~   &   ~   &   ~   &   ~   &   ~   &   ~   &   1.000   &   0.440   &   0.590   &   0.591\\
~   &   ~   &   ~   &   ~   &   ~   &   ~   &   ~   &   1.000   &   0.440   &   0.440\\
~   &   ~   &   ~   &   ~   &   ~   &   ~   &   ~   &   ~   &   1.000   &   0.590\\
~   &   ~   &   ~   &   ~   &   ~   &   ~   &   ~   &   ~   &   ~   &   1.000\\
\end{array}
\right)$$ For the sake of comparison, here the ALCA and SLCA filtered correlation matrices are both written with the same order of stocks of the sample correlation matrix. By comparing the sample and the filtered matrices one immediately notes that the filtered ones contain less information being defined by a number of distinct correlation coefficients equals to $n-1$ whereas the original matrix has $n(n-1)/2$ distinct correlation coefficients. The two filtering methods detect different information. In fact the ALCA uses the average correlation coefficient between distinct groups of elements whereas the SLCA uses the maximal correlation. The two choices filter correlation coefficients characterized by a different degree of representativeness and statistical reliability.

It is worth noting that the hierarchical methods reveal the sectorial structure 