| dis_swmd {mlmts} | R Documentation |
Constructs a pairwise distance matrix based on VPCA and SWMD
Description
dis_swmd returns a pairwise distance matrix based on variable-based
principal component analysis (VPCA) and a spatial weighted matrix distance
(SWMD) (He and Tan 2018).
Usage
dis_swmd(X, var_rate = 0.9, features = FALSE)
Arguments
X |
A list of MTS (numerical matrices). |
var_rate |
Rate of retained variability concerning the dimensionality-reduced MTS samples (default is 0.90). |
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_{SWMD}(\boldsymbol X_T, \boldsymbol Y_T)=\Big[\big(vec
(\boldsymbol Z^{\boldsymbol X_T})-vec(\boldsymbol Z^{\boldsymbol Y_T})\big)\boldsymbol
S\big(vec(\boldsymbol Z^{\boldsymbol X_T})-vec(\boldsymbol Z^{\boldsymbol Y_T})\big)^\top\Big]^{1/2},
where \boldsymbol Z^{\boldsymbol X_T} and \boldsymbol Z^{\boldsymbol Y_T} are the dimensionality-
reduced MTS samples associated with \boldsymbol X_T and
\boldsymbol Y_T, respectively, the operator vec(\cdot)
creates a vector by concatenating the columns of the matrix received as input
and \boldsymbol S is a matrix integrating the spatial dimensionality
difference between the corresponding elements.
Value
If features = FALSE (default), returns a distance matrix based on the distance d_{SWMD}. 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_{SWMD}.
Author(s)
Ángel López-Oriona, José A. Vilar
References
He H, Tan Y (2018). “Unsupervised classification of multivariate time series using VPCA and fuzzy clustering with spatial weighted matrix distance.” IEEE transactions on cybernetics, 50(3), 1096–1105.
See Also
Examples
toy_dataset <- AtrialFibrillation$data[1 : 10] # Selecting the first 10 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_swmd(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_swmd
feature_dataset <- dis_swmd(toy_dataset, features = TRUE) # Computing
# the corresponding dataset of features