| dis_qcf {mlmts} | R Documentation |
Constructs a pairwise distance matrix based on the quantile cross-covariance function
Description
dis_qcf returns a pairwise distance matrix based on a generalization of the
dissimilarity introduced by Lafuente-Rego and Vilar (2016).
Usage
dis_qcf(X, levels = c(0.1, 0.5, 0.9), max_lag = 1, features = FALSE)
Arguments
X |
A list of MTS (numerical matrices). |
levels |
The set of probability levels. |
max_lag |
The maximum lag considered to compute the cross-covariances. |
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_{QCF}(\boldsymbol X_T, \boldsymbol Y_T)=\Bigg(\sum_{l=1}^{L}\sum_{i=1}^{r}\sum_{i'=1}^{r}\sum_{j_1=1}^{d}
\sum_{j_2=1}^{d}\bigg(\widehat \gamma_{j_1,j_2}^{\boldsymbol X_T}(l,\tau_i,\tau_{i^\prime})-\widehat \gamma_{j_1,j_2}^{\boldsymbol Y_T}
(l,\tau_i,\tau_{i^\prime})\bigg)^2+
\sum_{i=1}^{r}\sum_{i'=1}^{r}\sum_{{j_1,j_2=1: j_1 > j_2}}^{d}
\bigg(\widehat \gamma_{j_1,j_2}^{\boldsymbol X_T}(0,\tau_i,\tau_{i^\prime})-
\widehat \gamma_{j_1,j_2}^{\boldsymbol Y_T}(0,\tau_i,\tau_{i^\prime})\bigg)^2\Bigg]^{1/2},
where \widehat \gamma_{j_1,j_2}^{\boldsymbol X_T}(l,\tau_i,\tau_{i^\prime}) and
\widehat \gamma_{j_1,j_2}^{\boldsymbol Y_T}(l,\tau_i,\tau_{i^\prime}) are estimates of the quantile cross-covariances
with respect to the variables j_1 and j_2 and probability levels \tau_i and \tau_{i^\prime} for
series \boldsymbol X_T and \boldsymbol Y_T, respectively.
Value
If features = FALSE (default), returns a distance matrix based on the distance d_{QCF}. 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_{QCF}.
Author(s)
Ángel López-Oriona, José A. Vilar
References
Lafuente-Rego B, Vilar JA (2016). “Clustering of time series using quantile autocovariances.” Advances in Data Analysis and classification, 10(3), 391–415.
See Also
Examples
toy_dataset <- AtrialFibrillation$data[1 : 10] # Selecting the first 10 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_qcf(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_qcf
feature_dataset <- dis_qcf(toy_dataset, features = TRUE) # Computing
# the corresponding dataset of features