unit_normalization()

Introduction

When analyzing numeric data, either discrete or continuous variables, it is often necessary or at least practical to normalize the values in order to get a more comprehensible scale to analyze the data in, this is, transforming the values to a \(0 ≤ x ≤ 1\) scale, where \(0\) is the lowest value and \(1\) the highest in the distribution.

We included two functions to normalize and rescale numeric vectors, unit_normalization() and ab_range_normalization(), respectively. The former takes a numeric vector x as input and outputs a normalized version of the same distribution.

Example

x <- 5:45
x_scaled <- unit_normalization(x)
x_scaled

##  [1] 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275
## [13] 0.300 0.325 0.350 0.375 0.400 0.425 0.450 0.475 0.500 0.525 0.550 0.575
## [25] 0.600 0.625 0.650 0.675 0.700 0.725 0.750 0.775 0.800 0.825 0.850 0.875
## [37] 0.900 0.925 0.950 0.975 1.000

Similarly the ab_range_normalization() function can be used to rescale a numeric vector x to an arbitrary range between a and b. E.g.:

x <- 5:45
a <- 1
b <- 100
x_scaled <- ab_range_normalization(x, a, b)
x_scaled

##  [1]   1.000   3.475   5.950   8.425  10.900  13.375  15.850  18.325  20.800
## [10]  23.275  25.750  28.225  30.700  33.175  35.650  38.125  40.600  43.075
## [19]  45.550  48.025  50.500  52.975  55.450  57.925  60.400  62.875  65.350
## [28]  67.825  70.300  72.775  75.250  77.725  80.200  82.675  85.150  87.625
## [37]  90.100  92.575  95.050  97.525 100.000

x <- rnorm(1000)
hist(x, main = "Original Distribution")

x_scaled <- unit_normalization(x)
hist(x_scaled, main = "Normalized Distribution")