dis_modwt: Constructs a pairwise distance matrix based on the maximum overlap discrete wavelet transform

Description

dis_modwt returns a pairwise distance matrix based on the dissimilarity introduced by d2012wavelets;textualmlmts.

Usage

dis_modwt(X, wf = "d4", J = floor(log(nrow(X[[1]]))) - 1, features = FALSE)

Value

If features = FALSE (default), returns a distance matrix based on the distance $d_{MODWT}$. Otherwise, the function returns a dataset of feature vectors, i.e., each row in the dataset contains the features employed to compute the distance $d_{MODWT}$.

Arguments

X: A list of MTS (numerical matrices).
wf: The wavelet filter (default is 'd4').
J: The maximum allowable number of scales.
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 $$d_{MODWT}(\boldsymbol X_T, \boldsymbol Y_T)=\Big|||\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{WV}- \widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{WV}||^2+||\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{WC}- \widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{WC}||^2\Big|^{1/2},$$ where $\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{WV}$ and $\widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{WV}$ are vectors containing the estimated wavelet variances within $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively, and $\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{WC}$ and $\widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{WC}$ are vectors containing the estimated wavelet correlations within $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively.

References

d2012waveletsmlmts

Examples

Run this code

toy_dataset <- AtrialFibrillation$data[1 : 10] # Selecting the first 10 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_modwt(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_cor
feature_dataset <- dis_modwt(toy_dataset, features = TRUE) # Computing
# the corresponding dataset of features

Run the code above in your browser using DataLab