Given a collection of MTS, the function returns the pairwise distance matrix,
where the distance between two MTS \(\boldsymbol X_T\) and \(\boldsymbol Y_T\) is defined
as $$d_{PPCA}(\boldsymbol X_{T}, \boldsymbol Y_{T})=\Big|\Big|vec\big(\widehat{\boldsymbol \Sigma}_a ^{\boldsymbol X_T}\big)
-vec\big(\widehat{\boldsymbol \Sigma}_a^{\boldsymbol Y_T}\big)\Big|\Big|,$$
where \(\widehat{\boldsymbol \Sigma}_a ^{\boldsymbol X_T}\) and \(\widehat{\boldsymbol \Sigma}_a ^{\boldsymbol Y_T}\)
are estimates of the covariance matrices based on a piecewise representation for which the
original MTS \(\boldsymbol X_T\) and \(\boldsymbol Y_T\), respectively,
are divided into a number of w local segments (in the time dimension).
If we use the function to perform dimensionality reduction (features = TRUE),
then for a given series \(\boldsymbol X_T\), matrix \(\widehat{\boldsymbol \Sigma}_a ^{\boldsymbol X_T}\)
is decomposed by executing the standard PCA and a certain number of
principal components are retained (according to the parameter var_rate).
Function dis_ppca returns the reduced counterpart of \(\boldsymbol X_T\),
which is constructed from \(\boldsymbol X_T\) by considering the
matrix of scores with respect to the retained principal components.