| Title: | Imputation of Multivariate Time Series Based on Dynamic Time Warping |
|---|---|
| Description: | Functions to impute large gaps within multivariate time series based on Dynamic Time Warping methods. Gaps of size 1 or inferior to a defined threshold are filled using simple average and weighted moving average respectively. Larger gaps are filled using the methodology provided by Phan et al. (2017) <DOI:10.1109/MLSP.2017.8168165>: a query is built immediately before/after a gap and a moving window is used to find the most similar sequence to this query using Dynamic Time Warping. To lower the calculation time, similar sequences are pre-selected using global features. Contrary to the univariate method (package 'DTWBI'), these global features are not estimated over the sequence containing the gap(s), but a feature matrix is built to summarize general features of the whole multivariate signal. Once the most similar sequence to the query has been identified, the adjacent sequence to this window is used to fill the gap considered. This function can deal with multiple gaps over all the sequences componing the input multivariate signal. However, for better consistency, large gaps at the same location over all sequences should be avoided. |
| Authors: | DEZECACHE Camille, PHAN Thi Thu Hong, POISSON-CAILLAULT Emilie |
| Maintainer: | POISSON-CAILLAULT Emilie <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0 |
| Built: | 2024-12-01 08:41:57 UTC |
| Source: | CRAN |
Functions to impute large gaps within multivariate time series based on Dynamic Time Warping methods. Gaps of size 1 or inferior to a defined threshold are filled using simple average and weighted moving average respectively. Larger gaps are filled using the methodology provided by Phan et al. (2017) <DOI:10.1109/MLSP.2017.8168165>: a query is built immediately before/after a gap and a moving window is used to find the most similar sequence to this query using Dynamic Time Warping. To lower the calculation time, similar sequences are pre-selected using global features. Contrary to the univariate method (package 'DTWBI'), these global features are not estimated over the sequence containing the gap(s), but a feature matrix is built to summarize general features of the whole multivariate signal. Once the most similar sequence to the query has been identified, the adjacent sequence to this window is used to fill the gap considered. This function can deal with multiple gaps over all the sequences componing the input multivariate signal. However, for better consistency, large gaps at the same location over all sequences should be avoided.
Index of help topics:
DTWUMI-package Imputation of Multivariate Time Series Based on
Dynamic Time Warping
DTWUMI_1gap_imputation
Imputation of a large gap based on DTW for
multivariate signals
DTWUMI_imputation Large gaps imputation based on DTW for
multivariate signals
Indexes_size_missing_multi
Indexing gaps size
dataDTWUMI A multivariate times series consisting of three
signals as example for DTWUMI package
imp_1NA Imputing gaps of size 1
DEZECACHE Camille, PHAN Thi Thu Hong, POISSON-CAILLAULT Emilie
Maintainer: POISSON-CAILLAULT Emilie <[email protected]>
Thi-Thu-Hong Phan, Emilie Poisson-Caillault, Alain Lefebvre, Andre Bigand. Dynamic time warping-based imputation for univariate time series data. Pattern Recognition Letters, Elsevier, 2017, <DOI:10.1016/j.patrec.2017.08.019>. <hal-01609256>
data(dataDTWUMI) dataDTWUMI_gap <- dataDTWUMI[["incomplete_signal"]] imputation <- DTWUMI_imputation(dataDTWUMI_gap, gap_size_threshold = 10, DTW_method = "DTW") plot(dataDTWUMI_gap[, 1], type = "l", lwd = 2) lines(imputation$output[, 1], col = "red") plot(dataDTWUMI_gap[, 2], type = "l", lwd = 2) lines(imputation$output[, 2], col = "red") plot(dataDTWUMI_gap[, 3], type = "l", lwd = 2) lines(imputation$output[, 3], col = "red")data(dataDTWUMI) dataDTWUMI_gap <- dataDTWUMI[["incomplete_signal"]] imputation <- DTWUMI_imputation(dataDTWUMI_gap, gap_size_threshold = 10, DTW_method = "DTW") plot(dataDTWUMI_gap[, 1], type = "l", lwd = 2) lines(imputation$output[, 1], col = "red") plot(dataDTWUMI_gap[, 2], type = "l", lwd = 2) lines(imputation$output[, 2], col = "red") plot(dataDTWUMI_gap[, 3], type = "l", lwd = 2) lines(imputation$output[, 3], col = "red")
A multivariate times series consisting of three signals as example for DTWUMI package
dataDTWUMIdataDTWUMI
A list storing two data frames with three columns each. The first table contains the original complete simulated data. The second table contains the same simulated data with one large gap added within each signal.
Fills a gap of size 'gap_size' begining at the position 'begin_gap' within a multivariate signal using DTW.
DTWUMI_1gap_imputation(data, id_sequence, begin_gap, gap_size, DTW_method = "DTW", threshold_cos = 0.995, thresh_cos_stop = 0.8, step_threshold = 2, ...)DTWUMI_1gap_imputation(data, id_sequence, begin_gap, gap_size, DTW_method = "DTW", threshold_cos = 0.995, thresh_cos_stop = 0.8, step_threshold = 2, ...)
data |
a multivariate signals containing gaps |
id_sequence |
id of the sequence containing the gap to fill (corresponding to the column number) |
begin_gap |
id of the begining of the gap to fill |
gap_size |
size of the gap to fill |
DTW_method |
DTW method used for imputation ("DTW", "DDTW", "AFBDTW"). By default "DTW" |
threshold_cos |
threshold used to define similar sequences to the query |
thresh_cos_stop |
Define the lowest cosine threshold acceptable to find a similar window to the query |
step_threshold |
step used within the loops determining the threshold and the most similar sequence to the query |
... |
additional arguments from dtw() function |
returns a list containing the following elements:
imputed_values: output vector containing the imputation proposal
id_imputation: a vector containing the position of the imputed values extracted
id_sim_win: a vector containing the position of the similar window to the query
id_gap: a vector containing the position gap considered
id_query: a vector containing the position of the query
DEZECACHE Camille, PHAN Thi Thu Hong, POISSON-CAILLAULT Emilie
data(dataDTWUMI) dataDTWUMI_gap <- dataDTWUMI[["incomplete_signal"]] t <- 207 ; T <- 40 imputation <- DTWUMI_1gap_imputation(dataDTWUMI_gap, id_sequence=1, t, T) plot(dataDTWUMI_gap[, 1], type = "l", lwd = 2) lines(y = imputation$imputed_values, x = imputation$id_gap, col = "red") lines(y = dataDTWUMI_gap[imputation$id_query, 1], x = imputation$id_query, col = "green") lines(y = dataDTWUMI_gap[imputation$id_sim_win, 1], x = imputation$id_sim_win, col = "blue") lines(y = dataDTWUMI_gap[imputation$id_imputation, 1], x = imputation$id_imputation, col = "orange")data(dataDTWUMI) dataDTWUMI_gap <- dataDTWUMI[["incomplete_signal"]] t <- 207 ; T <- 40 imputation <- DTWUMI_1gap_imputation(dataDTWUMI_gap, id_sequence=1, t, T) plot(dataDTWUMI_gap[, 1], type = "l", lwd = 2) lines(y = imputation$imputed_values, x = imputation$id_gap, col = "red") lines(y = dataDTWUMI_gap[imputation$id_query, 1], x = imputation$id_query, col = "green") lines(y = dataDTWUMI_gap[imputation$id_sim_win, 1], x = imputation$id_sim_win, col = "blue") lines(y = dataDTWUMI_gap[imputation$id_imputation, 1], x = imputation$id_imputation, col = "orange")
Fills all gaps within a multivariate signal. Gaps of size 1 are filled using the average values of nearest neighbours. Gaps of size >1 and <gap_size_threshold are filled using weighted moving average. Larger gaps are filled using DTW.
DTWUMI_imputation(data, gap_size_threshold, DTW_method = "DTW", threshold_cos = 0.995, thresh_cos_stop = 0.8, step_threshold = 2, ...)DTWUMI_imputation(data, gap_size_threshold, DTW_method = "DTW", threshold_cos = 0.995, thresh_cos_stop = 0.8, step_threshold = 2, ...)
data |
a multivariate signals containing gaps |
gap_size_threshold |
threshold above which dtw based imputation is computed. Below this threshold, a weighted moving average is calculated |
DTW_method |
DTW method used for imputation ("DTW", "DDTW", "AFBDTW"). By default "DTW" |
threshold_cos |
threshold used to define similar sequences to the query |
thresh_cos_stop |
Define the lowest cosine threshold acceptable to find a similar window to the query |
step_threshold |
step used within the loops determining the threshold and the most similar sequence to the query |
... |
additional arguments from dtw() function |
returns a list containing a dataframe of completed signals
DEZECACHE Camille, PHAN Thi Thu Hong, POISSON-CAILLAULT Emilie
data(dataDTWUMI) dataDTWUMI_gap <- dataDTWUMI[["incomplete_signal"]] imputation <- DTWUMI_imputation(dataDTWUMI_gap, gap_size_threshold = 10) plot(dataDTWUMI_gap[, 1], type = "l", lwd = 2) lines(imputation$output[, 1], col = "red") plot(dataDTWUMI_gap[, 2], type = "l", lwd = 2) lines(imputation$output[, 2], col = "red") plot(dataDTWUMI_gap[, 3], type = "l", lwd = 2) lines(imputation$output[, 3], col = "red")data(dataDTWUMI) dataDTWUMI_gap <- dataDTWUMI[["incomplete_signal"]] imputation <- DTWUMI_imputation(dataDTWUMI_gap, gap_size_threshold = 10) plot(dataDTWUMI_gap[, 1], type = "l", lwd = 2) lines(imputation$output[, 1], col = "red") plot(dataDTWUMI_gap[, 2], type = "l", lwd = 2) lines(imputation$output[, 2], col = "red") plot(dataDTWUMI_gap[, 3], type = "l", lwd = 2) lines(imputation$output[, 3], col = "red")
Imputes isolated missing values based on the average of nearest neighbours.
imp_1NA(data, pos1)imp_1NA(data, pos1)
data |
a univariate signal |
pos1 |
the position of the begining of gaps of size 1, as obtained using Indexes_size_missing_multi() function |
returns a new vector of same size with imputed values
DEZECACHE Camille, PHAN Thi Thu Hong, POISSON-CAILLAULT Emilie
Stores the position of the begining of each gap and their respective size within a multivariate signal.
Indexes_size_missing_multi(data)Indexes_size_missing_multi(data)
data |
multivariate signal |
returns a list with one element per signal. Within each element of this list, the first column gives the position of the begining of each gap and the second column its size.
DEZECACHE Camille, PHAN Thi Thu Hong, POISSON-CAILLAULT Emilie
data(dataDTWUMI) id_NA <- Indexes_size_missing_multi(dataDTWUMI$incomplete_signal)data(dataDTWUMI) id_NA <- Indexes_size_missing_multi(dataDTWUMI$incomplete_signal)