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Due to its computational complexity, graph cuts for cluster detection andidentification are used mostly in the form of convex relaxations. We propose toutilize the original graph cuts such as Ratio, Normalized or Cheeger Cut inorder to detect clusters in weighted undirected graphs by restricting the graphcut minimization to the subset of $st$-MinCut partitions. Incorporating avertex selection technique and restricting optimization to tightly connectedclusters, we therefore combine the efficient computability of $st$-MinCuts andthe intrinsic properties of Gomory-Hu trees with the cut quality of theoriginal graph cuts, leading to linear runtime in the number of vertices andquadratic in the number of edges. Already in simple scenarios, the resultingalgorithm Xist is able to approximate graph cut values better empirically thanspectral clustering or comparable algorithms, even for large network datasets.We showcase its applicability by segmenting images from cell biology andprovide empirical studies of runtime and classification rate.

A scalable clustering algorithm to approximate graph cuts