Calculate Contrasts of Arrays in Different Methods

Provides seven methods to baseline an array and calculate contrast.

Usage

baseline_array(x, along_dim, unit_dims = seq_along(dim(x))[-along_dim], ...)

# S3 method for class 'array'
baseline_array(
  x,
  along_dim,
  unit_dims = seq_along(dim(x))[-along_dim],
  method = c("percentage", "sqrt_percentage", "decibel", "zscore", "sqrt_zscore",
    "db_zscore", "subtract_mean"),
  baseline_indexpoints = NULL,
  baseline_subarray = NULL,
  ...
)

Arguments

x: array (tensor) to calculate contrast
along_dim: integer range from 1 to the maximum dimension of x. baseline along this dimension, this is usually the time dimension.
unit_dims: integer vector, baseline unit: see Details.
...: passed to other methods
method: character, baseline method; one of "percentage", "sqrt_percentage", "decibel", "zscore", "sqrt_zscore", "db_zscore", or "subtract_mean". See Details.
baseline_indexpoints: integer vector, which index points are counted into baseline window? Each index ranges from 1 to dim(x)[[along_dim]]. See Details.
baseline_subarray: sub-arrays that should be used to calculate baseline; default is NULL (automatically determined by baseline_indexpoints).

Value

Contrast array with the same dimension as x.

Details

Consider a scenario where we want to baseline a bunch of signals recorded from different locations. For each location, we record n sessions. For each session, the signal is further decomposed into frequency-time domain. In this case, we have the input x in the following form: $$session \times frequency \times time \times location$$ Now we want to calibrate signals for each session, frequency and location using the first 100 time points as baseline points, then the code will be baseline_array(x, along_dim=3, baseline_window=1:100, unit_dims=c(1,2,4)) along_dim=3 is dimension of time, in this case, it's the third dimension of x. baseline_indexpoints=1:100, meaning the first 100 time points are used to calculate baseline. unit_dims defines the unit signal. Its value c(1,2,4) means the unit signal is per session (first dimension), per frequency (second) and per location (fourth).

In some other cases, we might want to calculate baseline across frequencies then the unit signal is $frequency x time$, i.e. signals that share the same session and location also share the same baseline. In this case, we assign unit_dims=c(1,4).

There are seven baseline methods. They fit for different types of data. Denote $z$ is a unit signal and $z_0$ is its baseline slice. Then these baseline methods are:

"percentage": $$ \frac{z - \bar{z_{0}}}{\bar{z_{0}}} \times 100\% $$
"sqrt_percentage": $$ \frac{\sqrt{z} - \bar{\sqrt{z_{0}}}}{\bar{\sqrt{z_{0}}}} \times 100\% $$
"decibel": $$ 10 \times ( \log_{10}(z) - \bar{\log_{10}(z_{0})} ) $$
"zscore": $$ \frac{z-\bar{z_{0}}}{sd(z_{0})} $$
"sqrt_zscore": $$ \frac{\sqrt{z}-\bar{\sqrt{z_{0}}}}{sd(\sqrt{z_{0}})} $$
"db_zscore": Z-score applied in the decibel (10log10) domain: $$ \frac{10\log_{10}(z) - \bar{10\log_{10}(z_{0})}}{sd(10\log_{10}(z_{0}))} $$
"subtract_mean": Simple mean subtraction with no scaling: $$ z - \bar{z_{0}} $$

Examples


# Set ncores = 2 to comply to CRAN policy. Please don't run this line
ravetools_threads(n_threads = 2L)


library(ravetools)
set.seed(1)

# Generate sample data
dims = c(10,20,30,2)
x = array(rnorm(prod(dims))^2, dims)

# Set baseline window to be arbitrary 10 timepoints
baseline_window = sample(30, 10)

# ----- baseline percentage change ------

# Using base functions
re1 <- aperm(apply(x, c(1,2,4), function(y) {
  m <- mean(y[baseline_window])
  (y/m - 1) * 100
}), c(2,3,1,4))

# Using ravetools
re2 <- baseline_array(x, 3, c(1,2,4),
                      baseline_indexpoints = baseline_window,
                      method = 'percentage')

# Check different, should be very tiny (double precisions)
range(re2 - re1)
#> [1] -5.684342e-13  1.818989e-12

# \donttest{
# Check speed for large dataset, might take a while to profile

ravetools_threads(n_threads = -1)

dims <- c(200,20,300,2)
x <- array(rnorm(prod(dims))^2, dims)
# Set baseline window to be arbitrary 10 timepoints
baseline_window <- seq_len(100)
f1 <- function() {
  aperm(apply(x, c(1,2,4), function(y) {
    m <- mean(y[baseline_window])
    (y/m - 1) * 100
  }), c(2,3,1,4))
}
f2 <- function() {
  # equivalent as bl = x[,,baseline_window, ]
  #
  baseline_array(x, along_dim = 3,
                 baseline_indexpoints = baseline_window,
                 unit_dims = c(1,2,4), method = 'percentage')
}
range(f1() - f2())
#> [1] -1.818989e-12  2.273737e-12
microbenchmark::microbenchmark(f1(), f2(), times = 10L)
#> Unit: milliseconds
#>  expr       min         lq      mean   median        uq       max neval
#>  f1() 98.274976 100.607021 125.37235 106.6733 171.99038 184.49224    10
#>  f2()  7.996514   8.527884  10.15211  10.2730  11.46527  12.49923    10

# }