IncDTW (version 1.1.4.4)

lowerbound: lowerbound

Description

Calculate the lowerbound for the DTW distance measure in linear time.

Usage

lowerbound(C, ws, scale = c("z", "01", "none"),
           dist_method = c("norm1", "norm2", "norm2_square"), 
           Q = NULL, tube = NULL)
                     
lowerbound_tube(Q, ws, scale = c("z", "01", "none"))

Arguments

Q

vector or matrix, the query time series

C

vector or matrix, the query time series

dist_method

distance method, one of ("norm1", "norm2", "norm2_square")

scale

either "none", so no scaling is performed, or one of ("z", "01") to scale both Q and C. Also see dtw

ws

see dtw

tube

tube for lower bounding. "tube" can be the output from lowerbound_tube(). If tube = NULL, then Q must not be NULL, so that tube can be defined. If the tube is passed as argument to lowerbound(), then it is necessary that the scale parameter in the lowerbound() call is identical to the scaling method applied on Q before calculating the tube.

Value

lowerbound distance measure that is proven to be smaller than the DTW distance measure

Details

Lower Bounding: The following methods are implemented:

• LB_Keogh for univariate time series (Keogh et al. 2005)

• LB_MV for multivariate time series with the dist_method = "norm2_square", (Rath et al. 2002)

• Adjusted for different distance methods "norm1" and "norm2", inspired by (Rath et al. 2002).

References

• Keogh, Eamonn, and Chotirat Ann Ratanamahatana. "Exact indexing of dynamic time warping." Knowledge and information systems 7.3 (2005): 358-386.

• Rath, Toni M., and R. Manmatha. "Lower-bounding of dynamic time warping distances for multivariate time series." University of Massachusetts Amherst Technical Report MM 40 (2002).

• Sakurai, Yasushi, Christos Faloutsos, and Masashi Yamamuro. "Stream monitoring under the time warping distance." Data Engineering, 2007. ICDE 2007. IEEE 23rd International Conference on. IEEE, 2007.

Examples

# NOT RUN {
# }
# NOT RUN {
#--- Univariate time series Q and C
ws <- sample(2:40, size = 1)
dist_method <- "norm1"
N <- 50
N <- 50
Q <- cumsum(rnorm(N))
C <- cumsum(rnorm(N))
Q.z <- IncDTW::scale(Q, "z")
C.z <- IncDTW::scale(C, "z")

lb.z <- lowerbound(C = C.z, ws = ws, scale ="none", dist_method = dist_method, Q = Q.z)
lb <- lowerbound(C = C, ws = ws, scale ="z", dist_method = dist_method, Q = Q)
d1 <- dtw2vec(Q = Q.z, C = C.z, step_pattern = "symmetric1", 
  dist_method = dist_method, ws = ws)$distance
d2 <- dtw2vec(Q = Q.z, C = C.z, step_pattern = "symmetric2", 
  dist_method = dist_method, ws = ws)$distance

c(lb, lb.z, d1, d2)


#--- with pre-calculated tube
ws <- sample(2:40, size = 1)
dist_method <- "norm1"
N <- 50
N <- 50
Q <- cumsum(rnorm(N))
C <- cumsum(rnorm(N))
Q.z <- IncDTW::scale(Q, "z")
C.z <- IncDTW::scale(C, "z")

tube <- lowerbound_tube(Q, ws, scale = "z")

lb.z <- lowerbound(C = C.z, ws = ws, scale ="none", dist_method = dist_method, tube = tube)
lb <- lowerbound(C = C, ws = ws, scale ="z", dist_method = dist_method, tube = tube)
d1 <- dtw2vec(Q = Q.z, C = C.z, step_pattern = "symmetric1", 
  dist_method = dist_method, ws = ws)$distance
d2 <- dtw2vec(Q = Q.z, C = C.z, step_pattern = "symmetric2", 
  dist_method = dist_method, ws = ws)$distance

c(lb, lb.z, d1, d2)



#--- Multivariate time series Q and C
ws <- sample(2:40, size = 1)
dist_method <- sample(c("norm1", "norm2", "norm2_square"), size = 1)
N <- 50
Q <- matrix(cumsum(rnorm(N * 3)), ncol = 3)
C <- matrix(cumsum(rnorm(N * 3)), ncol = 3)
Q.z <- IncDTW::scale(Q, "z")
C.z <- IncDTW::scale(C, "z")

lb.z <- lowerbound(C = C.z, ws = ws, scale ="none", dist_method = dist_method, Q = Q.z)
lb <- lowerbound(C = C, ws = ws, scale ="z", dist_method = dist_method, Q = Q)
d1 <- dtw2vec(Q = Q.z, C = C.z, step_pattern = "symmetric1", 
  dist_method = dist_method, ws = ws)$distance
d2 <- dtw2vec(Q = Q.z, C = C.z, step_pattern = "symmetric2", 
  dist_method = dist_method, ws = ws)$distance

c(lb, lb.z, d1, d2)

# }