| dis_mahalanobis {mlmts} | R Documentation |
Constructs a pairwise distance matrix based on the Mahalanobis distance
Description
dis_mahalanobis returns a pairwise distance matrix based on the
Mahalanobis divergence introduced by Singhal and Seborg (2005).
Usage
dis_mahalanobis(X)
Arguments
X |
A list of MTS (numerical matrices). |
Details
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_{MD}^*(\boldsymbol X_T, \boldsymbol Y_T)=\frac{1}{2}\Big(d_{MD}
(\boldsymbol X_T, \boldsymbol Y_T)+d_{MD}(\boldsymbol Y_T, \boldsymbol X_T)\Big),
with
d_{MD}(\boldsymbol X_T, \boldsymbol Y_T)=\sqrt{(\overline{\boldsymbol X}_T
-\overline{\boldsymbol Y}_T)\boldsymbol \Sigma_{\boldsymbol X_T}^{*-1}(\overline
{\boldsymbol X}_T-\overline{\boldsymbol Y}_T)^\top},
where \overline{\boldsymbol X}_T and \overline{\boldsymbol Y}_T
are vectors containing the column-wise means concerning series
\boldsymbol X_T and \boldsymbol Y_T, respectively,
\boldsymbol \Sigma_{\boldsymbol X_T} is the covariance matrix of \boldsymbol X_T and
\boldsymbol \Sigma_{\boldsymbol X_T}^{*-1} is the pseudo-inverse of \boldsymbol
\Sigma_{\boldsymbol X_T} calculated using SVD.
In the computation of d_{MD}^*, MTS \boldsymbol X_T is assumed to be the reference series.
Value
The computed pairwise distance matrix.
Author(s)
Ángel López-Oriona, José A. Vilar
References
Singhal A, Seborg DE (2005). “Clustering multivariate time-series data.” Journal of Chemometrics: A Journal of the Chemometrics Society, 19(8), 427–438.
See Also
Examples
toy_dataset <- AtrialFibrillation$data[1 : 10] # Selecting the first 10 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_mahalanobis(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_mahalanobis.