Spectral Analysis of Signed Graphs for Clustering, Prediction and Visualization

Previous chapter Next chapter Full AccessProceedings Proceedings of the 2010 SIAM International Conference on Data Mining (SDM)Spectral Analysis of Signed Graphs for Clustering, Prediction and VisualizationJérôme Kunegis, Stephan Schmidt, Andreas Lommatzsch, Jürgen Lerner, Ernesto W. De Luca, and Sahin AlbayrakJérôme Kunegis, Stephan Schmidt, Andreas Lommatzsch, Jürgen Lerner, Ernesto W. De Luca, and Sahin Albayrakpp.559 - 570Chapter DOI:https://doi.org/10.1137/1.9781611972801.49PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract 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. Previous chapter Next chapter RelatedDetails Published:2010ISBN:978-0-89871-703-7eISBN:978-1-61197-280-1 https://doi.org/10.1137/1.9781611972801Book Series Name:ProceedingsBook Code:PR136Book Pages:1-953