Spectral Analysis of Signed Graphs for Clustering, Prediction and Visualization
نویسندگان
چکیده
We study the application of spectral clustering, prediction and visualization methods to graphs with negatively weighted edges. We show that several characteristic matrices of graphs can be extended to graphs with positively and negatively weighted edges, giving signed spectral clustering methods, signed graph kernels and network visualization methods that apply to signed graphs. In particular, we review a signed variant of the graph Laplacian. We derive our results by considering random walks, graph clustering, graph drawing and electrical networks, showing that they all result in the same formalism for handling negatively weighted edges. We illustrate our methods using examples from social networks with negative edges and bipartite rating graphs.
منابع مشابه
On the Spectral Evolution of Large Networks
In this thesis, I study the spectral characteristics of large dynamic networks and formulate the spectral evolution model. The spectral evolution model applies to networks that evolve over time, and describes their spectral decompositions such as the eigenvalue and singular value decomposition. The spectral evolution model states that over time, the eigenvalues of a network change while its eig...
متن کاملCheeger constants, structural balance, and spectral clustering analysis for signed graphs
We introduce a family of multi-way Cheeger-type constants {h k , k = 1, 2, . . . , N} on a signed graph Γ = (G, σ) such that h k = 0 if and only if Γ has k balanced connected components. These constants are switching invariant and bring together in a unified viewpoint a number of important graph-theoretical concepts, including the classical Cheeger constant, the non-bipartiteness parameter of D...
متن کاملOn spectral partitioning of signed graphs
Classical spectral clustering is based on a spectral decomposition of a graph Laplacian, obtained from a graph adjacency matrix representing positive graph edge weights describing similarities of graph vertices. In signed graphs, the graph edge weights can be negative to describe disparities of graph vertices, for example, negative correlations in the data. Negative weights lead to possible neg...
متن کاملSigned Laplacian for spectral clustering revisited
Classical spectral clustering is based on a spectral decomposition of a graph Laplacian, obtained from a graph adjacency matrix representing positive graph edge weights describing similarities of graph vertices. In signed graphs, the graph edge weights can be negative to describe disparities of graph vertices, for example, negative correlations in the data. Negative weights lead to possible neg...
متن کاملOn Spectral Analysis of Signed and Dispute Graphs
This paper presents a spectral analysis of signed networks from both theoretical and practical aspects. On the theoretical aspect, we conduct theoretical study based on matrix perturbation theorem for analyzing community structures of complex signed networks and show how the negative edges affect distributions and patterns of node spectral coordinates in the spectral space. We prove and demonst...
متن کامل