Convex clustering is an attractive clustering algorithm with favorable properties such as efficiency and optimality owing to its convex formulation. It is thought to generalize both k-means clustering and agglomerative clustering. However, it is not known whether convex clustering preserves desirable properties of these algorithms. A common expectation is that convex clustering may learn difficult cluster types such as non-convex ones. Current understanding of convex clustering is limited to only consistency results on well-separated clusters. We show new understanding of its solutions. We prove that convex clustering can only learn convex clusters. We then show that the clusters have disjoint bounding balls with significant gaps. We further characterize the solutions, regularization hyperparameters, inclusterable cases and consistency.
翻译:混凝土集群是一种有吸引力的集群算法,其优点包括效率和最佳性,因为其配方具有效益和最佳性,据认为它一般化了k- means集群和聚集群,然而,尚不清楚混凝土集群是否保留了这些算法的可取特性。一个共同的预期是,混凝土集群可能学习非混凝土等困难的集群类型。目前对混凝土集群的理解仅限于井然分离的集群的一致结果。我们显示了对其解决办法的新理解。我们证明,混凝土集群只能学习convex集群。我们然后表明,这些集群的交错球与重大差距是分不开的。我们进一步描述解决办法,在可分类的案例中,将超参数正规化为超参数和一致性。