DBA: Dynamic Time Warping Barycenter Averaging

In IncDTW: Incremental Calculation of Dynamic Time Warping

Dynamic Time Warping Barycenter Averaging

Description

Average multiple time series that are non-linearly aligned by Dynamic Time Warping. Find the centroid of a list of time series.

Usage

dba(lot, m0 = NULL, iterMax = 10, eps = NULL, 
                dist_method = c("norm1", "norm2", "norm2_square"),
                step_pattern = c("symmetric2", "symmetric1"),
                ws = NULL,
                iter_dist_method = c("dtw_norm1", "dtw_norm2",
                                     "norm1","norm2", "max", "min"), 
                plotit = FALSE)
                
# deprecated
DBA(lot, m0 = NULL, iterMax = 10, eps = NULL, 
                dist_method = c("norm1", "norm2", "norm2_square"),
                step_pattern = c("symmetric2", "symmetric1"),
                ws = NULL,
                iter_dist_method = c("dtw_norm1", "dtw_norm2",
                                     "norm1","norm2", "max", "min"), 
                plotit = FALSE)
                
centroid(lot, dist_method = c("norm1", "norm2", "norm2_square"),
              step_pattern = c("symmetric2", "symmetric1"),
              normalize = TRUE, ws = NULL, ncores = NULL,
              useRcppParallel = TRUE)


              
## S3 method for class 'dba'
print(x, digits = getOption("digits"),  ...)

## S3 method for class 'dba'
summary(object, ...)              

is.dba(x)             
              

Arguments

lot	List of time series. Each entry of the list is a time series as described in dtw2vec.
m0	time series as vector or matrix. If m0 is NULL, the initial time series m0 is determined by centroid as the centroid of lot, which is the one time series of lot with the minimum average DTW distance to all other time series of lot.
iterMax	integer, number of maximum iterations
eps	numeric, threshold parameter that causes the algorithm to break if the distance of two consecutive barycenters are closer than eps
dist_method	character, describes the method of distance measure. See also dtw.
step_pattern	character, describes the step pattern. See also dtw.
ws	integer, describes the window size for the sakoe chiba window. If NULL, then no window is applied. (default = NULL)
iter_dist_method	character, that describes how the distance between two consecutive barycenter iterations are defined (default = "dtw")
plotit	logical, if the iterations should be plotted or not (only possible for univariate time series)
normalize	logical, default is TRUE, passed to dtw_dismat
ncores	integer, default = NULL, passed to dtw_dismat
useRcppParallel	logical, default is TRUE, passed to dtw_dismat
x	output from dba
object	any R object
digits	passed to round and print
...	additional arguments, e.g. passed to print or summary

Details

The parameter iter_dist_method describes the method to measure the progress between two iterations. For two consecutive centroid candidates m1 and m2 the following methods are implemented:

'dtw_norm1': dtw2vec(m1, m2, dist_method = "norm1", step_pattern = "symmetric2")$normalized_distance

'idm_dtw2': dtw2vec(m1, m2, dist_method = "norm2", step_pattern = "symmetric2")$normalized_distance

'idm_norm1': sum(abs(m1-m2))/(ncol(m1) * 2 * nrow(m1))

'idm_norm2': sqrt(sum((m1-m2)^2))/(ncol(m1) * 2 * nrow(m1))

'idm_max': max(abs(m1-m2))

'idm_min': min(abs(m1-m2))

Value

call	function call
m1	new centroid/ bary center of the list of time series
iterations	list of time series that are the best centroid of the respective iteration
iterDist_m2lot	list of distances of the iterations to lot
iterDist_m2lot_norm	list of normalized distances of the iterations to lot
iterDist_m2m	vector of distances of the iterations to their ancestors
centroid_index	integer giving the index of the centroid time series of lot
dismat_result	list of results of dtw_dismat called by centroid

References

• Leodolter, M.; Pland, C.; Brändle, N; IncDTW: An R Package for Incremental Calculation of Dynamic Time Warping. Journal of Statistical Software, 99(9), 1-23. doi: 10.18637/jss.v099.i09

• Sakoe, H.; Chiba, S., Dynamic programming algorithm optimization for spoken word recognition, Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on , vol.26, no.1, pp. 43-49, Feb 1978. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1163055

• Petitjean, F; Ketterlin, A; Gancarski, P, A global averaging method for dynamic time warping, with applications to clustering, Pattern Recognition, Volume 44, Issue 3, 2011, Pages 678-693, ISSN 0031-3203

Examples

## Not run: 
data("drink_glass")
# initialize with any time series 
m1 <- dba(lot = drink_glass[1:10], m0 = drink_glass[[1]], 
          dist_method = "norm2", iterMax = 20)

# initialize with the centroid

tmp <- centroid(drink_glass)
cent <- drink_glass[[tmp$centroid_index]]
m1 <- dba(lot = drink_glass[1:10], m0 = cent, 
          dist_method = "norm2", iterMax = 20)

# plot all dimensions of the barycenters m_n per iteration:
plot(m1)

# plot the distances of the barycenter of one iteration m_n
# to the barycenter of the previous iteration m_n-1:
plot(m1, type = "m2m")

# plot the average distances of the barycenter m_n 
# to the list of time series:
plot(m1, type = "m2lot")


## End(Not run)

IncDTW documentation built on March 18, 2022, 6:43 p.m.