In this article, we analyse the usefulness of multidimensional scaling in relation to performing K-means clustering on a dissimilarity matrix, when the dimensionality of the objects is unknown. In this situation, traditional algorithms cannot be used, and so K-means clustering procedures are being performed directly on the basis of the observed dissimilarity matrix. Furthermore, the application of criteria originally formulated for two-mode data sets to determine the number of clusters depends on their possible reformulation in a one-mode situation. The linear invariance property in K-means clustering for squared dissimilarities, together with the use of multidimensional scaling, is investigated to determine the cluster membership of the observations and to address the problem of selecting the number of clusters in K-means for a dissimilarity matrix. In particular, we analyse the performance of K-means clustering on the full dimensional scaling configuration and on the equivalently partitioned configuration related to a suitable translation of the squared dissimilarities. A Monte Carlo experiment is conducted in which the methodology examined is compared with the results obtained by procedures directly applicable to a dissimilarity matrix.

在本文中，当对象的维度未知时，我们分析了多维缩放在对相异矩阵执行K均值聚类方面的有用性。在这种情况下，无法使用传统算法，因此直接基于观察到的相异矩阵执行K均值聚类程序。此外，最初为双模式数据集制定的标准的应用来确定集群的数量取决于它们在单模式情况下可能的重新制定。K 中的线性不变性对平方相异性的均值聚类以及多维标度的使用进行了研究，以确定观测值的聚类成员并解决在K均值中为相异性矩阵选择聚类数的问题。特别是，我们分析了K均值聚类在全维缩放配置和与平方差异的合适转换相关的等效分区配置上的性能。进行了蒙特卡罗实验，其中将检验的方法与通过直接适用于相异矩阵的程序获得的结果进行比较。