k -means clustering is a well-known procedure for classifying multivariate observations. The resulting centroid matrix of clusters by variables is noted for interpreting which variables characterize clusters. However, between-clusters differences are not always clearly captured in the centroid matrix. We address this problem by proposing a new procedure for obtaining a centroid matrix, so that it has a number of exactly zero elements. This allows easy interpretation of the matrix, as we may focus on only the nonzero centroids. The development of an iterative algorithm for the constrained minimization is described. A cardinality selection procedure for identifying the optimal cardinality is presented, as well as a modified version of the proposed procedure, in which some restrictions are imposed on the positions of nonzero elements. The behaviors of our proposed procedure were evaluated in simulation studies and are illustrated with three real data examples, which demonstrate that the performances of the procedure is promising.

中文翻译：

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一种用于获得基数约束质心矩阵的改进 k 均值聚类程序

k 均值聚类是用于对多变量观察进行分类的众所周知的过程。由变量产生的簇的质心矩阵用于解释哪些变量表征簇。然而，在质心矩阵中并不总是清楚地捕捉到集群之间的差异。我们通过提出一种获得质心矩阵的新程序来解决这个问题，以便它具有许多恰好为零的元素。这允许轻松解释矩阵，因为我们可能只关注非零质心。描述了用于约束最小化的迭代算法的开发。提出了用于识别最佳基数的基数选择程序，以及所提出程序的修改版本，其中对非零元素的位置施加了一些限制。