通过显著性评估合并模态簇
Merging Modal Clusters via Significance Assessment
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中文总结 AI 辅助
本文提出基于Morse函数性质与Kullback-Leibler散度的模态簇合并方法，可减少冗余簇数量，层次聚类树可确定簇数，数值实验表明其聚类结果更准确且具吸引力。
中文摘要 AI 辅助
为处理冗余簇并减少实践中常需的簇数量，本文提出一种模态簇合并方法。基于本文建立的Morse函数的若干新性质，该方法以顺序方式合并簇，不会造成不必要的密度失真。通过将簇的密度截断至适当水平，使用Kullback-Leibler散度或其对数似然近似，评估每个簇相对于其他簇的显著性。随后利用本文定义的簇邻接这一新概念，将显著性最低的簇合并至其相邻簇之一。所得层次聚类树可用于确定簇的数量，以满足特定用户需求或形成一般有意义的结果。数值研究表明，与文献中几种其他流行聚类方法相比，该新方法能很好地处理困难的聚类问题，且常产生直观上更具吸引力、数值上更准确的聚类结果。
英文摘要
To deal with superfluous clusters and to reduce the number of clusters as often desired in practice, a modal cluster merging procedure is proposed. Based on some new properties established in this paper for Morse functions, the procedure merges clusters in a sequential manner without causing unnecessary density distortion. Each cluster is evaluated for its significance relative to the other clusters, using the Kullback-Leibler divergence or its log-likelihood approximation, by truncating the density for the cluster at an appropriate level. The least significant cluster is then merged into one of its adjacent clusters, using the novel concept of cluster adjacency defined in this paper. The resulting hierarchical clustering tree is useful for determining the number of clusters, as may be preferred by a specific user or in a general, meaningful manner. Numerical studies show that the new procedure deals well with difficult clustering problems and often produces intuitively appealing and numerically more accurate clustering results, as compared with several other popular clustering methods in the literature.
发表机构
- The University of Auckland（奥克兰大学）
机构由 AI 辅助整理，请以论文原文为准。
