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Adaptive Empirical Pattern Transformation
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README.md

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Overview

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.

Installation

Install adept package from GitHub.

# install.packages("devtools")
devtools::install_github("martakarass/adept")

Example 1

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    297 103 0.9992482          1
#> 5    399  95 0.9987941          1
#> 6    495 103 0.9992482          1
#> 7    597  95 0.9987941          1
#> 8    697  95 0.9987941          1
#> 9    792 103 0.9992482          1
#> 10   894  95 0.9987941          1

The segmentation result is a data frame, where each row describes one identified pattern occurrence:

  • tau_i - index of x where pattern starts,
  • T_i - pattern duration, expressed in x vector length,
  • sim_i - similarity between a template and x,
  • template_i - index of a template best matched to a time-series x (here: one template was used, hence all template_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          1

Example 2

We 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          2

We 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          2

We 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          2

Vignettes

Vignettes are available to better demonstrate package methods usgae.

  1. Vignette Introduction to adept package introduces ADEPT algorithm and demonstrates the usage of segmentPattern function which implements ADEPT approach. Here, we focus on examples with simulated data.

  2. Vignette Walking strides segmentation with adept provides an example of segmentation of walking strides (two consecutive steps) in sub-second accelerometry data with adept package. The exemplary dataset is a part of the adeptdata package. 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:

    1. with the use of stride templates that were pre-computed based on data from an external study (attached to adeptdata package),
    2. by deriving new stride templates in a semi-manual manner.

References

  1. 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.
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