Fig. 5.

Hierarchical clustering on principal components of neuropsychological (T) scores for subject group identification using Ward’s D2 criterion (Murtagh & Legendre, 2014). PCA is used on the subject cognitive matrix $\mathbf{P}\in {\mathbb{R}}^{K\times L}$ to remove highly correlated continuous variables. Next, we apply hierarchical clustering using Ward’s D2 method on the distance matrix $\mathbf{D}$ to select the clusters based on the height of the hierarchical tree. The distance matrix $\mathbf{D}\in {\mathbb{R}}^{K\times K}$ is computed using the dissimilarity measure such as the distance correlation (Székely, Rizzo, & Bakirov, 2007) of the PCs. The initial number of clusters $N_{C_k}$ is assessed according to the compactness metrics (Halkidi, Batistakis, & Vazirgiannis, 2002a, 2002b), and the cluster stability is evaluated using the Jaccard similarity index (Jaccard, 1912) via a nonparametric bootstrap technique with a number of repetitions $n=1000$ (see detailed protocol in Supplementary Methods Section 3.1). We select significant clusters based on the approximately unbiased probability $p$-values (Efron, Halloran, & Holmes, 1996), as shown in Fig. 6a. We provide the final clustering solution by applying the $K$-means algorithm to the hierarchical clustering output.