k\\
            &                 \nonumber \\
            &    b_{ij}=b_{ij} & 
                               ~~~~\text{ otherwise, }\\
    \end{aligned} \right.\end{aligned}$$ where $n_h$ and $n_k$ are the number of elements belonging respectively to the cluster $h$ and to the cluster $k$ before the merging operation. Note that if the dimension of ${\bf{B}}$ is $m \times m$ then the dimension of the redefined ${\bf{B}}$ is $(m-1) \times (m-1)$ because of the merging of clusters $h$ and $k$ into the cluster $q$.

5.  If the dimension of ${\bf{B}}$ is larger than 1 then go to step (ii), else Stop.

By replacing point $(iv)$ of the above algorithm with the following item\
(iv)$'$ Redefine the matrix ${\bf{B}}$: $$\label{negspin2}
\left \{ \begin{aligned}
        &  b_{qj}= Max \left[b_{hj}, b_{kj}\right] & 
                           ~~~~\text{ if } j\notin h \,{\rm{and}} \, j\notin k \nonumber\\
        &  b_{ij}=b_{ij} & 
                           ~~~~\text{ otherwise, }\\
\end{aligned} \right.$$ one obtains an algorithm performing the SLCA and the associated filtered correlation matrix ${\bf{C}}^<_{SLCA}$.

The hierarchical trees obtained from the sample correlation matrix of Eq. (\[corrmat\]) by applying the ALCA and the SLCA are given in Fig. \[dendroALCA\] and in Fig. \[dendroSLCA\] respectively. A hierarchical tree is a rooted tree, i.e. a tree in which a special node (the root) is singled out. In our example this 