(Robust) Scaling and Centering

Centers and scales the columns of a numeric matrix. The conventional version uses mean and standard deviation, the robust one median and MAD (see Details).

Usage

scaleX(x, center = TRUE, scale = TRUE, robust = FALSE, na.rm = TRUE)

Arguments

x

a numeric matrix-like object

center

logical scalar or numeric vector. If TRUE, the column means (or medians, for robust = TRUE) are subtracted; if FALSE, no centering is performed. Alternatively, a numeric vector of length ncol(x) supplies the values to subtract directly.

scale

logical scalar or numeric vector. If TRUE, the columns are divided by their standard deviation (or MAD, for robust = TRUE); if FALSE, no scaling is performed. Alternatively, a numeric vector of length ncol(x) supplies the divisors directly.

robust

logical; whether to standardize by median and MAD rather than by mean and standard deviation

na.rm

logical; if TRUE (default), missing values are omitted when the column centers and scales are computed. Ignored for whichever of center and scale is given as a numeric vector. Missing entries of x itself always remain missing in the result.

Value

the centered and scaled matrix. The numeric centerings and scalings used (if any) are returned as attributes "scaled:center" and "scaled:scale".

Details

The R base function base::scale() centers each column by its mean and divides by the root mean square of the centered column, which for centered data is the standard deviation. Both are sensitive to outliers: a single extreme value moves the mean and inflates the standard deviation, so the remaining observations are compressed towards zero.

If robust is set to TRUE the column median takes the place of the mean and the median absolute deviation (stats::mad()) that of the standard deviation. Both have a breakdown point of 50 percent, so the standardization reflects the bulk of the data rather than its extremes, and genuine outliers keep large scores instead of being pulled in.

Whichever is chosen, center and scale accept either a logical flag or a numeric vector of values to use directly, in which case that vector must have one entry per column of x, as in base::scale().

The two versions differ in one further respect. The MAD is invariant to location shifts, so for robust = TRUE the returned "scaled:scale" is the same whether or not the columns were centered first, and does not depend on center. The root mean square is not invariant; for robust = FALSE it is computed after centering, matching base::scale(), which is what makes it equal the standard deviation when center is TRUE and not otherwise.

A zero or non-finite scaling factor can produce undefined or non-finite results. scaleX emits a warning naming the affected columns rather than failing, since the result may still be usable when those columns are subsequently dropped.

See also

base::scale(), base::sweep(), stats::mad(), rangeX(), bedrock::linScale()

Other transform: boxCox(), boxCoxLambda(), logSt(), yeoJohnson()

Examples

x <- bedrock::Pizza$temperature

# robust standardization is far less affected by the extreme values
plot(scaleX(x, robust = TRUE), col = "black", pch = 16, cex = 0.4,
     ylab = "standardized temperature")
points(scaleX(x), col = "red", pch = 16, cex = 0.4)
legend("topright", legend = c("robust (median/MAD)", "conventional"),
       col = c("black", "red"), pch = 16, bty = "n")


# the centerings and scalings used are recoverable
z <- scaleX(cbind(a = c(1, 2, 3, 4, 100), b = c(10, 20, 30, 40, 50)))
attr(z, "scaled:center")
#>  a  b 
#> 22 30 
attr(z, "scaled:scale")
#>        a        b 
#> 43.61766 15.81139 

# compared to the robust version, which the extreme value barely moves
attr(scaleX(cbind(a = c(1, 2, 3, 4, 100)), robust = TRUE), "scaled:scale")
#>      a 
#> 1.4826 

# supplying the values directly, as base::scale allows
scaleX(matrix(1:6, ncol = 2), center = c(0, 0), scale = c(1, 2))
#>      [,1] [,2]
#> [1,]    1  2.0
#> [2,]    2  2.5
#> [3,]    3  3.0
#> attr(,"scaled:center")
#> [1] 0 0
#> attr(,"scaled:scale")
#> [1] 1 2