论文标题
通过MM的凸聚类：一种有效的算法来执行层次聚类
Convex Clustering through MM: An Efficient Algorithm to Perform Hierarchical Clustering
论文作者
论文摘要
凸聚类是一种现代方法，具有层次结构和$ k $ - 均值聚类特征。尽管凸聚类可以捕获隐藏在数据中的复杂聚类结构，但现有的凸聚类算法无法扩展到大于数千个样本量的大数据集。此外，众所周知，凸聚类有时无法产生完整的分层聚类结构。如果群集分裂或可能的簇数量最小数量大于所需的簇数，则会出现此问题。在本文中，我们提出了通过大型化最小化（CCMM）的凸聚类 - 一种迭代算法，该算法使用群集融合和使用对角线大量化得出的高效更新方案。此外，我们探索了不同的策略，以确保分层聚类结构终止单个集群。使用当前的台式计算机，CCMM有效地解决了凸聚类问题，该问题在七维空间中具有超过一百万个对象，平均达到了51秒的解决方案时间。
Convex clustering is a modern method with both hierarchical and $k$-means clustering characteristics. Although convex clustering can capture complex clustering structures hidden in data, the existing convex clustering algorithms are not scalable to large data sets with sample sizes greater than several thousands. Moreover, it is known that convex clustering sometimes fails to produce a complete hierarchical clustering structure. This issue arises if clusters split up or the minimum number of possible clusters is larger than the desired number of clusters. In this paper, we propose convex clustering through majorization-minimization (CCMM) -- an iterative algorithm that uses cluster fusions and a highly efficient updating scheme derived using diagonal majorization. Additionally, we explore different strategies to ensure that the hierarchical clustering structure terminates in a single cluster. With a current desktop computer, CCMM efficiently solves convex clustering problems featuring over one million objects in seven-dimensional space, achieving a solution time of 51 seconds on average.
