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

翻译：由于其计算复杂性，基于图割的聚类检测与识别通常以凸松弛的形式实现。我们提出利用原始图割（如比率割、标准化割或切格尔割）来检测加权无向图中的聚类，方法是将图割最小化限制在$st$-最小割划分的子集上。通过引入顶点选择技术并将优化限制在紧密连接的聚类上，我们将$st$-最小割的高效可计算性及戈莫里-胡树的内在特性与原始图割的割质量相结合，从而实现与顶点数量呈线性、边数量呈二次方的运行时间复杂度。即便在简单场景中，所提出的Xist算法在经验上也能比谱聚类或同类算法更优地近似图割值，甚至适用于大规模网络数据集。我们通过细胞生物学图像分割展示了其适用性，并提供了运行时间和分类率的实证研究。