图结构数据的凸层次聚类
Convex Hierarchical Clustering for Graph-Structured Data
摘要：
凸聚类是一个最近稳定的替代层次聚类。它制定了逐步合并集群的恢复作为一个正规化的凸问题。虽然凸聚类最初是为了处理数据点之间的欧氏距离而设计的，但在越来越多的应用中，数据直接由相似性矩阵或加权图来表征。在本文中，我们扩展了强大的层次聚类方法，这些更广泛的类的相似性。在定义了一个适当的凸目标之后，这种适应的关键在于我们能够提供：（a）正则化路径的有效恢复和（b）使用我们方法的经验证明。我们通过一个近端对偶算法解决第一个挑战，为此我们描述了一组实验的理论效率和经验性能。最后，我们强调了我们的方法的潜力，通过展示其应用到几个现实生活中的数据集，从而提供了一个自然的扩展到当前的凸聚类的应用范围。
英文摘要：
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling Euclidean distances between data points, in a growing number of applications, the data is directly characterized by a similarity matrix or weighted graph. In this paper, we extend the robust hierarchical clustering approach to these broader classes of similarities. Having defined an appropriate convex objective, the crux of this adaptation lies in our ability to provide: (a) an efficient recovery of the regularization path and (b) an empirical demonstration of the use of our method. We address the first challenge through a proximal dual algorithm, for which we characterize both the theoretical efficiency as well as the empirical performance on a set of experiments. Finally, we highlight the potential of our method by showing its application to several real-life datasets, thus providing a natural extension to the current scope of applications of convex clustering.
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