| dis_mcc {mlmts} | R Documentation |
Constructs a pairwise distance matrix based on maximal cross-correlations
Description
dis_mcc returns a pairwise distance matrix based on an extension of
the procedure proposed by Egri et al. (2017). The
function can also be used for dimensionality reduction purposes.
Usage
dis_mcc(X, max_lag = 20, delta = 0.7, features = F)
Arguments
X |
A list of MTS (numerical matrices). |
max_lag |
The maximum number of lags for the computation of the cross-correlations (default is 20). |
delta |
The threshold value concerning the maximal cross-correlations (default is 0.7). |
features |
Logical. If |
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_{MCC}(\boldsymbol X_{T}, \boldsymbol Y_{T})=\Big|\Big|vec\big(\widehat{\boldsymbol \Theta}^{\boldsymbol X_T}\big)
-vec\big(\widehat{\boldsymbol \Theta}^{\boldsymbol Y_T}\big)\Big|\Big|,
where \widehat{\boldsymbol \Theta}^{\boldsymbol X_T} and \widehat{\boldsymbol \Theta}^{\boldsymbol Y_T}
are matrices containing pairwise estimated maximal cross-correlations
(in absolute value) for series \boldsymbol X_T and \boldsymbol Y_T, respectively,
and the operator vec(\cdot) creates a vector by concatenating the columns
of the matrix received as input. If we use the function to perform dimensionality
reduction (features = TRUE), then for a given series \boldsymbol X_T,
a new matrix \widehat{\boldsymbol \Theta}^{\boldsymbol X_T}_\delta is
constructed by keeping the entries of matrix \widehat{\boldsymbol \Theta}^{\boldsymbol X_T}
which are above \delta (and setting all the remaining entries to zero).
The connected components of the graph defined by matrix
\widehat{\boldsymbol \Theta}^{\boldsymbol X_T}_\delta are computed
along with their corresponding centers (variables). Function dis_mcc
returns the reduced counterpart of \boldsymbol X_T, which is constructed
from \boldsymbol X_T by removing all the variables which were not
selected as centers of the corresponding components.
Value
The computed pairwise distance matrix.
Author(s)
Ángel López-Oriona, José A. Vilar
References
Egri A, Horváth I, Kovács F, Molontay R, Varga K (2017). “Cross-correlation based clustering and dimension reduction of multivariate time series.” In 2017 IEEE 21st International Conference on Intelligent Engineering Systems (INES), 000241–000246. IEEE.
Examples
reduced_dataset <- dis_mcc(RacketSports$data[1], features = TRUE) # Reducing
# the dimensionality of the first MTS in dataset RacketSports
reduced_dataset
distance_matrix <- dis_mcc(Libras$data) # Computing the
# corresponding distance matrix for all MTS in dataset Libras
# (by default, features = F)