node is $\alpha_1$. In the rooted tree, we distinguish between leaves and internal nodes . Specifically, vertices of degree $1$ represent leaves (vertices labeled $1, 2,..., 10$ in Fig. \[dendroALCA\]) while vertices of degree greater than 1 represent internal nodes (vertices labeled $\alpha_1$, $\alpha_2$,..., $\alpha_9$ in Fig. \[dendroALCA\]). The two trees are slightly different showing that each clustering method produce a different output putting emphasis on different aspects of the sample correlation matrix.

The filtered correlation matrix associated with the ALCA is $$\label{corrmatALCA}
{\bf{C}}^<_{ALCA}=\left(
\begin{array}{cccccccccc}
1.000   &   0.501   &   0.501   &   0.501   &   0.501   &   0.412   &   0.308   &   0.412   &   0.308   &   0.308\\
~   &   1.000   &   0.536   &   0.577   &   0.577   &   0.412   &   0.308   &   0.412   &   0.308   &   0.308\\
~   &   ~   &   1.000   &   0.536   &   0.536   &   0.412   &   0.308   &   0.412   &   0.308   &   0.308\\
~   &   ~   &   ~   &   1.000   &   0.664   &   0.412   &   0.308   &   0.412   &   0.308   &   0.308\\
~   &   ~   &   ~   &   ~   &   1.000   &   0.412   &   0.308   &   0.412   &   0.308   &   0.308\\
~   &   ~   &   ~   &   ~   &   ~   &   1.000   &   0.308   &   0.582   &   0.308   &   0.308\\
~   