about a quantity called motif conductance, rather than a biased version used in previous experiments. Experimental results on synthetic datasets and real world graphs show that HG-CRD enhances the clustering quality.

scholarly journals Local Graph Clustering with Network Lasso

2020 ◽  
pp. 1-1
Author(s):  
Alexander Jung ◽  
Yasmin Sarcheshmehpour
Keyword(s):  
Graph Clustering ◽  
Local Graph

scholarly journals Use of 3D imaging for providing insights into high-order structure of mitotic chromosomes

Chromosoma ◽  
2018 ◽  
Vol 128 (1) ◽  
pp. 7-13 ◽  
Author(s):  
Mohammed Yusuf ◽  
Kohei Kaneyoshi ◽  
Kiichi Fukui ◽  
Ian Robinson
Keyword(s):  
3D Imaging ◽  
High Order ◽  
Order Structure ◽  
High Order Structure ◽  
Mitotic Chromosomes

How Accurate is Qcbed ? -- the Case of Rutile (TiO2)

2001 ◽  
Vol 7 (S2) ◽  
pp. 368-369
Author(s):  
B. Jiang ◽  
J. Friis ◽  
J.C.H. Spence
Keyword(s):  
Systematic Errors ◽  
Mean Value ◽  
Order Structure ◽  
Data Sets ◽  
X Ray ◽  
Silicon Crystals ◽  
Structure Factors ◽  
The Mean ◽  
Mott Formula ◽  
Better Than

An accuracy of better than 1% is needed to measure the changes in charge density due to bonding. Here we report an accuracy up to 0.025% (random error) obtained in rutile crystal structure factors measurement by QCBED. This error is the standard deviation in the mean value obtained from ten data sets. Systematic errors may be present. Figure 1 gives an example of the (200) refinement results. Table 1 lists several low order structure factor refinement results. The accuracy of the measured electron structure factors was 0.1-0.2% but after conversion to x-ray structure factors, the accuracy for low orders improved due to the Mott formula [1] For (110) and (101) reflections, the accuracy in x-ray structure factors became 0.025% and 0.048% respectively. This accuracy is equivalent to that of the X-ray single crystal Pendellosung method on silicon crystals [2].The experiments were done on a Leo 912 Omega TEM.

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