dis_2dsvd: 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 weng2008classification;textualmlmts.

Usage

dis_2dsvd(X, var_u = 0.9, var_v = 0.9, features = FALSE)

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 $d_{2dSVD}$.

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 features = FALSE (default), a distance matrix is returned. Otherwise, the function returns a dataset of feature vectors.

Author

Ángel López-Oriona, José A. Vilar

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 $b$th 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.

References

weng2008classificationmlmts

Examples

Run this code

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

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