  This paper proposes a clustering procedure for samples of multivariate
functions in $(L^2(I))^{J}$, with $J\geq1$. This method is based on a k-means
algorithm in which the distance between the curves is measured with a metrics
that generalizes the Mahalanobis distance in Hilbert spaces, considering the
correlation and the variability along all the components of the functional
data. The proposed procedure has been studied in simulation and compared with
the k-means based on other distances typically adopted for clustering
multivariate functional data. In these simulations, it is shown that the
k-means algorithm with the generalized Mahalanobis distance provides the best
clustering performances, both in terms of mean and standard deviation of the
number of misclassified curves. Finally, the proposed method has been applied
to two real cases studies, concerning ECG signals and growth curves, where the
results obtained in simulation are confirmed and strengthened.
