idtw {IncDTW}

Incremental DTW

Description

Update the DTW distance, cost matrices and direction matrices including the warping path for new observations of two time series.

Usage

idtw(Q, C, newObs, gcm, dm, 
      dist_method = c("norm1", "norm2", "norm2_square"),
      step_pattern = c("symmetric2", "symmetric1"),
      diffM = NULL, ws = NULL, 
      return_cm = FALSE,
      return_diffM = FALSE,
      return_wp = FALSE,
      return_diffp = FALSE,
      return_QC = FALSE)

Arguments

Q

numeric vector, or matrix (see also dtw)

C

numeric vector, or matrix

newObs

vector or matrix of new observations to be appended to C

gcm

global cost matrix, output from dtw(Q, C, ...)

dm

direction matrix, output from dtw(Q, C, ...)

dist_method

character, describes the method of distance measure. See also dtw.

step_pattern

character, describes the step pattern. See also dtw.

diffM

differences matrix, output from dtw(Q, C, ...). This matrix is an optional input parameter (default = NULL) that is necessary to return the path of differences. Only for univariate time series Q and C.

ws

integer, describes the window size for the sakoe chiba window. If NULL, then no window is applied. (default = NULL)

return_cm

logical, if TRUE then the Matrix of costs (the absolute value) is returned. (default = FALSE)

return_diffM

logical, if TRUE then the Matrix of differences (not the absolute value) is returned. (default = FALSE)

return_wp

logical, if TRUE then the warping path is returned. (default = FALSE) If return_diffp == TRUE, then return_wp is set to TRUE as well.

return_diffp

logical, if TRUE then the path of differences (not the absolute value) is returned. (default = FALSE)

return_QC

logical, if TRUE then the input vectors Q and C are appended to the returned list. This is useful for the plot.idtw function. (default = FALSE)

Details

The dynamic time warping distance is the element in the last row and last column of the global cost matrix.

Value

distance

the DTW distance, that is the element of the last row and last column of gcm

gcm

global cost matrix

dm

direction matrix (3=up, 1=diagonal, 2=left)

wp

warping path

ii

indices of Q of the optimal path

jj

indices of C of the optimal path

cm

Matrix of costs

diffM

Matrix of differences

diffp

path of differences

Q

input Q

C

input C

normalized_distance

the normalized DTW distance, see also link{dtw}

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

Examples

#--- Compare the incremental calculation with the basic
# calculation from scratch.
Q <- cumsum(rnorm(100))
C <- Q[11:100] + rnorm(90, 0, 0.5)
newObs <-  c(2, 3)# new observation
base <- dtw(Q = Q, C = C, ws = 15, return_diffM = TRUE) 
base

# recalculation from scratch with new observations
result0 <- dtw(Q = Q, C = c(C, newObs), ws = 15,  return_diffM = TRUE)

# the incremental step with new observations
result1 <- idtw(Q, C, ws = 15, newO = newObs, gcm = base$gcm, 
                dm = base$dm, diffM = base$diffM, return_diffp = TRUE,  
                return_diffM = TRUE, return_QC = TRUE) 
print(result1, digits = 2)
plot(result1)


#--- Compare the incremental calculation with external calculated 
# costMatrix cm_add with the basic calculation from scratch.
cm_add <- cm(Q, newObs)
result2 <- idtw(Q = cm_add, C = "cm_add", ws = 15, newO = newObs, 
                gcm = base$gcm, dm = base$dm) 

c(result0$distance, result1$distance, result2$distance)