Provides five methods to baseline an array and calculate contrast.
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)
#> [1] -4.547474e-13 1.818989e-12
# 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)
}