Package 'mlmts'

Description

Multivariate time series (MTS) of movements of tongue and lips during speech. The data were collected from multiple native English speakers producing 25 words.

Usage

data(ArticularlyWordRecognition)

Format

A list with two elements, which are:

data

A list with 575 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 144 rows (time points) indicating movement and 9 columns (variables) indicating sensors. The first 275 elements correspond to the training set, whereas the last 300 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 25, indicating that there are 25 different classes in the database. Each class is associated with a different word produced by the speaker. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata1", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata1::ArticularyWordRecognition".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) of two-channel ECG recordings of atrial fibrillation. The database has been created from data used in the Computers in Cardiology Challenge 2004.

Usage

data(AtrialFibrillation)

Format

A list with two elements, which are:

data

A list with 30 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 640 rows (time points) indicating ECG measures and 2 columns (variables) indicating ECG leads. The first 15 elements correspond to the training set, whereas the last 15 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 3, indicating that there are 3 different classes in the database. Each class is associated with a different type of atrial fibrillation. For more information, see Bagnall et al. (2018).

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) of four students performing four activities while wearing a smart watch.

Usage

data(BasicMotions)

Format

A list with two elements, which are:

data

A list with 80 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 100 rows (time points) indicating movement and 6 columns (variables). The first 40 elements correspond to the training set, whereas the last 40 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 4, indicating that there are 4 different classes in the database. Each class is associated with a different physical activity. For more information, Bagnall et al. (2018).

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) of character samples, captured using a WACOM tablet. Data was recorded at 200Hz.

Usage

data(CharacterTrajectories)

Format

A list with two elements, which are:

data

A list with 80 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 182 rows (time points) indicating velocity trajectory and 3 columns (variables) indicating spatial dimension. The first 1422 elements correspond to the training set, whereas the last 1436 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 20, indicating that there are 20 different classes in the database. Each class is associated with a different alphabetical character. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata1", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata1::CharacterTrajectories".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) of four cricket umpires performing twelve signals, each with ten repetitions.

Usage

data(Cricket)

Format

A list with two elements, which are:

data

A list with 180 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 1197 rows (time points) indicating acceleration and 6 columns (variables) indicating spatial dimension with regards to two accelerometers. The first 108 elements correspond to the training set, whereas the last 72 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 12, indicating that there are 12 different classes in the database. Each class is associated with a different event signaled by the umpire. For more information, see Bagnall et al. (2018). Run install.packages("ueadata1", repos="https://anloor7.github.io/drat") to access this dataset and use the syntax ueadata1::Cricket.

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

dis_2dsvd returns a pairwise distance matrix based on the 2dSVD distance measure proposed by Weng and Shen (2008).

Usage

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

Arguments

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.

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 $d_{2dSVD}$.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Weng X, Shen J (2008). “Classification of multivariate time series using two-dimensional singular value decomposition.” Knowledge-Based Systems, 21(7), 535–539.

Examples

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

Description

dis_cor returns a pairwise distance matrix based on a generalization of the dissimilarity introduced by D'Urso and Maharaj (2009).

Usage

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

Arguments

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

$d_{COR}(\boldsymbol X_T, \boldsymbol Y_T)=\Big|||\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{AC}- \widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{AC}||^2+||\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{CC}- \widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{CC}||^2\Big|^{1/2},$

where $\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{AC}$ and $\widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{AC}$ are vectors containing the estimated autocorrelations within $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively, and $\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{CC}$ and $\widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{CC}$ are vectors containing the estimated cross-correlations within $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively.

Value

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

Author(s)

Ángel López-Oriona, José A. Vilar

References

D'Urso P, Maharaj EA (2009). “Autocorrelation-based fuzzy clustering of time series.” Fuzzy Sets and Systems, 160(24), 3565–3589.

Examples

toy_dataset <- AtrialFibrillation$data[1 : 10] # Selecting the first 10 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_cor(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_cor
distance_matrix <- dis_cor(toy_dataset, lag_max = 5) # Considering
# auto and cross-correlations up to lag 5 in the computation of the distance
feature_dataset <- dis_cor(toy_dataset, features = TRUE) # Computing
# the corresponding dataset of features

Description

dis_dtw_1 returns a pairwise distance matrix based on one of the multivariate extensions of the well-known dynamic time warping distance (Shokoohi-Yekta et al. 2017).

Usage

dis_dtw_1(X, normalization = FALSE, ...)

Arguments

Details

Given a collection of MTS, the function returns the pairwise distance matrix, where the distance between two MTS is defined as the sum of the standard dynamic time warping distances between each corresponding pair of dimensions (univariate time series)

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Shokoohi-Yekta M, Hu B, Jin H, Wang J, Keogh E (2017). “Generalizing DTW to the multi-dimensional case requires an adaptive approach.” Data mining and knowledge discovery, 31(1), 1–31.

See Also

dis_dtw_2, dis_mahalanobis_dtw

Examples

toy_dataset <- AtrialFibrillation$data[1 : 5] # Selecting the first 5 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_dtw_1(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_dtw_1 without normalization
distance_matrix_normalized <- dis_dtw_1(toy_dataset, normalization = TRUE)
# Computing the pairwise distance matrix based
# on the distance dis_dtw_1 with normalization

Description

dis_dtw_2 returns a pairwise distance matrix based on one of the multivariate extensions of the well-known dynamic time warping distance (Shokoohi-Yekta et al. 2017).

Usage

dis_dtw_2(X, normalization = FALSE, ...)

Arguments

Details

Given a collection of MTS, the function returns the pairwise distance matrix, where the distance between two MTS is defined as the multivariate extension of the dynamic time warping distance which forces all dimensions to warp identically, in a single warping matrix.

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Shokoohi-Yekta M, Hu B, Jin H, Wang J, Keogh E (2017). “Generalizing DTW to the multi-dimensional case requires an adaptive approach.” Data mining and knowledge discovery, 31(1), 1–31.

See Also

dis_dtw_2, dis_mahalanobis_dtw

Examples

toy_dataset <- AtrialFibrillation$data[1 : 10] # Selecting the first 10 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_dtw_2(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_dtw1 without normalization
distance_matrix_normalized <- dis_dtw_2(toy_dataset, normalization = TRUE)
# Computing the pairwise distance matrix based
# distance matrix based on the distance dis_dtw1 with normalization

Description

dis_eros returns a pairwise distance matrix based on the Eros distance proposed by Yang and Shahabi (2004).

Usage

dis_eros(X, method = "mean", normalization = FALSE, cor = TRUE)

Arguments

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 $d_{Eros}(\boldsymbol X_T, \boldsymbol Y_T)=\sqrt{2-2Eros(\boldsymbol X_T, \boldsymbol Y_T)}$, where

$Eros(\boldsymbol X_T, \boldsymbol Y_T)=\sum_{i=1}^{d}w_i|<\boldsymbol x_i,\boldsymbol y_i>|= \sum_{i=1}^{d}w_i|\cos \theta_i|,$

where $\{\boldsymbol x_1, \ldots, \boldsymbol x_d\}$, $\{\boldsymbol y_1, \ldots, \boldsymbol y_d\}$ are sets of eigenvectors concerning the covariance or correlation matrix of series $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively, $<\boldsymbol x_i,\boldsymbol y_i>$ is the inner product of $\boldsymbol x_i$ and $\boldsymbol y_i$, $\boldsymbol w=(w_1, \ldots, w_d)$ is a vector of weights which is based on the eigenvalues of the MTS dataset with $\sum_{i=1}^{d}w_i=1$ and $\theta_i$ is the angle between $\boldsymbol x_i$ and $\boldsymbol y_i$.

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Yang K, Shahabi C (2004). “A PCA-based similarity measure for multivariate time series.” In Proceedings of the 2nd ACM international workshop on Multimedia databases, 65–74.

Examples

toy_dataset <- BasicMotions$data[1 : 10] # Selecting the first 10 MTS from the
# dataset BasicMotions
distance_matrix <- dis_eros(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_eros
distance_matrix <- dis_eros(toy_dataset, method = 'max', normalization = TRUE)
# Considering the function max as aggregation function and the normalized
# eigenvalues for the computation of the weights

Description

dis_eucl returns a pairwise distance matrix based on the Euclidean distance between MTS

Usage

dis_eucl(X)

Arguments

Details

Given a collection of MTS, the function returns the pairwise distance matrix, where the distance between two MTS is defined as the sum of the standard Euclidean distances between each corresponding pair of dimensions (univariate time series)

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

Examples

toy_dataset <- AtrialFibrillation$data[1 : 10] # Selecting the first 10 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_eucl(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_eucl

Description

dis_frechet returns a pairwise distance matrix based on the Frechet distance between MTS

Usage

dis_frechet(X, ...)

Arguments

Details

Given a collection of MTS, the function returns the pairwise distance matrix, where the distance between two MTS is defined as the sum of the standard Frechet distances between each corresponding pair of dimensions (univariate time series)

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

See Also

diss.FRECHET

Examples

toy_dataset <- Libras$data[1 : 5] # Selecting the first 5 MTS from the
# dataset Libras
distance_matrix <- dis_frechet(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_frechet

Description

dis_gcc returns a pairwise distance matrix based on the generalized cross-correlation measure introduced by Alonso and Pena (2019).

Usage

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

Arguments

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 $j$th 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 Alonso and Pena (2019).

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

Alonso AM, Pena D (2019). “Clustering time series by linear dependency.” Statistics and Computing, 29(4), 655–676.

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

Description

dis_hwl returns a pairwise distance matrix based on the feature extraction procedure proposed by Hyndman et al. (2015).

Usage

dis_hwl(X, features = FALSE)

Arguments

Details

Given a collection of MTS, the function returns the pairwise distance matrix, where the distance between two MTS is defined as the Euclidean distance between the corresponding feature vectors

Value

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

Author(s)

Ángel López-Oriona, José A. Vilar

References

Hyndman RJ, Wang E, Laptev N (2015). “Large-scale unusual time series detection.” In 2015 IEEE international conference on data mining workshop (ICDMW), 1616–1619. IEEE.

Examples

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

Description

dis_lpp returns a pairwise distance matrix based on the dissimilarity introduced by Weng and Shen (2008).

Usage

dis_lpp(X, approach = 1, k = 2, t = 1, features = FALSE)

Arguments

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

$d_{LPP}(\boldsymbol X_T, \boldsymbol Y_T)= \big| \big| {\boldsymbol \varphi^{\boldsymbol X_T} \boldsymbol A_{LPP} - \boldsymbol \varphi^{\boldsymbol Y_T} \boldsymbol A_{LPP}} \big| \big|,$

where $\boldsymbol \varphi^{\boldsymbol X_T}$ and $\boldsymbol \varphi^{\boldsymbol Y_T}$ are the feature vectors constructed from Li's first (approach=1) or Li's second (approach=2) approach with respect to series $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively and $\boldsymbol A_{LPP}$ is the matrix of locality preserving projections whose columns are eigenvectors solving the generalized eigenvalue problem defined by matrix $\boldsymbol S$.

Value

If features = FALSE (default), returns a distance matrix based on the distance $d_{QCD}$. Otherwise, the function returns a dataset of feature vectors, i.e., each row in the dataset contains the features resulting from applying Li's first (approach=1) or Li's second (approach=2).

Author(s)

Ángel López-Oriona, José A. Vilar

References

Weng X, Shen J (2008). “Classification of multivariate time series using locality preserving projections.” Knowledge-Based Systems, 21(7), 581–587.

Examples

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

Description

dis_mahalanobis returns a pairwise distance matrix based on the Mahalanobis divergence introduced by Singhal and Seborg (2005).

Usage

dis_mahalanobis(X)

Arguments

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

$d_{MD}^*(\boldsymbol X_T, \boldsymbol Y_T)=\frac{1}{2}\Big(d_{MD} (\boldsymbol X_T, \boldsymbol Y_T)+d_{MD}(\boldsymbol Y_T, \boldsymbol X_T)\Big),$

with

$d_{MD}(\boldsymbol X_T, \boldsymbol Y_T)=\sqrt{(\overline{\boldsymbol X}_T -\overline{\boldsymbol Y}_T)\boldsymbol \Sigma_{\boldsymbol X_T}^{*-1}(\overline {\boldsymbol X}_T-\overline{\boldsymbol Y}_T)^\top},$

where $\overline{\boldsymbol X}_T$ and $\overline{\boldsymbol Y}_T$ are vectors containing the column-wise means concerning series $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively, $\boldsymbol \Sigma_{\boldsymbol X_T}$ is the covariance matrix of $\boldsymbol X_T$ and $\boldsymbol \Sigma_{\boldsymbol X_T}^{*-1}$ is the pseudo-inverse of $\boldsymbol \Sigma_{\boldsymbol X_T}$ calculated using SVD. In the computation of $d_{MD}^*$, MTS $\boldsymbol X_T$ is assumed to be the reference series.

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Singhal A, Seborg DE (2005). “Clustering multivariate time-series data.” Journal of Chemometrics: A Journal of the Chemometrics Society, 19(8), 427–438.

See Also

dis_mahalanobis_dtw

Examples

toy_dataset <- AtrialFibrillation$data[1 : 10] # Selecting the first 10 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_mahalanobis(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_mahalanobis.

Description

dis_mahalanobis_dtw returns a pairwise distance matrix based on a dynamic time warping distance in which the local cost matrix is computed by using the Mahalanobis distance (Mei et al. 2015).

Usage

dis_mahalanobis_dtw(X, M = NULL, ...)

Arguments

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 a dynamic time warping-type distance in which the local cost matrix is constructed by using the Mahalanobis distance.

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Mei J, Liu M, Wang Y, Gao H (2015). “Learning a mahalanobis distance-based dynamic time warping measure for multivariate time series classification.” IEEE transactions on Cybernetics, 46(6), 1363–1374.

See Also

dis_dtw_1, dis_dtw_2, dis_mahalanobis_dtw

Examples

toy_dataset <- Libras$data[1 : 10] # Selecting the first 10 MTS from the
# dataset Libras
distance_matrix <- dis_mahalanobis_dtw(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_mahalanobis_dtw

Description

dis_mcc returns a pairwise distance matrix based on an extension of the procedure proposed by Egri et al. (2017). The function can also be used for dimensionality reduction purposes.

Usage

dis_mcc(X, max_lag = 20, delta = 0.7, features = F)

Arguments

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

$d_{MCC}(\boldsymbol X_{T}, \boldsymbol Y_{T})=\Big|\Big|vec\big(\widehat{\boldsymbol \Theta}^{\boldsymbol X_T}\big) -vec\big(\widehat{\boldsymbol \Theta}^{\boldsymbol Y_T}\big)\Big|\Big|,$

where $\widehat{\boldsymbol \Theta}^{\boldsymbol X_T}$ and $\widehat{\boldsymbol \Theta}^{\boldsymbol Y_T}$ are matrices containing pairwise estimated maximal cross-correlations (in absolute value) for series $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively, and the operator $vec(\cdot)$ creates a vector by concatenating the columns of the matrix received as input. If we use the function to perform dimensionality reduction (features = TRUE), then for a given series $\boldsymbol X_T$, a new matrix $\widehat{\boldsymbol \Theta}^{\boldsymbol X_T}_\delta$ is constructed by keeping the entries of matrix $\widehat{\boldsymbol \Theta}^{\boldsymbol X_T}$ which are above $\delta$ (and setting all the remaining entries to zero). The connected components of the graph defined by matrix $\widehat{\boldsymbol \Theta}^{\boldsymbol X_T}_\delta$ are computed along with their corresponding centers (variables). Function dis_mcc returns the reduced counterpart of $\boldsymbol X_T$, which is constructed from $\boldsymbol X_T$ by removing all the variables which were not selected as centers of the corresponding components.

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Egri A, Horváth I, Kovács F, Molontay R, Varga K (2017). “Cross-correlation based clustering and dimension reduction of multivariate time series.” In 2017 IEEE 21st International Conference on Intelligent Engineering Systems (INES), 000241–000246. IEEE.

Examples

reduced_dataset <- dis_mcc(RacketSports$data[1], features = TRUE) # Reducing
# the dimensionality of the first MTS in dataset RacketSports
reduced_dataset
distance_matrix <- dis_mcc(Libras$data) # Computing the
# corresponding distance matrix for all MTS in dataset Libras
# (by default, features = F)

Description

dis_modwt returns a pairwise distance matrix based on the dissimilarity introduced by D'Urso and Maharaj (2012).

Usage

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

Arguments

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.

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 $d_{MODWT}$.

Author(s)

Ángel López-Oriona, José A. Vilar

References

D'Urso P, Maharaj EA (2012). “Wavelets-based clustering of multivariate time series.” Fuzzy Sets and Systems, 193, 33–61.

See Also

modwt

Examples

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

Description

dis_eros returns a pairwise distance matrix based on the PCA similarity factor proposed by Singhal and Seborg (2005).

Usage

dis_pca(X, retained_components = 3)

Arguments

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 $d_{PCA}(\boldsymbol X_{T}, \boldsymbol Y_{T})=1-S_{PCA} (\boldsymbol X_{T}, \boldsymbol Y_{T})$, with

$S_{PCA}(\boldsymbol X_{T}, \boldsymbol Y_{T})=\frac{\sum_{i=1}^{k}\sum_{j=1}^{k} (\lambda^i_{\boldsymbol X_T} \lambda^j_{\boldsymbol Y_T})\cos^2 \theta_{ij}}{\sum_{i=1}^{k} \lambda^i_{\boldsymbol X_T} \lambda^i_{\boldsymbol Y_T}},$

where $\theta_{ij}$ is the angle between the $i$th eigenvector of $\boldsymbol X_{T}$ and the $j$th eigenvector of series $\boldsymbol Y_{T}$, respectively, and $\lambda^i_{\boldsymbol Y_T}$ and $\lambda^i_{\boldsymbol Y_T}$ are the $i$th eigenvalues of $\boldsymbol X_{T}$ and the $j$th eigenvalues of series $\boldsymbol Y_{T}$ respectively.

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Singhal A, Seborg DE (2005). “Clustering multivariate time-series data.” Journal of Chemometrics: A Journal of the Chemometrics Society, 19(8), 427–438.

Examples

toy_dataset <- BasicMotions$data[1 : 10] # Selecting the first 10 MTS from the
# dataset BasicMotions
distance_matrix <- dis_pca(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_pca

Description

dis_ppca returns a pairwise distance matrix based on an extension of the procedure proposed by Wan et al. (2022). The function can also be used for dimensionality reduction purposes.

Usage

dis_ppca(X, w = 2, var_rate = 0.9, features = F)

Arguments

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

$d_{PPCA}(\boldsymbol X_{T}, \boldsymbol Y_{T})=\Big|\Big|vec\big(\widehat{\boldsymbol \Sigma}_a ^{\boldsymbol X_T}\big) -vec\big(\widehat{\boldsymbol \Sigma}_a^{\boldsymbol Y_T}\big)\Big|\Big|,$

where $\widehat{\boldsymbol \Sigma}_a ^{\boldsymbol X_T}$ and $\widehat{\boldsymbol \Sigma}_a ^{\boldsymbol Y_T}$ are estimates of the covariance matrices based on a piecewise representation for which the original MTS $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively, are divided into a number of w local segments (in the time dimension). If we use the function to perform dimensionality reduction (features = TRUE), then for a given series $\boldsymbol X_T$, matrix $\widehat{\boldsymbol \Sigma}_a ^{\boldsymbol X_T}$ is decomposed by executing the standard PCA and a certain number of principal components are retained (according to the parameter var_rate). Function dis_ppca returns the reduced counterpart of $\boldsymbol X_T$, which is constructed from $\boldsymbol X_T$ by considering the matrix of scores with respect to the retained principal components.

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Wan X, Li H, Zhang L, Wu YJ (2022). “Dimensionality reduction for multivariate time-series data mining.” The Journal of Supercomputing, 78(7), 9862–9878.

Examples

reduced_dataset <- dis_ppca(RacketSports$data[1], features = TRUE) # Reducing
# the dimensionality of the first MTS in dataset RacketSports
reduced_dataset
distance_matrix <- dis_ppca(RacketSports$data) # Computing the
# corresponding distance matrix for all MTS in dataset RacketSports
# (by default, features = F)

Description

dis_qcd returns a pairwise distance matrix based on the dissimilarity introduced by Lopez-Oriona and Vilar (2021).

Usage

dis_qcd(X, levels = c(0.1, 0.5, 0.9), freq = NULL, features = FALSE, ...)

Arguments

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

$d_{QCF}(\boldsymbol X_T, \boldsymbol Y_T)=\Bigg[\sum_{j_1=1}^{d}\sum_{j_2=1}^{d}\sum_{i=1}^{r} \sum_{i'=1}^{r}\sum_{k=1}^{K}\Big(\Re\big({\widehat G_{j_1,j_2}^{\boldsymbol X_T}(\omega_{k}, \tau_{i}, \tau_{i^ {\prime}})}\big) -\Re\big({\widehat G_{j_1,j_2}^{\boldsymbol Y_T}(\omega_{k}, \tau_{i}, \tau_{i^ {\prime}})\big)}\Big)^2+$

$\sum_{j_1=1}^{d}\sum_{j_2=1}^{d}\sum_{i=1}^{r}\sum_{i'=1}^{r}\sum_{k=1}^{K}\Big(\Im\big({\widehat G_{j_1,j_2} ^{\boldsymbol X_T}(\omega_{k}, \tau_{i}, \tau_{i^ {\prime}})}\big) -\Im\big({\widehat G_{j_1,j_2}^{\boldsymbol Y_T}(\omega_{k}, \tau_{i}, \tau_{i^ {\prime}})\big)}\Big)^2\Bigg]^{1/2},$

where ${\widehat G_{j_1,j_2}^{\boldsymbol X_T}(\omega_{k}, \tau_{i}, \tau_{i^ {\prime}})}$ and ${\widehat G_{j_1,j_2}^{\boldsymbol Y_T}(\omega_{k}, \tau_{i}, \tau_{i^ {\prime}})}$ are estimates of the quantile cross-spectral densities (so-called smoothed CCR-periodograms) 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, and $\Re(\cdot)$ and $\Im(\cdot)$ denote the real part and imaginary part operators, respectively.

Value

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

Lopez-Oriona A, Vilar JA (2021). “Quantile cross-spectral density: A novel and effective tool for clustering multivariate time series.” Expert Systems with Applications, 185, 115677.

See Also

dis_qcf

Examples

toy_dataset <- AtrialFibrillation$data[1 : 4] # Selecting the first 4 MTS from the
# dataset AtrialFibrillation
distance_matrix <- dis_qcd(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_qcd
distance_matrix <- dis_qcd(toy_dataset, levels = c(0.4, 0.8)) # Changing
# the probability levels to compute the QCD-based estimators
distance_matrix <- dis_qcd(toy_dataset, freq = 0.5) # Considering only
# a single frequency for the computation of d_qcd
feature_dataset <- dis_qcd(toy_dataset, features = TRUE) # Computing
# the corresponding dataset of features

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

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

dis_qcd

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

Description

dis_spectral returns a pairwise distance matrix based on the dissimilarities introduced by Kakizawa et al. (1998).

Usage

dis_spectral(X, method = "j_divergence", alpha = 0.5, features = FALSE)

Arguments

Details

Given a collection of MTS, the function returns a pairwise distance matrix. If method="j_divergence" then the distance between two MTS $\boldsymbol X_T$ and $\boldsymbol Y_T$ is defined as

$d_{JSPEC}(\boldsymbol X_T, \boldsymbol Y_T)=\frac{1}{2T} \sum_{k=1}^{K}\bigg(tr\Big(\widehat{\boldsymbol f}_{\boldsymbol X_T}(\omega_k) \widehat{\boldsymbol f}_{\boldsymbol Y_T}^{-1}(\omega_k)\Big) +tr\Big(\widehat{\boldsymbol f}_{\boldsymbol Y_T}(\omega_k) \widehat{\boldsymbol f}_{\boldsymbol X_T}^{-1}(\omega_k)\Big)-2d\bigg),$

where $\widehat{\boldsymbol f}_{\boldsymbol X_T}(\omega_k)$ and $\widehat{\boldsymbol f}_{\boldsymbol Y_T}(\omega_k)$ are the estimated spectral density matrices from the series $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively, evaluated at frequency $\omega_k$, and $tr(\cdot)$ denotes the trace of a square matrix. If method="chernoff_divergence", then the distance between two MTS $\boldsymbol X_T$ and $\boldsymbol Y_T$ is defined as

$d_{CSPEC}(\boldsymbol X_T, \boldsymbol Y_T)=$

$\frac{1}{2T} \sum_{k=1}^{K}\bigg(\log{\frac{\Big|\alpha\widehat{\boldsymbol f}^{\boldsymbol X_T}(\omega_k) +(1-\alpha)\widehat{\boldsymbol f}^{\boldsymbol Y_T}(\omega_k)\Big |} {\Big|\widehat{\boldsymbol f}^{\boldsymbol Y_T}(\omega_k)\Big|}}+ \log{\frac{\Big|\alpha\widehat{\boldsymbol f}^{\boldsymbol Y_T}(\omega_k) + (1-\alpha)\widehat{\boldsymbol f}^{\boldsymbol X_T}(\omega_k)\Big |} {\Big|\widehat{\boldsymbol f}^{\boldsymbol X_T}(\omega_k)\Big|}}\bigg),$

where $\alpha \in (0,1)$.

Value

If features = FALSE (default), returns a distance matrix based on the distance $d_{JSPEC}$ as long as we set method="j_divergence", and based on the alternative distance $d_{CSPEC}$ as long as we set method= "chernoff_divergence". Otherwise, if features = TRUE, the function returns a dataset of feature vectors, i.e., each row in the dataset contains the features employed to compute either $d_{JSPEC}$ or $d_{CSPEC}$. These vectors are vectorized versions of the estimated spectral matrices.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Kakizawa Y, Shumway RH, Taniguchi M (1998). “Discrimination and clustering for multivariate time series.” Journal of the American Statistical Association, 93(441), 328–340.

Examples

toy_dataset <- Libras$data[1 : 10] # Selecting the first 10 MTS from the
# dataset Libras
distance_matrix_j <- dis_spectral(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_jspec
distance_matrix_c <- dis_spectral(toy_dataset,
method = 'chernoff_divergence') # Computing the pairwise
# distance matrix based on the distance dis_cspec
feature_dataset <- dis_qcd(toy_dataset, features = TRUE) # Computing
# the corresponding dataset of features for d_cpec

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

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

vpca_clustering

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

Description

dis_cor returns a pairwise distance matrix based on a generalization of the dissimilarity introduced by Piccolo (1990).

Usage

dis_var_1(X, max_p = 1, criterion = "AIC", features = FALSE)

Arguments

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

$d_{VAR}(\boldsymbol X_T, \boldsymbol Y_T)=||\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{VAR}- \widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{VAR}||,$

where $\widehat{\boldsymbol \theta}^{\boldsymbol X_T}_{VAR}$ and $\widehat{\boldsymbol \theta}^{\boldsymbol Y_T}_{VAR}$ are vectors containing the estimated VAR parameters for $\boldsymbol X_T$ and $\boldsymbol Y_T$, respectively. If VAR models of different orders are fitted to $\boldsymbol X_T$ and $\boldsymbol Y_T$, then the shortest vector is padded with zeros until it reaches the length of the longest vector.

Value

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

Author(s)

Ángel López-Oriona, José A. Vilar

References

Piccolo D (1990). “A distance measure for classifying ARIMA models.” Journal of time series analysis, 11(2), 153–164.

See Also

dis_var_2, diss.AR.PIC

Examples

toy_dataset <- Libras$data[1 : 2] # Selecting the first 2 MTS from the
# dataset Libras
distance_matrix <- dis_var_1(toy_dataset) # Computing the pairwise
# distance matrix based on the distance dis_var_1
feature_dataset <- dis_var_1(toy_dataset, features = TRUE) # Computing
# the corresponding dataset of features

Description

dis_var_2 returns a pairwise distance matrix based on testing whether each pair of series are or not generated from the same VARMA model (Maharaj 1999).

Usage

dis_var_2(X, max_p = 2, criterion = "BIC")

Arguments

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 $1-p$, where $p$ is the $p$-value of the test of hypothesis proposed by . This test is based on checking the equality of the underlying VARMA models of both series. The VARMA structures are approximated by truncated VAR($\infty)$ models with a common order $k = \max{(k_x, k_y)}$, where $k_x$ and $k_y$ are determined by the BIC or AIC criterion. The VAR coefficients are automatically fitted. The dissimilarity between both series is given by $1-p$ because this quantity is expected to take larger values the more different both generating processes are. The procedure is able to compare two dependent MTS.

Value

The computed pairwise distance matrix.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Maharaj EA (1999). “Comparison and classification of stationary multivariate time series.” Pattern Recognition, 32(7), 1129–1138.

See Also

dis_var_1, diss.AR.MAH

Examples

toy_dataset <- Libras$data[c(1, 2)] # Selecting the first two MTS from the
# dataset Libras
distance_matrix <- dis_var_2(toy_dataset, max_p = 1) # Computing the pairwise
# distance matrix based on the distance dis_var_2

Description

dis_www returns a pairwise distance matrix based on the feature extraction procedure proposed by Wang et al. (2007).

Usage

dis_www(X, h = 20, features = FALSE)

Arguments

Details

Given a collection of MTS, the function returns the pairwise distance matrix, where the distance between two MTS is defined as the Euclidean distance between the corresponding feature vectors

Value

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

Author(s)

Ángel López-Oriona, José A. Vilar

References

Wang X, Wirth A, Wang L (2007). “Structure-based statistical features and multivariate time series clustering.” In Seventh IEEE international conference on data mining (ICDM 2007), 351–360. IEEE.

Examples

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

Description

dis_zagorecki returns a pairwise distance matrix based on the feature extraction procedure proposed by Zagorecki (2015).

Usage

dis_zagorecki(set, features = FALSE)

Arguments

Details

Given a collection of MTS, the function returns the pairwise distance matrix, where the distance between two MTS is defined as the Euclidean distance between the corresponding feature vectors

Value

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

Author(s)

Ángel López-Oriona, José A. Vilar

References

Zagorecki A (2015). “A versatile approach to classification of multivariate time series data.” In 2015 Federated Conference on Computer Science and Information Systems (FedCSIS), 407–410. IEEE.

Examples

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

Description

Multivariate time series (MTS) of five species of geese.

Usage

data(DuckDuckGeese_1)

Format

A list with two elements, which are:

data

A list with 50 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 270 rows (time points) indicating frequency and 1345 columns (variables) indicating recording. The first 50 elements of the whole dataset are stored here. All these elements pertain to the training set. The numeric vector classes is formed by integers from 1 to 5, indicating that there are 5 different classes in the database. Each class is associated with a different species of geese. For more information, Bagnall et al. (2018). Run "install.packages("ueadata3", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata3::DuckDuckGeese_1".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) of five species of geese.

Usage

data(DuckDuckGeese_2)

Format

A list with two elements, which are:

data

A list with 50 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 270 rows (time points) indicating frequency and 1345 columns (variables) indicating recording. The last 50 elements of the whole dataset are stored here. All these elements pertain to the test set. The numeric vector classes is formed by integers from 1 to 5, indicating that there are 5 different classes in the database. Each class is associated with a different species of geese. For more information, Bagnall et al. (2018). Run "install.packages("ueadata4", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata4::DuckDuckGeese_2".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating the movement of the worm Caenorhabditis elegans. The motion of worms in an agar plate is recorded as a combination of six base shapes.

Usage

data(EigenWorms_1)

Format

A list with two elements, which are:

data

A list with 130 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 17984 rows (time points) indicating velocity trajectory and 3 columns (variables) indicating spatial dimension. The first 1422 elements correspond to the training set, whereas the last 1436 elements correspond to the test set. The first 130 elements of the whole dataset are stored here. All these elements but the last two pertain to the training set. The numeric vector classes is formed by integers from 1 to 20, indicating that there are 20 different classes in the database. Each class is associated with a different alphabetical character. For more information, see Bagnall et al. (2018). To access this dataset, run "install.packages("ueadata5", repos="https://anloor7.github.io/drat")" and use the syntax "ueadata5::EigenWorms_1".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating the movement of the worm Caenorhabditis elegans. The motion of worms in an agar plate is recorded as a combination of six base shapes.

Usage

data(EigenWorms_2)

Format

A list with two elements, which are:

data

A list with 129 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 17984 rows (time points) indicating velocity trajectory and 3 columns (variables) indicating spatial dimension. The first 1422 elements correspond to the training set, whereas the last 1436 elements correspond to the test set. The last 129 elements of the whole dataset are stored here. All these elements pertain to the test set. The numeric vector classes is formed by integers from 1 to 20, indicating that there are 20 different classes in the database. Each class is associated with a different alphabetical character. For more information, see Bagnall et al. (2018). To access this dataset, run "install.packages("ueadata6", repos="https://anloor7.github.io/drat")" and use the syntax "ueadata6::EigenWorms_2".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) of some participants simulating several activities. In particular, data was collected from 6 participants using a tri-axial accelerometer on the dominant wrist while conducting 4 different activities

Usage

data(Epilepsy)

Format

A list with two elements, which are:

data

A list with 275 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 206 rows (time points) indicating acceleration trajectory and 3 columns (variables) indicating the axis in the accelerometer. The first 137 elements correspond to the training set, whereas the last 138 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 4, indicating that there are 4 different classes in the database. Each class is associated with a different activity. For more information, see Bagnall et al. (2018).

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating the movement of the worm Caenorhabditis elegans. The motion of worms in an agar plate is recorded as a combination of six base shapes.

Usage

data(ERing)

Format

A list with two elements, which are:

data

A list with 300 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 65 rows (time points) indicating time measurements and 4 columns (variables) indicating electrodes. The first 30 elements correspond to the training set, whereas the last 270 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 6, indicating that there are 6 different classes in the database. Each class is associated with a different posture of the hand. For more information, see Bagnall et al. (2018).

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating the concentration of ethanol of several water-and-ethanol solutions in 44 distinct, real-whisky bottles.

Usage

data(EthanolConcentration)

Format

A list with two elements, which are:

data

A list with 524 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 1751 rows (time points) indicating time measurements and 3 columns (variables) indicating recording. The first 261 elements correspond to the training set, whereas the last 263 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 4, indicating that there are 4 different classes in the database. Each class is associated with a different concentration of ethanol. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata1", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata1::EthanolConcentration".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

f4_classifier computes the F4 classifier for MTS proposed by Lopez-Oriona and Vilar (2021).

Usage

f4_classifier(
  training_data,
  new_data = NULL,
  classes,
  levels = c(0.1, 0.5, 0.9),
  cv_folds = 5,
  var_rate = 0.9
)

Arguments

Details

This function constructs the classifier F4 of . Given a set of MTS with associated class labels, estimates of the quantile cross-spectral density (QCD) and the maximum overlap discrete wavelet transform (MODWT) are first computed for each series. Then Principal Components Analysis (PCA) is applied over the dataset of QCD-based features and a given number of principal components are retained according to a criterion of explained variability. Next, each series is decribed by means of the concatenation of the QCD-based transformed features and the MODWT-based features. Finally, a traditional random forest classifier is executed in the resulting dataset.

Value

If new_data = NULL (default), returns a fitted model of class train (see train). Otherwise, the function returns the predicted class labels for the elements in new_data.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Lopez-Oriona A, Vilar JA (2021). “F4: An All-Purpose Tool for Multivariate Time Series Classification.” Mathematics, 9(23), 3051.

Examples

predictions <- f4_classifier(training_data = Libras$data[1 : 20],
new_data = Libras$data[181 : 200], classes = Libras$classes[181 : 200])
# Computing the predictions for the test set of dataset Libras

Description

Dataset containing 50 financial MTS associated with companies in the S&P 500 index.

Usage

data(FinancialData)

Format

A list with two elements, which are:

data

A list with 50 MTS.

classes

A character vector indicating the abbreviations associated with the series (companies) in data.

Details

Each element in data is a matrix formed by 654 rows (series length) and 2 columns (dimensions). Each MTS represents a company in the top 50 of the S&P 500 index according to market capitalization. One dimension measures the daily returns of the company, whereas the other measures the daily change in trading volume. The sample period spans from 6th July 2015 to 7th February 2018.

Description

Multivariate time series (MTS) indicating the finger movements of a subject while typing at a computer keyboard.

Usage

data(FingerMovements)

Format

A list with two elements, which are:

data

A list with 416 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 50 rows (time points) indicating EEG observations and 28 columns (variables) indicating EEG channel. The first 316 elements correspond to the training set, whereas the last 100 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 2, indicating that there are 2 different classes in the database. Each class is associated with a different side (left and right). For more information, see Bagnall et al. (2018). Run "install.packages("ueadata1", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata1::FingerMovements".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating the movement of a joystick by two subjects with their hand and wrist.

Usage

data(HandMovementDirection)

Format

A list with two elements, which are:

data

A list with 234 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 400 rows (time points) indicating MEG observations and 10 columns (variables) indicating MEG channel. The first 160 elements correspond to the training set, whereas the last 74 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 4, indicating that there are 4 different classes in the database. Each class is associated with a different direction (right, up, down and left). For more information, see Bagnall et al. (2018). Run "install.packages("ueadata1", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata1::HandMovementDirection".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating writing from a subject wearing a smartwatch.

Usage

data(Handwriting)

Format

A list with two elements, which are:

data

A list with 1000 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 152 rows (time points) indicating acceleration trajectory and 3 columns (variables) indicating accelerometer value. The first 150 elements correspond to the training set, whereas the last 850 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 26, indicating that there are 26 different classes in the database. Each class is associated with a different alphabetical character. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata1", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata1::Handwriting".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating heart sound from healthy patients and pathological patients (with a confirmed cardiac diagnosis).

Usage

data(Heartbeat)

Format

A list with two elements, which are:

data

A list with 409 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 405 rows (time points) indicating readings in a spectrogram and 61 columns (variables) indicating frequency band from the spectrogram. The first 204 elements correspond to the training set, whereas the last 205 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 2, indicating that there are 2 different classes in the database. Each class is associated with a different alphabetical character. For more information, see Bagnall et al. (2018). To access this dataset, run "install.packages("ueadata1", repos="https://anloor7.github.io/drat")" and use the syntax "ueadata1::Heartbeat".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating voice recordings of nine Japanese male speakers saying the vowels 'a' and 'e'.

Usage

data(JapaneseVowels)

Format

A list with two elements, which are:

data

A list with 640 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 29 rows (time points) indicating time recordings and 12 columns (variables) indicating modified raw recordings. The first 270 elements correspond to the training set, whereas the last 370 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 9, indicating that there are 9 different classes in the database. Each class is associated with a different speaker. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata1", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata1::JapaneseVowels".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

knn_classifier returns the predictions for a test set concerning a nearest neighbours-based classifier.

Usage

knn_classifier(dataset, classes, index_test, distance, k, ...)

Arguments

Details

Given a collection of MTS containing the training and test set, the function constructs a nearest neighbours-based classifier based on a given dissimilarity measure. The corresponding predictions for the elements in the test set are returned.

Value

The class labels for the elements in the test set.

Author(s)

Ángel López-Oriona, José A. Vilar

Examples

predictions_1_nn <- knn_classifier(BasicMotions$data[1 : 10], BasicMotions$classes[1 : 10],
index_test = 6 : 10, distance = 'dis_modwt', k = 1) # Computing the
# predictions for the test elements in dataset BasicMotions according to
# a 1-nearest neighbour classifier based on dis_modtw.
predictions_1_nn

Description

Multivariate time series (MTS) indicating hand movement concerning the official brazilian sign language from 4 different people, during 2 sessions.

Usage

data(Libras)

Format

A list with two elements, which are:

data

A list with 360 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 45 rows (time points) indicating time points in video recordings and 2 columns (variables) indicating video sessions. The first 180 elements correspond to the training set, whereas the last 180 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 15, indicating that there are 15 different classes in the database. Each class is associated with a hand movement type. For more information, see Bagnall et al. (2018).

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) of simulated light curves imitating astronomical time series from the Large Synoptic Survey Telescope (LSST). The simulated series are measurements of an object's brightness as a function of time

Usage

data(LSST)

Format

A list with two elements, which are:

data

A list with 4925 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 36 rows (time points) indicating time recordings and 6 columns (variables) indicating different astronomical filters. The first 2459 elements correspond to the training set, whereas the last 2466 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 14, indicating that there are 14 different classes in the database. Each class is associated with a different astronomical object. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata1", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata1::LSST".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

mc2pca_clustering performs the clustering algorithm proposed by Li (2019), which is based on common principal component analysis (CPCA).

Usage

mc2pca_clustering(X, k, var_rate = 0.9, max_it = 1000, tol = 1e-05)

Arguments

Details

This function executes the crisp clustering method proposed by . The algorithm is a $K$-means-type procedure where the distance between a given MTS and a centroid is given by the reconstruction error taking place when the series is reconstructed from the common space obtained by considering all the series in the cluster associated with the corresponding centroid (the common space is the centroid).

Value

A list with two elements:

• cluster. A vector defining the clustering solution.

• iterations. The number of iterations before the algorithm stopped.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Li H (2019). “Multivariate time series clustering based on common principal component analysis.” Neurocomputing, 349, 239–247.

Examples

clustering_algorithm <- mc2pca_clustering(BasicMotions$data, k = 4, var_rate = 0.30)
# Executing the clustering algorithm in the dataset BasicMotions (var_rate = 0.30,
# i.e., we keep only a few principal components for computing the reconstructed series)
clustering_algorithm$cluster # The clustering solution
clustering_algorithm$iterations # The number of iterations before the algorithm
library(ClusterR)
external_validation(clustering_algorithm$cluster, BasicMotions$classes,
summary_stats = TRUE) # Evaluating the clustering algorithms vs the true partition
# stopped

Description

mlmts provides an implementation of several machine learning algorithms for multivariate time series. The package includes functions allowing the execution of clustering, classification or outlier detection methods, among others. It also incorporates a collection of multivariate time series datasets which can be used to analyse the performance of new proposed algorithms. Practitioners from a broad variety of fields could benefit from the general framework provided by mlmts.

Description

Multivariate time series (MTS) involving imagined movements performed by a subject with either the left small finger or the tongue. The time series of the electrical brain activity were stored during the corresponding trials

Usage

data(MotorImagery)

Format

A list with two elements, which are:

data

A list with 378 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 3000 rows (time points) indicating time recordings in EEG and 64 columns (variables) indicating EEG electrodes. The first 278 elements correspond to the training set, whereas the last 100 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 2, indicating that there are 2 different classes in the database. Each class is associated with the label 'finger' or 'tongue' (the imagined movements). For more information, see Bagnall et al. (2018). To access this dataset, execute the code "install.packages("ueadata2", repos="https://anloor7.github.io/drat")" and use the following syntax: "ueadata2::MotorImagery".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

mts_forecasting computes a general forecasting method for MTS based on fitting standard regression models to lag-embedding matrices.

Usage

mts_forecasting(X, max_lag = 1, model_caret = "lm", h = 1)

Arguments

Details

This function performs a forecasting procedure based on lag-embedding matrices. Given a list of MTS, it returns the corresponding list of $h$-step ahead forecasts. We assume we want to forecast a given MTS $\boldsymbol X_T$ with certain univariate components for a given forecasting horizon $h$ and a maximum number of lags $L$. For each component, the corresponding lag-embedded matrix is constructed by considering the past information about that component and all the remaining ones. The selected regression model is fitted to all the constructed matrices (considering the last column as the response variables), and the fitted models are used to construct the $h$-step ahead forecasts in a recursive manner.

Value

A list containing the $h$-step ahead forecast (matrix) for each one of the MTS.

Author(s)

Ángel López-Oriona, José A. Vilar

Examples

predictions <- mts_forecasting(RacketSports$data[1], model_caret = 'lm', h = 1)
# Obtaining the predictions for the first series in dataset RacketSports
# by using standard linear regression and a forecasting horizon of 1
predictions <- mts_forecasting(RacketSports$data[1], model_caret = 'rf', h = 3)
# Obtaining the predictions for the first series in dataset RacketSports
# by using the random forest and a forecasting horizon of 3

Description

mts_plot constructs a plot of a MTS. Each univariate series comprising the MTS object is displayed in a different colour.

Usage

mts_plot(series, title = "")

Arguments

Details

Given a MTS, the function constructs the corresponding plot, in which a different colour is used for each univariate series comprising the MTS object. Therefore, the MTS is represented as a collection of univariate series in a single graph.

Value

The corresponding plot.

Author(s)

Ángel López-Oriona, José A. Vilar

Examples

mts_plot(BasicMotions$data[[1]]) # Represents the first MTS in dataset
# BasicMotions

Description

Multivariate time series (MTS) related to several Naval Air Training and Operating Procedures Standardization-type motions used to control plane movements.

Usage

data(NATOPS)

Format

A list with two elements, which are:

data

A list with 360 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 51 rows (time points) indicating time recordings and 24 columns (variables) indicating sensors placed in a particular part of the body and associated with a particular coordinate. The first 180 elements correspond to the training set, whereas the last 180 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 6, indicating that there are 6 different classes in the database. Each class is associated with a separate action performed by the subjects. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata2", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata2::NATOPS".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

outlier_detection computes the outlier detection method for MTS proposed by Lopez-Oriona and Vilar (2021).

Usage

outlier_detection(X, levels = c(0.1, 0.5, 0.9), alpha = NULL)

Arguments

Details

This function performs outlier detection according to the procedure proposed by Lopez-Oriona and Vilar (2021). Specifically, each MTS in the original set is described by means of a multivariate functional datum by using an estimate of its quantile cross- spectral density. Given the corresponding set of multivariate functional data, the functional depth of each object is computed. Based on depth computations, the outlying elements are the objects with low values for the depths.

Value

A list with two elements:

• Depths. The functional depths associated with elements in X, sorted in increasing order.

• Indexes. The corresponding indexes associated with the vector Depths.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Lopez-Oriona A, Vilar JA (2021). “Outlier detection for multivariate time series: A functional data approach.” Knowledge-Based Systems, 233, 107527.

See Also

dis_qcd

Examples

outliers <- outlier_detection(SyntheticData2$data[c(1 : 3, 65)])
outliers$Indexes[1] # The first outlying MTS in dataset SyntheticData2
outliers$Depths[1] # The corresponding value for the depths

Description

Multivariate time series (MTS) indicating occupancy rate of different car lanes.

Usage

data(PEMS_SF_1)

Format

A list with two elements, which are:

data

A list with 220 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 144 rows (time points) indicating minutes and 3 columns (variables) indicating sensors. The first 220 elements of the whole dataset are stored here. All these elements pertain to the training set. The numeric vector classes is formed by integers from 1 to 7, indicating that there are 7 different classes in the database. Each class is associated with a different day of the week. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata7", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata7::PEMS_SF_1".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating occupancy rate of different car lanes.

Usage

data(PEMS_SF_2)

Format

A list with two elements, which are:

data

A list with 220 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 144 rows (time points) indicating minutes and 3 columns (variables) indicating sensors. The last 220 elements of the whole dataset are stored here. The last 173 elements of this dataset pertain to the test set. The numeric vector classes is formed by integers from 1 to 7, indicating that there are 7 different classes in the database. Each class is associated with a different day of the week. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata8", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata8::PEMS_SF_2".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) indicating writing of 44 people drawing the digits from 0 to 9. Each instance is made up of the x and y coordinates of the pen-tip traced accross a digital screen.

Usage

data(PenDigits)

Format

A list with two elements, which are:

data

A list with 10992 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 8 rows (time points) spatial points and 2 columns (variables) indicating coordinate. The first 7494 elements correspond to the training set, whereas the last 3498 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 10, indicating that there are 10 different classes in the database. Each class is associated with a different digit. For more information, see Bagnall et al. (2018).

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

Multivariate time series (MTS) involving segmented audios of male and female speakers collected from Google Translate.

Usage

data(Phoneme)

Format

A list with two elements, which are:

data

A list with 6668 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 217 rows (time points) indicating readings in a spectrogram and 11 columns (variables) indicating frequency band from the spectrogram. The first 3315 elements correspond to the training set, whereas the last 3353 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 39, indicating that there are 39 different classes in the database. Each class is associated with a different phoneme. For more information, see Bagnall et al. (2018). Run "install.packages("ueadata2", repos="https://anloor7.github.io/drat")" to access this dataset and use the syntax "ueadata2::Phoneme".

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.

Description

plot_2d_scaling represents a 2-dimensional scaling plane starting from a dissimilarity matrix.

Usage

plot_2d_scaling(distance_matrix, cluster_labels = NULL, title = "")

Arguments

Details

Given a distance matrix, the function constructs the corresponding 2-dimensional scaling, which is a 2d plane in which the distances between the points represent the original distances as correctly as possible. If the vector cluster_labels is provided to the function, points in the 2d plane are coloured according to the given class labels.

Value

The 2-dimensional scaling plane.

Author(s)

Ángel López-Oriona, José A. Vilar

Examples

distance_matrix_qcd <- dis_qcd(SyntheticData1$data[1 : 30]) # Computing the pairwise
# distance matrix for the first 30 elements in dataset SyntheticData1 based on dis_qcd
plot_2d_scaling(distance_matrix_qcd, cluster_labels = SyntheticData1$classes[1 : 30])
# Constructing the corresponding 2d-scaling plot. Each class is represented
# in a different colour

Description

Multivariate time series (MTS) collected from university students playing badminton or squash while wearing a smartwatch. The watch recorded the x, y, z coordinates for both a gyroscope and an accelerometer to an android phone.

Usage

data(RacketSports)

Format

A list with two elements, which are:

data

A list with 303 MTS.

classes

A numeric vector indicating the corresponding classes associated with the elements in data.

Details

Each element in data is a matrix formed by 30 rows (time points) indicating time recordings over an interval of 3 seconds and 6 columns (variables) indicating gyroscope or accelerometer and the corresponding coordinate. The first 151 elements correspond to the training set, whereas the last 152 elements correspond to the test set. The numeric vector classes is formed by integers from 1 to 4, indicating that there are 4 different classes in the database. Each class is associated with a sport and stroke a particular player is making. For more information, see Bagnall et al. (2018).

References

Bagnall A, Dau HA, Lines J, Flynn M, Large J, Bostrom A, Southam P, Keogh E (2018). “The UEA multivariate time series classification archive, 2018.” arXiv preprint arXiv:1811.00075.

Ruiz AP, Flynn M, Large J, Middlehurst M, Bagnall A (2021). “The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances.” Data Mining and Knowledge Discovery, 35(2), 401–449.

Bagnall A, Lines J, Vickers W, Keogh E (2022). “The UEA & UCR Time Series Classification Repository.” www.timeseriesclassification.com.