Spectral subspace clustering for graphs with feature vectors

Clustering graphs annotated with feature vectors has recently gained much attention. The goal is to detect groups of vertices that are densely connected in the graph as well as similar with respect to their feature values. While early approaches treated all dimensions of the feature space as equally important, more advanced techniques consider the varying relevance of dimensions for different groups. In this work, we propose a novel clustering method for graphs with feature vectors based on the principle of spectral clustering. Following the idea of subspace clustering, our method detects for each cluster an individual set of relevant features. Since spectral clustering is based on the eigendecomposition of the affinity matrix, which strongly depends on the choice of features, our method simultaneously learns the grouping of vertices and the affinity matrix. To tackle the fundamental challenge of comparing the clustering structures for different feature subsets, we define an objective function that is unbiased regarding the number of relevant features. We develop the algorithm SSCG and we show its application for multiple real-world datasets.