Z-Standardisation

This function transform the input data via z-standardisation. See the Details section below for further information.

Usage

zStandardisation(x, robust = FALSE, by = c("rows", "cols"), na.rm = TRUE)

Arguments

x: a (named) numerical vector or a matrix features-by-samples.
robust: logical, whether to compute a robust z-standardisation.
by: character string, indicating whether to compute the standardisation by rows or columns of x. It is used when x is a matrix.
na.rm: logical, whether to remove NA values before the computation.

Value

A numerical vector or matrix, containing the output of the transformation.

Details

The z-standardisation (or z-score normalisation) is a method for transforming the data so that it has a mean of zero and a standard deviation of one. It is computed as:

$$z(x) = \frac{x - \mu}{\sigma}$$

where $\mu$ and $\sigma$ are the mean and standard deviation of the population, respectively.

Since z-scores can be affected by unusually large or small data values, we can also compute a more robust modified version as:

$$z(x) = \frac{x - \mathrm{median}}{\mathrm{MAD}}$$

where $\mathrm{MAD}$ is the median absolute deviation of the population.

Author

Alessandro Barberis

Examples

#set seed for reproducibility
set.seed(seed = 5381L)

#x is a vector
x = sample(x = -10:10, size = 10)
#Standard z-score transformation
zStandardisation(x)
#>  [1] -1.41475949 -0.23579325  0.64843143 -0.08842247  0.20631909 -1.12001793
#>  [7] -0.97264715  1.53265611  1.38528533  0.05894831
#Robust z-score transformation
zStandardisation(x=x,robust=TRUE)
#>  [1] -1.16502949 -0.18395203  0.55185608 -0.06131734  0.18395203 -0.91976013
#>  [7] -0.79712544  1.28766418  1.16502949  0.06131734

#x is a matrix
#Define row/col size
nr = 20
nc = 10

#Create input matrix
x = matrix(
 data = stats::runif(n = nr*nc, min = 0, max = 1000),
 nrow = nr,
 ncol = nc,
 dimnames = list(
   paste0("g",seq(nr)),
   paste0("S",seq(nc))
 )
)
#Standardise the features
zStandardisation(x=x,by="rows")
#>             S1         S2         S3          S4         S5         S6
#> g1   0.2624428  1.3983881 -1.2758636  0.39909284 -0.9867582 -1.2788577
#> g2   0.6523120 -0.7437961  0.2621862  1.19488521 -0.7478923  1.4920740
#> g3   0.5847869  1.2768872 -0.5757830 -0.03202588 -1.2299604 -0.7867920
#> g4  -0.5617825  0.5872960 -0.8746203  2.08259570  0.6642502 -0.7662553
#> g5   1.1165266  0.9268175  0.0958604 -0.41205776  0.7865037 -1.4131087
#> g6  -0.4444489 -1.3039473 -0.2113584  0.29304713 -1.1270272  0.5192974
#> g7   1.5895720  0.7187668 -0.0182766 -1.29355304 -0.4509851 -1.3759829
#> g8   0.1819454 -1.4511335 -1.3353409  1.36179270  0.7494688 -0.8841805
#> g9  -0.9635881  0.2449203  0.1162947 -1.23515323  1.3458378  1.5182848
#> g10 -0.2687879 -1.2355109  1.4876072  1.07157927  0.2922403 -0.5319888
#> g11 -1.3776246 -0.4602545  0.6368065  1.13916871 -1.3658621  0.5293702
#> g12  1.1815417  1.1183107 -0.6148590 -2.12087803  0.3811298  0.1477492
#> g13 -0.2007323 -1.1445889  1.4490767 -0.88046583  0.9096155  0.5500329
#> g14 -0.9547043 -1.2967449  0.8282594  0.98531315  1.4846790 -1.1695634
#> g15  0.9961759  0.1775545 -1.0283102  1.14208651 -1.8502588 -0.8952862
#> g16 -1.4807871 -0.7475768 -0.1406406  0.21670002  1.3159851  1.0663156
#> g17  0.9903776 -1.1880350  0.1330936  0.25051540  1.1031101 -0.7374619
#> g18  1.1567776  0.1638224 -0.9447115  0.03774972 -0.6517946  1.1554756
#> g19  0.7391937 -1.6999425  0.1864886  1.21838844 -0.1822111 -1.5290585
#> g20  0.7186636  0.5768870 -1.0179943  0.07429993 -0.7470519  1.1552963
#>              S7         S8          S9        S10
#> g1   0.64955437  0.4577074 -0.78184676  1.1561407
#> g2   0.85198985 -1.0994598 -0.74358737 -1.1187117
#> g3  -0.47076522  1.7788413  0.44457901 -0.9897679
#> g4  -0.80413002  0.5319365  0.24495524 -1.1042455
#> g5   0.69212634 -1.3897165  0.69529523 -1.0982469
#> g6   0.26783845  0.7982746 -0.80877350  2.0170977
#> g7  -0.78457318  0.6317676 -0.09497461  1.0782390
#> g8  -0.28603707  0.5548376 -0.10741738  1.2160648
#> g9  -1.18502405  0.8449683 -0.31169904 -0.3748415
#> g10  0.12817198 -0.7571421 -1.33093955  1.1447705
#> g11  1.24381157 -1.0926921  0.27111483  0.4761615
#> g12 -0.20350400  0.9338379 -0.24185057 -0.5814778
#> g13 -0.39212572  1.1614591  0.01120639 -1.4634778
#> g14  0.84917935 -0.1948104  0.10677267 -0.6383805
#> g15  0.74855161  0.2320067 -0.33622947  0.8137094
#> g16  0.07359999  0.9911408 -1.50959375  0.2148567
#> g17 -1.92223436  1.0004672  0.15252811  0.2176392
#> g18 -1.24658113  1.2860775  0.33259622 -1.2894118
#> g19  0.36658272  0.4797967 -0.57071152  0.9914735
#> g20 -1.42887574  1.3811833  0.35547671 -1.0678849