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      Hierarchical Clustering With Prototypes via Minimax Linkage.

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          Abstract

          Agglomerative hierarchical clustering is a popular class of methods for understanding the structure of a dataset. The nature of the clustering depends on the choice of linkage-that is, on how one measures the distance between clusters. In this article we investigateminimax linkage, a recently introduced but little-studied linkage. Minimax linkage is unique in naturally associating a prototype chosen from the original dataset with every interior node of the dendrogram. These prototypes can be used to greatly enhance the interpretability of a hierarchical clustering. Furthermore, we prove that minimax linkage has a number of desirable theoretical properties; for example, minimax-linkage dendrograms cannot have inversions (unlike centroid linkage) and is robust against certain perturbations of a dataset. We provide an efficient implementation and illustrate minimax linkage's strengths as a data analysis and visualization tool on a study of words from encyclopedia articles and on a dataset of images of human faces.

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          Author and article information

          Journal
          J Am Stat Assoc
          Journal of the American Statistical Association
          0162-1459
          0162-1459
          January 1 2011
          : 106
          : 495
          Affiliations
          [1 ] Department of Statistics, Stanford University, Stanford, CA 94305.
          [2 ] Department of Health Research and Policy and Department of Statistics, Stanford University, Stanford, CA 94305.
          Article
          NIHMS637357
          10.1198/jasa.2011.tm10183
          4527350
          26257451
          a3b670bc-a4ac-4465-96a1-89572315c08a
          History

          Dendrogram,Agglomerative,Unsupervised learning
          Dendrogram, Agglomerative, Unsupervised learning

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