For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized for focusing solely on inertia so that the first components do not necessarily retain the structure of interest for clustering. To address this limitation, a new tandem clustering approach based on invariant coordinate selection (ICS) is proposed. By jointly diagonalizing two scatter matrices, ICS is designed to find structure in the data while providing affine invariant components. Certain theoretical results have been previously derived and guarantee that under some elliptical mixture models, the group structure can be highlighted on a subset of the first and/or last components. However, ICS has garnered minimal attention within the context of clustering. Two challenges associated with ICS include choosing the pair of scatter matrices and selecting the components to retain. For effective clustering purposes, it is demonstrated that the best scatter pairs consist of one scatter matrix capturing the within-cluster structure and another capturing the global structure. For the former, local shape or pairwise scatters are of great interest, as is the minimum covariance determinant (MCD) estimator based on a carefully chosen subset size that is smaller than usual. The performance of ICS as a dimension reduction method is evaluated in terms of preserving the cluster structure in the data. In an extensive simulation study and empirical applications with benchmark data sets, various combinations of scatter matrices as well as component selection criteria are compared in situations with and without outliers. Overall, the new approach of tandem clustering with ICS shows promising results and clearly outperforms the PCA-based approach.

翻译：针对多元数据，串联聚类是一种旨在通过初始降维改善聚类识别的经典技术。然而，常规的主成分分析方法因仅关注惯性而受到批评，导致前几个主成分未必保留聚类所需的结构。为解决这一局限，本文提出了一种基于不变坐标选择的新串联聚类方法。通过联合对角化两个散度矩阵，ICS旨在发现数据结构的同时提供仿射不变分量。已有的若干理论结果保证，在某些椭圆混合模型下，群结构可在前/后部分分量子集上得到凸显。但ICS在聚类领域尚未获得足够关注。ICS面临的两大挑战包括散度矩阵对的选择与保留分量的选取。为有效聚类，研究表明最佳散度对应包含一个捕获簇内结构的散度矩阵与一个捕获全局结构的散度矩阵。对于前者，局部形状散度或成对散度具有重要价值，基于精心选取的比常规更小子集大小的最小协方差行列式估计亦是如此。本文评估了ICS作为降维方法在保留数据簇结构方面的性能。通过大规模仿真研究与基准数据集上的实证应用，分别在无异常值与存在异常值场景下比较了多种散度矩阵组合及分量选择准则。总体而言，基于ICS的串联聚类新方法展现出良好前景，并显著优于基于PCA的方法。