Title
Directed Graph Clustering Algorithms, Topology, and Weak Links
Abstract
In this article, a general approach for directed graph clustering and two new density-based clustering objectives are presented. First, using an equivalence between the clustering objective functions and a trace maximization expression, the directed graph clustering objectives are converted into the corresponding weighted kernel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -means problems. Then, a nonspectral algorithm, which covers both the direction and weight information of the directed graphs, is thus proposed. Next, with Rayleigh’s quotient, the upper and lower bounds of clustering objectives are obtained. After that, we introduce a new definition of weak links to characterize the effectiveness of clustering. Finally, illustrative examples are given to demonstrate effectiveness of the results. This article provides a glance at the potential connection between density-based and pattern-based clustering. Compared with other approaches for directed graph clustering, the method proposed in this article naturally avoids the loss of the nonsymmetric edge data because there is no need for any additional symmetrization.
Year
DOI
Venue
2022
10.1109/TSMC.2021.3087591
IEEE Transactions on Systems, Man, and Cybernetics: Systems
Keywords
DocType
Volume
Directed graph clustering,nonspectral algorithm,Rayleigh’s quotient,weighted kernel k-means
Journal
52
Issue
ISSN
Citations 
6
2168-2216
0
PageRank 
References 
Authors
0.34
23
5
Name
Order
Citations
PageRank
Xiao Zhang183.16
Bosen Lian212.38
FRANK L. LEWIS35782402.68
Yan Wan441.75
Daizhan Cheng500.34