Cluster validation in k-Means clustering based on PCA-guided k-Means and procrustean transformation of PC scores

PCA-guided k-Means is a technique for analytically estimating a relaxed solution for k-Means clustering, while the derived cluster indicator is a rotated solution and the rotation matrix cannot be explicitly estimated. Then, an approach such as visualization by ordering of samples in connectivity matrices is applied for visually accessing cluster structures. This paper introduces a technique for estimating a rotation matrix by Procrustean transformation of principal component scores in order to select the optimal solution from multiple solutions derived by k-Means, and proposes a cluster validation measure calculating the deviation between k-Means solutions and a re-constructed membership indicator matrix.