Spectral Analysis of Signed Graphs for Clustering, Prediction and Visualization

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.

• Type: Conference
• Year: 2010
• Where: SDM
• Authors: Jérôme Kunegis, Stephan Schmidt, Andreas Lommatzsch, Jürgen Lerner, Ernesto William De Luca, Sahin Albayrak
• Keywords: Data Mining, SDM 2010, Spectral Clustering, Visualization Methods, Weighted Edges