Pattern segmentation with `adept` package

The examples below are organized into suites. Examples within one suite share data simulation settings, for example: Examples 1: signal with no noise, same-length pattern.

Examples 1: signal with no noise, same-length pattern

Simulate data

We simulate a time-series x. We assume that

x is collected at a frequency of 100 Hz,
there is one shape of pattern present within x,
each pattern lasts 1 second,
there is no noise in the collected data.

true.pattern <- cos(seq(0, 2 * pi, length.out = 100))
x <- c(true.pattern[1], replicate(10, true.pattern[-1]))

data.frame(x = seq(0, 1, length.out = 100), y = true.pattern) %>%
  ggplot() + geom_line(aes(x = x, y = y), color = "red") + 
  theme_bw(base_size = 9) + labs(x = "Phase", y = "Value", title = "Pattern")

data.frame(x = seq(0, by = 0.01, length.out = length(x)), y = x) %>%
  ggplot() + geom_line(aes(x = x, y = y)) +  theme_bw(base_size = 9) + 
  labs(x = "Time [s]", y = "Value", title = "Time-series x")

Example 1(a): segment pattern

We use segmentPattern to segment pattern from a time-series x. 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.

out <- 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)
out
#>    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          1

`segmentPattern` output

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).

See ?segmentPattern for details.

Example 1(b): use `pattern.dur.seq` to modify a grid of pattern duration

We next generate a dense grid of potential pattern durations, including value 1.0 seconds used in the x simulation. A perfect match (sim_i = 1) between a time-series x and a template is obtained.

out <- 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)
out
#>    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 1(c): use `x.fs` to modify `x` time-series frequency

We use x.fs to modify x time-series frequency, expressed in a number of observations in seconds, and we adjust pattern.dur.seq accordingly. We observe that results are the same as in Example 1(b).

out <- segmentPattern(
  x = x,
  x.fs = 10,   ## Assumed data frequency of 10 observations per second
  template = true.pattern,
  pattern.dur.seq = c(0.9, 0.95, 1, 1.03, 1.1) * 10, ## Adjusted accordingly
  similarity.measure = "cor",
  compute.template.idx = TRUE)
out
#>    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

Examples 2: signal with no noise, pattern duration varies

Simulate data

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 present within x,
patterns have various duration,
there is no noise in the collected data.

set.seed(1)
true.pattern <- cos(seq(0, 2 * pi, length.out = 200))
x <- numeric()
for (vl in seq(70, 130, by = 10)){
  true.pattern.s <- approx(
    seq(0, 1, length.out = 200), 
    true.pattern, xout = seq(0, 1, length.out = vl))$y
  x <- c(x, true.pattern.s[-1])
  if (vl == 70) x <- c(true.pattern.s[1], x)
}

data.frame(x = seq(0, by = 0.01, length.out = length(x)), y = x) %>%
  ggplot() + geom_line(aes(x = x, y = y)) +  theme_bw(base_size = 9) + 
  labs(x = "Time [s]", y = "Value", title = "Time-series x")


## Function to plot segmentation results with ggplot2
library(ggplot2)
out.plot1 <- function(val, out, fs = 100){
  yrange <- c(-1, 1) * max(abs(val))
  y.h <- 0
  plt <- ggplot()
  for (i in 1:nrow(out)){
    tau1_i <- out[i, "tau_i"]
    tau2_i <- tau1_i + out[i, "T_i"] - 1
    tau1_i <- tau1_i/fs
    tau2_i <- tau2_i/fs
    plt <- 
      plt + 
      geom_vline(xintercept = tau1_i, color = "red") + 
      geom_vline(xintercept = tau2_i, color = "red") + 
      annotate(
        "rect",
        fill = "pink", 
        alpha = 0.3,
        xmin = tau1_i, 
        xmax = tau2_i, 
        ymin = yrange[1],
        ymax = yrange[2]
    )
  }
  geom_line.df <- data.frame(x = seq(0, by = 1/fs, length.out = length(val)), y = val)
  plt <- 
    plt + 
    geom_line(data = geom_line.df, 
              aes(x = x, y = y), 
              color = "black", 
              size = 0.3) + 
    theme_bw(base_size = 9) + 
    labs(x = "Time [s]", y = "Black line: x",
         title = "Black line: signal x\nRed vertical lines: start and end points of identified pattern occurrence\nRed shaded area: area corresponding to identified pattern occurrence")
  plot(plt)
}

Example 2(a): segment pattern

We use a dense grid of potential pattern duration, including all values used in the x simulation to again obtain the perfect match (sim_i = 1). In this example, the start and the end points of identified patterns are connected (see figure below).

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = true.pattern,
  pattern.dur.seq = 60:130 * 0.01,
  similarity.measure = "cor",
  compute.template.idx = TRUE)
out
#>   tau_i T_i sim_i template_i
#> 1     1  70     1          1
#> 2    70  80     1          1
#> 3   149  90     1          1
#> 4   238 100     1          1
#> 5   337 110     1          1
#> 6   446 120     1          1
#> 7   565 130     1          1

out.plot1(x, out)

Example 2(b): use `pattern.dur.seq` to modify a grid of pattern duration

Next, we use a less dense grid of potential pattern duration. We observe that perfect match (sim_i = 1) between a template and time-series x is no longer obtained. Note:

A less dense pattern.dur.seq grid yields a shorter time of method execution.
As explained later, when peak detection tuning is used, having a “maximally dense” pattern duration grid does not contribute much.

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = true.pattern,
  pattern.dur.seq = c(0.6, 0.9, 1.2),
  similarity.measure = "cor",
  compute.template.idx = TRUE)
out
#>   tau_i T_i     sim_i template_i
#> 1     6  60 0.9954038          1
#> 2    80  60 0.9887682          1
#> 3   149  90 1.0000000          1
#> 4   243  90 0.9976255          1
#> 5   347  90 0.9934059          1
#> 6   446 120 1.0000000          1
#> 7   570 120 0.9985549          1

out.plot1(x, out)

Example 2(c): use `similarity.measure` to modify similarity statistic

We use similarity.measure to modify the similarity statistic. We observe that sim_i values in the result data frame change and the segmentation results change slightly too. The explanation is that a change of similarity statistic takes an effect on ADEPT iterative maximization procedure.

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = true.pattern,
  pattern.dur.seq = c(0.6, 0.9, 1.2),
  similarity.measure = "cov",  ## Use covariance as a similarity statistic
  compute.template.idx = TRUE)
out
#>   tau_i T_i     sim_i template_i
#> 1     6  60 0.6440590          1
#> 2    65  90 0.7338618          1
#> 3   154  90 0.6711920          1
#> 4   243  90 0.6675955          1
#> 5   332 120 0.7320470          1
#> 6   451 120 0.6883499          1
#> 7   570 120 0.6786581          1

out.plot1(x, out)

Examples 3: signal with no noise, pattern duration and pattern shape vary

Simulate data

We simulate a time-series x. We assume that

x is collected at a frequency of 100 Hz,
there are two shapes of pattern present within x,
patterns have various duration,
there is no noise in the collected data.

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)
}

data.frame(x = seq(0, by = 0.01, length.out = length(x)), y = x) %>%
  ggplot() + geom_line(aes(x = x, y = y)) +  theme_bw(base_size = 9) + 
  labs(x = "Time [s]", y = "Value", title = "Time-series x")

plt1 <- 
  data.frame(x = seq(0, 1, length.out = length(true.pattern.1)), y = true.pattern.1) %>%
  ggplot() + geom_line(aes(x = x, y = y), color = "red") + 
  theme_bw(base_size = 9) + labs(x = "Phase", y = "Value", title = "Pattern 1") + 
  scale_y_continuous(limits = c(-1,1))
plt2 <- 
  data.frame(x = seq(0, 1, length.out = length(true.pattern.2)), y = true.pattern.2) %>%
  ggplot() + geom_line(aes(x = x, y = y), color = "red") + 
  theme_bw(base_size = 9) + labs(x = "Phase", y = "Value", title = "Pattern 2") + 
  scale_y_continuous(limits = c(-1,1))
plt1;plt2

Example 3(a): segment pattern

To segment pattern from x, we use a dense grid of potential pattern duration. We use a template object consisting of one of the two true patterns used in x simulation.

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = true.pattern.1, ## Template consisting of one out of two true patterns
  pattern.dur.seq = 60:130 * 0.01,
  similarity.measure = "cor",
  compute.template.idx = TRUE)
out
#>    tau_i T_i     sim_i template_i
#> 1      1  70 1.0000000          1
#> 2     70  70 0.9290889          1
#> 3    139  80 1.0000000          1
#> 4    218  80 0.9291321          1
#> 5    297  90 1.0000000          1
#> 6    386  90 0.9287727          1
#> 7    475 100 1.0000000          1
#> 8    574 100 0.9287316          1
#> 9    673 110 1.0000000          1
#> 10   782 110 0.9285349          1
#> 11   891 120 1.0000000          1
#> 12  1010 120 0.9284384          1
#> 13  1129 130 1.0000000          1
#> 14  1258 130 0.9283518          1

out.plot1(x, out)

Example 3(b): use `similarity.measure.thresh` to modify the threshold of minimal similarity

We use a similarity threshold to segment only those patterns for which similarity (here: correlation) is greater than 0.95. Note that using the threshold may substantially speed up method execution when working with a large data set.

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = true.pattern.1,
  pattern.dur.seq = 60:130 * 0.01,
  similarity.measure = "cor",
  similarity.measure.thresh = 0.95, 
  compute.template.idx = TRUE)
out
#>   tau_i T_i sim_i template_i
#> 1     1  70     1          1
#> 2   139  80     1          1
#> 3   297  90     1          1
#> 4   475 100     1          1
#> 5   673 110     1          1
#> 6   891 120     1          1
#> 7  1129 130     1          1

out.plot1(x, out)

Example 3(c): use multiple templates simultaneously

We next use a template object consisting of both true patterns used in x simulation. We observe that the index of a pattern template best matched to a pattern in the time-series x is 1 and 2 interchangeably.

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = list(true.pattern.1, true.pattern.2),
  pattern.dur.seq = 60:130 * 0.01,
  similarity.measure = "cor",
  compute.template.idx = TRUE)
out
#>    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

out.plot1(x, out)

Examples 4: signal with noise, pattern duration and pattern shape vary

Simulate data

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 present within x,
patterns have various duration,
there is noise in the collected data.

## Generate `x` as a noisy version of a time-series generated in *Examples 3*.  
set.seed(1)
x <- x + rnorm(length(x), sd = 0.5)

data.frame(x = seq(0, by = 0.01, length.out = length(x)), y = x) %>%
  ggplot() + geom_line(aes(x = x, y = y), size = 0.3) +  theme_bw(base_size = 9) + 
  labs(x = "Time [s]", y = "Value", title = "Time-series x")

Example 4(a): segment pattern

We use two templates simultaneously in segmentation.

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = list(true.pattern.1, true.pattern.2),
  pattern.dur.seq =  60:130 * 0.01,
  similarity.measure = "cor",
  compute.template.idx = TRUE)
out
#>    tau_i T_i     sim_i template_i
#> 1      4  63 0.8615665          1
#> 2     76  62 0.7351057          2
#> 3    137  84 0.7708233          1
#> 4    220  76 0.6768561          2
#> 5    295  92 0.8507212          1
#> 6    391  83 0.7404364          2
#> 7    473 106 0.8300020          1
#> 8    582  87 0.6515298          2
#> 9    668 118 0.8047385          1
#> 10   785 106 0.6958617          2
#> 11   890 123 0.7927484          1
#> 12  1015 113 0.6789908          1
#> 13  1129 130 0.7938183          1
#> 14  1265 123 0.7686607          2

out.plot1(x, out)

Example 4(b): use `x.adept.ma.W` to smooth `x` for similarity matrix computation

We use x.adept.ma.W to define a length of a smoothing window to smooth x for similarity matrix computation; x.adept.ma.W is expressed in seconds and the default is NULL (no smoothing applied).

Smoothing of a time-series x

Function windowSmooth allows observing the effect of smoothing for different values of smoothing window length W. W is expressed in seconds. Here, W = 0.1 seconds seems to be a plausible choice.

x.smoothed <- windowSmooth(x = x, x.fs = 100, W = 0.1)
  
data.frame(x = seq(0, by = 0.01, length.out = length(x.smoothed)), y = x.smoothed) %>%
  ggplot() + geom_line(aes(x = x, y = y)) +  theme_bw(base_size = 9) + 
  labs(x = "Time [s]", y = "Value", title = "Time-series x smoothed")
#> Warning: Removed 8 row(s) containing missing values (geom_path).

Use x.adept.ma.W = 0.1 and compare with results from Example 4(a). Observe that using a smoothed version of x in similarity matrix computation is pronounced in sim_i values in the output data frame, as well as in a slight change in tau_i and T_i values.

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = list(true.pattern.1, true.pattern.2),
  pattern.dur.seq =  60:130 * 0.01,
  similarity.measure = "cor",
  x.adept.ma.W = 0.1,
  compute.template.idx = TRUE)
out
#>    tau_i T_i     sim_i template_i
#> 1      4  63 0.9931174          1
#> 2     75  63 0.9683646          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

out.plot1(x, out)

Example 4(c): use fine-tune procedure for peak detection

We employ a fine-tuning procedure for stride identification.

Fine-tune procedure "maxima"

Fine-tune procedure "maxima" tunes preliminarily identified start and end of a pattern occurrence so as they correspond to local maxima of x found within neighborhoods of the preliminary locations.

The parameter finetune.maxima.nbh.W, expressed in seconds, defines a length of the two neighborhoods within which we search for local maxima.
Smoothed version of x may be used for local maxima search (as presented later).

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = list(true.pattern.1, true.pattern.2),
  pattern.dur.seq =  60:130 * 0.01,
  x.adept.ma.W = 0.1,
  finetune = "maxima",
  finetune.maxima.nbh.W = 0.3,
  compute.template.idx = TRUE)
out
#>    tau_i T_i     sim_i template_i
#> 1      4  67 0.7183698          1
#> 2     70  78 0.4250660          2
#> 3    147  60 0.6161509          1
#> 4    206  98 0.5407526          2
#> 5    303  78 0.7570218          1
#> 6    380  83 0.3459633          2
#> 7    462 117 0.7566122          1
#> 8    578  93 0.5045821          2
#> 9    670 105 0.7153597          1
#> 10   774 113 0.5760463          2
#> 11   893 128 0.6794591          1
#> 12  1020 112 0.4026054          1
#> 13  1131 123 0.6736391          1
#> 14  1253 125 0.5570096          2

out.plot1(x, out)

We observe that almost all identified pattern occurrence start/end points are hitting the time point which our eyes identify as local x maxima.

Example 4(d): use fine-tune procedure and smooth signal for peak detection

We smooth x for both similarity matrix computation (set x.adept.ma.W = 0.1) and for fine-tune peak detection procedure (set finetune.maxima.nbh.W = 0.3).

Here, W = 0.5 seconds seems to be a plausible choice for fine-tune peak detection procedure as it removes (“smooth together”) multiple local maxima of x, leaving out a single one.

x.smoothed.2 <- windowSmooth(x = x, x.fs = 100, W = 0.5)

data.frame(x = seq(0, by = 0.01, length.out = length(x.smoothed.2)), y = x.smoothed.2) %>%
  ggplot() + geom_line(aes(x = x, y = y)) +  theme_bw(base_size = 9) + 
  labs(x = "Time [s]", y = "Value", title = "Time-series x smoothed aggresively")
#> Warning: Removed 48 row(s) containing missing values (geom_path).

out <- segmentPattern(
  x = x,
  x.fs = 100,
  template = list(true.pattern.1, true.pattern.2),
  pattern.dur.seq =  60:130 * 0.01,
  similarity.measure = "cor",
  x.adept.ma.W = 0.1,  ## smoothing parameter for similarity matrix computation
  finetune = "maxima",  ## use fine-tuning
  finetune.maxima.ma.W = 0.5, ## smoothing parameter for peak detection in fine-tuning
  finetune.maxima.nbh.W = 0.3,  ## neighborhoods length in fine-tuning
  compute.template.idx = TRUE)
out
#>    tau_i T_i     sim_i template_i
#> 1      1  72 0.9931174          1
#> 2     72  71 0.9683646          2
#> 3    142  80 0.9688902          1
#> 4    221  78 0.9785617          2
#> 5    298  89 0.9802473          1
#> 6    386  90 0.9632459          2
#> 7    475 101 0.9855837          1
#> 8    575 101 0.9766671          2
#> 9    675 107 0.9887225          1
#> 10   781 118 0.9706882          2
#> 11   898 111 0.9734575          1
#> 12  1008 122 0.9703118          1
#> 13  1133 128 0.9652139          1
#> 14  1260 114 0.9593345          2

We plot segmentation results.

## Function to plot nice results visualization 
out.plot2 <- function(val, val.sm, out, fs = 100){
  yrange <- c(-1, 1) * max(abs(val))
  y.h <- 0
  geom_line.df1 <- data.frame(
    x = seq(0, by = 1/fs, length.out = length(val)), y = val)
  plt <- 
    ggplot() + 
    geom_line(data = geom_line.df1,
              aes(x = x, y = y), 
              color = "grey") 
  for (i in 1:nrow(out)){
    tau1_i <- out[i, "tau_i"]
    tau2_i <- tau1_i + out[i, "T_i"] - 1
    tau1_i <- tau1_i/fs
    tau2_i <- tau2_i/fs
    plt <- 
      plt + 
      geom_vline(xintercept = tau1_i, color = "red") + 
      geom_vline(xintercept = tau2_i, color = "red") + 
      annotate(
        "rect",
        fill = "pink", 
        alpha = 0.3,
        xmin = tau1_i, 
        xmax = tau2_i, 
        ymin = yrange[1],
        ymax = yrange[2]
    )
  }
  geom_line.df2 <- data.frame(
    x = seq(0, by = 1/fs, length.out = length(val.sm)), y = val.sm)
  plt <- 
    plt + 
    geom_line(data = geom_line.df2, 
              aes(x = x, y = y), 
              color = "black", size = 0.6, alpha = 0.8) + 
    theme_bw(base_size = 9) + 
    labs(x = "Time [s]", 
         y = "Black line: smoothed x", 
         title ="Light gray line: signal x\nBlack line: smoothed signal x\nRed vertical lines: start and end points of identified pattern occurrence\nRed shaded area: area corresponding to identified pattern occurrence")
  plot(plt)
}

out.plot2(x, windowSmooth(x = x, x.fs = 100, W = 0.5), out)
#> Warning: Removed 48 row(s) containing missing values (geom_path).

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.↩︎
Karas, M., Crainiceanu, C., Urbanek, J.: Walking strides segmentation with adept vignette to the ‘adept’ package.↩︎

Introduction to adept package

Marta Karas

Ciprian Crainiceanu

Jacek Urbanek

2021-01-31

Introduction

ADEPT method

Pattern template

Install and load `adept` package

Pattern segmentation with `adept` package

Examples 1: signal with no noise, same-length pattern

Simulate data

Example 1(a): segment pattern

`segmentPattern` output

Example 1(b): use `pattern.dur.seq` to modify a grid of pattern duration

Example 1(c): use `x.fs` to modify `x` time-series frequency

Examples 2: signal with no noise, pattern duration varies

Simulate data

Example 2(a): segment pattern

Example 2(b): use `pattern.dur.seq` to modify a grid of pattern duration

Example 2(c): use `similarity.measure` to modify similarity statistic

Examples 3: signal with no noise, pattern duration and pattern shape vary

Simulate data

Example 3(a): segment pattern

Example 3(b): use `similarity.measure.thresh` to modify the threshold of minimal similarity

Example 3(c): use multiple templates simultaneously

Examples 4: signal with noise, pattern duration and pattern shape vary

Simulate data

Example 4(a): segment pattern

Example 4(b): use `x.adept.ma.W` to smooth `x` for similarity matrix computation

Example 4(c): use fine-tune procedure for peak detection

Example 4(d): use fine-tune procedure and smooth signal for peak detection

References

Introduction to adept package

Marta Karas

Ciprian Crainiceanu

Jacek Urbanek

2021-01-31

Introduction

ADEPT method

Pattern template

Install and load adept package

Pattern segmentation with adept package

Examples 1: signal with no noise, same-length pattern

Simulate data

Example 1(a): segment pattern

segmentPattern output

Example 1(b): use pattern.dur.seq to modify a grid of pattern duration

Example 1(c): use x.fs to modify x time-series frequency

Examples 2: signal with no noise, pattern duration varies

Simulate data

Example 2(a): segment pattern

Example 2(b): use pattern.dur.seq to modify a grid of pattern duration

Example 2(c): use similarity.measure to modify similarity statistic

Examples 3: signal with no noise, pattern duration and pattern shape vary

Simulate data

Example 3(a): segment pattern

Example 3(b): use similarity.measure.thresh to modify the threshold of minimal similarity

Example 3(c): use multiple templates simultaneously

Examples 4: signal with noise, pattern duration and pattern shape vary

Simulate data

Example 4(a): segment pattern

Example 4(b): use x.adept.ma.W to smooth x for similarity matrix computation

Example 4(c): use fine-tune procedure for peak detection

Example 4(d): use fine-tune procedure and smooth signal for peak detection

References

Install and load `adept` package

Pattern segmentation with `adept` package

`segmentPattern` output

Example 1(b): use `pattern.dur.seq` to modify a grid of pattern duration

Example 1(c): use `x.fs` to modify `x` time-series frequency

Example 2(b): use `pattern.dur.seq` to modify a grid of pattern duration

Example 2(c): use `similarity.measure` to modify similarity statistic

Example 3(b): use `similarity.measure.thresh` to modify the threshold of minimal similarity

Example 4(b): use `x.adept.ma.W` to smooth `x` for similarity matrix computation