| dis_2dsvd {mlmts} | R Documentation |
Constructs a pairwise distance matrix based on two-dimensional singular value decomposition (2dSVD)
Description
dis_2dsvd returns a pairwise distance matrix based on the 2dSVD
distance measure proposed by Weng and Shen (2008).
Usage
dis_2dsvd(X, var_u = 0.9, var_v = 0.9, features = FALSE)
Arguments
X |
A list of MTS (numerical matrices). |
var_u |
Rate of retained variability concerning the row-row covariance matrix. |
var_v |
Rate of retained variability concerning the column-column covariance matrix. |
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_{2dSVD}(\boldsymbol X_T, \boldsymbol Y_T)=\sum_{b=1}^s||{\boldsymbol M}^{\boldsymbol X_T}_{\bullet, b}-
{\boldsymbol M}^{\boldsymbol Y_T}_{\bullet, b}||,
where {\boldsymbol M}^{\boldsymbol X_T}_{\bullet, b} and {\boldsymbol M}^{\boldsymbol Y_T}_{\bullet, b} are the
bth columns of matrices {\boldsymbol M}^{\boldsymbol X_T}
and {\boldsymbol M}^{\boldsymbol Y_T}, which are obtained by
decomposing the time series \boldsymbol X_T and \boldsymbol Y_T, respectively,
by means of the 2dSVD procedure (average row-row and column-column covariance matrices
are taken into account), and s is the number of first retained eigenvectors
concerning the average column-column covariance matrices.
Value
If features = FALSE (default), returns a distance matrix based on the distance d_{2dSVD}. Otherwise, the function
returns a dataset of feature vectors, i.e., each row in the dataset contains the features employed to compute the
distance d_{2dSVD}.
Author(s)
Ángel López-Oriona, José A. Vilar
References
Weng X, Shen J (2008). “Classification of multivariate time series using two-dimensional singular value decomposition.” Knowledge-Based Systems, 21(7), 535–539.
Examples
toy_dataset <- BasicMotions$data[1 : 10] # Selecting the first 10 MTS from the
# dataset BasicMotions
distance_matrix <- dis_2dsvd(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_2dsvd
feature_dataset <- dis_2dsvd(toy_dataset, features = TRUE) # Computing
# the corresponding dataset of features