dipsaus (version 0.3.1)

baseline_array: Calculate Contrasts of Arrays in Different Methods

Description

Provides five methods to baseline an array and calculate contrast.

Usage

baseline_array(
  x,
  along_dim,
  baseline_indexpoints,
  unit_dims = seq_along(dim(x))[-along_dim],
  method = c("percentage", "sqrt_percentage", "decibel", "zscore", "sqrt_zscore",
    "subtract_mean")
)

Value

Contrast array with the same dimension as x.

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.

baseline_indexpoints

integer vector, which index points are counted into baseline window? Each index ranges from 1 to dim(x)[[along_dim]]. See Details.

unit_dims

integer vector, baseline unit: see Details.

method

character, baseline method options are: "percentage", "sqrt_percentage", "decibel", "zscore", and "sqrt_zscore"

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: $$session x frequency x time x location$$ 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 $$baseline_array(x, along_dim=3, 1:100, unit_dims=c(1,2,4))$$ 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 five baseline methods. They fit for different types of data. Denote \(z\) is an unit signal, \(z_0\) 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"

$$ \frac{\sqrt{z}-\bar{\sqrt{z_{0}}}}{sd(\sqrt{z_{0}})} $$

Examples

library(dipsaus)
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 dipsaus
re2 <- baseline_array(x, 3, baseline_window, c(1,2,4),
                      method = 'percentage')

# Check different, should be very tiny (double precisions)
range(re2 - re1)

# Check speed for large dataset
if(interactive()){
  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 = 'sqrt_percentage')
  }
  microbenchmark::microbenchmark(f1(), f2(), times = 3L)
}