dis_gcc: Constructs a pairwise distance matrix based on the...

In mlmts: Machine Learning Algorithms for Multivariate Time Series

Constructs a pairwise distance matrix based on the generalized cross-correlation

Description

dis_gcc returns a pairwise distance matrix based on the generalized cross-correlation measure introduced by \insertCitealonso2019clustering;textualmlmts.

Usage

dis_gcc(X, lag_max = 1, features = FALSE)

Arguments

X	A list of MTS (numerical matrices).
lag_max	The maximum lag considered to compute the generalized cross-correlation.
features	Logical. If features = FALSE (default), a distance matrix is returned. Otherwise, the function returns a dataset of feature vectors.

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_{GCC}(\boldsymbol X_T, \boldsymbol Y_T)=\Bigg[\sum_{j_1,j_2=1, j_1 \ne j_2}^{d} \bigg(\widehat{GCC}(\boldsymbol X_{T,j_1}, \boldsymbol X_{T,j_2} )-\widehat{GCC}(\boldsymbol Y_{T,j_1},\boldsymbol Y_{T,j_2})\bigg)^2\Bigg]^{1/2},

where \boldsymbol X_{T,j} and \boldsymbol Y_{T,j} are the jth dimensions (univariate time series) of \boldsymbol X_T and \boldsymbol Y_T, respectively, and \widehat{GCC}(\cdot, \cdot) is the estimated genelarized cross-correlation measure between univariate series proposed by \insertCitealonso2019clustering;textualmlmts.

Value

If features = FALSE (default), returns a distance matrix based on the distance d_{GCC}. 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_{GCC}.

Author(s)

Ángel López-Oriona, José A. Vilar

References

\insertRef

alonso2019clusteringmlmts

Examples

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

mlmts documentation built on Sept. 11, 2024, 6:41 p.m.