The adept package implements ADaptive Empirical Pattern Transformation
(ADEPT) method[1] for pattern segmentation from a time-series. ADEPT
is optimized to perform fast, accurate walking strides segmentation from
high-density data collected with a wearable accelerometer during
walking. The method was validated using data collected with sensors worn
at left wrist, left hip and both ankles.
Install adept package from GitHub.
# install.packages("devtools")
devtools::install_github("martakarass/adept")We simulate a time-series x. We assume that x is collected at a
frequency of 100 Hz, there is one shape of a pattern within x, each
pattern lasts 1 second, and there is no noise in collected data.
true.pattern <- cos(seq(0, 2 * pi, length.out = 100))
x <- c(true.pattern[1], replicate(10, true.pattern[-1]))
par(mfrow = c(1,2), cex = 1)
plot(true.pattern, type = "l", xlab = "", ylab = "", main = "Pattern")
plot(x, type = "l", xlab = "", ylab = "", main = "Time-series x")
We segment pattern from data. We assume that a perfect template is
available. We use a grid of potential pattern durations of {0.9, 0.95,
1.03, 1.1} seconds; the grid is imperfect in a sense it does not contain
the duration of the true pattern used in x simulation.
library(adept)
segmentPattern(
x = x,
x.fs = 100,
template = true.pattern,
pattern.dur.seq = c(0.9, 0.95, 1.03, 1.1),
similarity.measure = "cor",
compute.template.idx = TRUE)
#> tau_i T_i sim_i template_i
#> 1 4 95 0.9987941 1
#> 2 98 103 0.9992482 1
#> 3 202 95 0.9987941 1
#> 4 296 103 0.9992482 1
#> 5 400 95 0.9987941 1
#> 6 494 103 0.9992482 1
#> 7 598 95 0.9987941 1
#> 8 692 103 0.9992482 1
#> 9 796 95 0.9987941 1
#> 10 895 95 0.9987941 1The segmentation result is a data frame, where each row describes one identified pattern occurrence:
tau_i- index ofxwhere pattern starts,T_i- pattern duration, expressed inxvector length,sim_i- similarity between a template andx,template_i- index of a template best matched to a time-seriesx(here: one template was used, hence alltemplate_i’s equal 1).
We then assume a grid of potential pattern durations which contains the
duration of the true pattern used in data simulation. A perfect match
(sim_i = 1) between a time-series x and a template is obtained.
segmentPattern(
x = x,
x.fs = 100,
template = true.pattern,
pattern.dur.seq = c(0.9, 0.95, 1, 1.03, 1.1),
similarity.measure = "cor",
compute.template.idx = TRUE)
#> tau_i T_i sim_i template_i
#> 1 1 100 1 1
#> 2 100 100 1 1
#> 3 199 100 1 1
#> 4 298 100 1 1
#> 5 397 100 1 1
#> 6 496 100 1 1
#> 7 595 100 1 1
#> 8 694 100 1 1
#> 9 793 100 1 1
#> 10 892 100 1 1We simulate a time-series x. We assume that x is collected at a
frequency of 100 Hz, there are two shapes of a pattern within x,
patterns have various duration, and there is no noise in collected data.
Then, we generate x2 as a noisy version of x.
true.pattern.1 <- cos(seq(0, 2 * pi, length.out = 200))
true.pattern.2 <- true.pattern.1
true.pattern.2[70:130] <- 2 * true.pattern.2[min(70:130)] + abs(true.pattern.2[70:130])
x <- numeric()
for (vl in seq(70, 130, by = 10)){
true.pattern.1.s <- approx(
seq(0, 1, length.out = 200),
true.pattern.1, xout = seq(0, 1, length.out = vl))$y
true.pattern.2.s <- approx(
seq(0, 1, length.out = 200),
true.pattern.2, xout = seq(0, 1, length.out = vl))$y
x <- c(x, true.pattern.1.s[-1], true.pattern.2.s[-1])
if (vl == 70) x <- c(true.pattern.1.s[1], x)
}
set.seed(1)
x2 <- x + rnorm(length(x), sd = 0.5)
par(mfrow = c(1,2), cex = 1)
plot(true.pattern.1, type = "l", xlab = "", ylab = "", main = "Pattern 1")
plot(true.pattern.2, type = "l", xlab = "", ylab = "", main = "Pattern 2")
par(mfrow = c(1,1), cex = 1)
plot(x, type = "l", xlab = "", ylab = "", main = "Time-series x")
plot(x2, type = "l", xlab = "", ylab = "", main = "Time-series x2")
We segment x. We assume a perfect grid of potential pattern duration,
{0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3} seconds.
segmentPattern(
x = x,
x.fs = 100,
template = list(true.pattern.1, true.pattern.2),
pattern.dur.seq = seq(0.7, 1.3, by = 0.1),
similarity.measure = "cor",
compute.template.idx = TRUE)
#> tau_i T_i sim_i template_i
#> 1 1 70 1 1
#> 2 70 70 1 2
#> 3 139 80 1 1
#> 4 218 80 1 2
#> 5 297 90 1 1
#> 6 386 90 1 2
#> 7 475 100 1 1
#> 8 574 100 1 2
#> 9 673 110 1 1
#> 10 782 110 1 2
#> 11 891 120 1 1
#> 12 1010 120 1 2
#> 13 1129 130 1 1
#> 14 1258 130 1 2We segment x2.
segmentPattern(
x = x2,
x.fs = 100,
template = list(true.pattern.1, true.pattern.2),
pattern.dur.seq = seq(0.7, 1.3, by = 0.1),
similarity.measure = "cor",
compute.template.idx = TRUE)
#> tau_i T_i sim_i template_i
#> 1 1 70 0.8585451 1
#> 2 138 80 0.7624002 1
#> 3 218 80 0.7025577 2
#> 4 297 90 0.8500864 1
#> 5 390 80 0.6931671 2
#> 6 469 110 0.8286013 1
#> 7 579 90 0.6373846 2
#> 8 668 120 0.8027177 1
#> 9 787 100 0.6666713 2
#> 10 888 130 0.7894766 1
#> 11 1017 110 0.6599280 1
#> 12 1129 130 0.7938183 1
#> 13 1267 120 0.7655408 2We now use x.adept.ma.W argument to smooth x2 before similarity
matrix computation in the segmentation procedure (see ?segmentPattern
for details). We also assume a more dense grid of potential pattern
duration. We observe that sim_i values obtained are higher than in the
previous segmentation case.
par(mfrow = c(1,1), cex = 1)
plot(windowSmooth(x = x2, x.fs = 100, W = 0.1),
type = "l", xlab = "", ylab = "", main = "Time-series x2 smoothed")
segmentPattern(
x = x2,
x.fs = 100,
template = list(true.pattern.1, true.pattern.2),
pattern.dur.seq = 70:130 * 0.01,
similarity.measure = "cor",
x.adept.ma.W = 0.1,
compute.template.idx = TRUE)
#> tau_i T_i sim_i template_i
#> 1 1 70 0.9865778 1
#> 2 70 70 0.9533684 2
#> 3 139 79 0.9683054 1
#> 4 217 80 0.9748040 2
#> 5 296 94 0.9802473 1
#> 6 391 82 0.9462213 2
#> 7 472 106 0.9855837 1
#> 8 578 93 0.9608881 2
#> 9 670 115 0.9887225 1
#> 10 784 107 0.9562694 2
#> 11 896 113 0.9734575 1
#> 12 1008 127 0.9703118 1
#> 13 1134 116 0.9606235 1
#> 14 1266 122 0.9593345 2Vignettes are available to better demonstrate package methods usage.
-
Vignette Introduction to adept package introduces ADEPT algorithm and demonstrates the usage of
segmentPatternfunction which implements ADEPT approach. Here, we focus on examples with simulated data. -
Vignette Walking strides segmentation with adept provides an example of segmentation of walking strides (two consecutive steps) in sub-second accelerometry data with
adeptpackage. The exemplary dataset is a part of theadeptdatapackage. We demonstrate that ADEPT can be used to perform automatic and precise walking stride segmentation from data collected during a combination of running, walking and resting exercises. We introduce how to segment data:- with the use of stride templates that were pre-computed based on
data from an external study (attached to
adeptdatapackage), - by deriving new stride templates in a semi-manual manner.
- with the use of stride templates that were pre-computed based on
data from an external study (attached to
- Karas, M., Straczkiewicz, M., Fadel, W., Harezlak, J., Crainiceanu, C., Urbanek, J.K. Adaptive empirical pattern transformation (ADEPT) with application to walking stride segmentation, Submitted to Biostatistics, 2018.