Invert feature scaling

Question

In my dataset I have a binary Target (0 or 1) variable, and 8 features: nchar, rtc, Tmean, week_day, hour, ntags, nlinks and nex. week_day is a factor while the others are numeric. I built a decision tree classifier, but my question concerns the feature scaling:

library(caTools)
set.seed(123)
split = sample.split(dataset$Target, SplitRatio = 0.75)
training_set = subset(dataset, split == TRUE)
test_set = subset(dataset, split == FALSE)
# Feature Scaling
training_set[-c(2,4)] = scale(training_set[-c(2,4)])
test_set[-c(2,4)] = scale(test_set[-c(2,4)])

The model returns that Tmean=-0.057 and ntags=2 are two splitting points. How can I recover the original value of these two features, that is, that assumed by the variables before the rescaling operation performed by scale().

Answer 1

If the data were scaled with scale, the following function unscale might be of help solving the question.
The original vector and the unscaled one are all.equal but not identical, due to floating-point precision.

unscale <- function(x){
  xbar <- attr(x, "scaled:center")
  se <- attr(x, "scaled:scale")
  if(is.null(xbar) & is.null(se)){
    x
  } else {
    y <- t(se * t(x) + xbar)
    attr(y, "scaled:center") <- NULL
    attr(y, "scaled:scale") <- NULL
    y
  }
}

set.seed(2020)
A <- matrix(rnorm(120, sd = 16), ncol = 5)
s <- scale(A)
identical(A, unscale(s))  #FALSE

zeros <- as.vector(A - unscale(s))
all.equal(zeros, rep(0, 120))  
#[1] TRUE

The function also works with data.frames but the class of its output is "matrix", not the original "data.frame". This is the result of scale's output.

B <- as.data.frame(matrix(A, ncol = 5))
s2 <- scale(B)
B2 <- as.data.frame(unscale(s2))
all.equal(B, B2)
#[1] TRUE

But the right way of scaling/unscaling an object with a dim attribute, such as a data.frame, is vector by vector. This can be done with a lapply loop, for instance.

s3 <- B
s3[] <- lapply(B, scale)

B3 <- s3
B3[] <- lapply(s3, unscale)
all(B - B3 < .Machine$double.eps^0.5)
#[1] TRUE