Skip to contents

Preprocessing Functions for Data Normalization and Standardization

Source: R/preprocess.R
preprocess.Rd

A collection of functions to preprocess numeric data, including standardization, L2 norm normalization, Min-Max scaling, centered-type normalization, interval-type normalization, extreme-value-based normalization, initial-value-based normalization, mean-based normalization, and negative-to-positive transformation. These functions transform a numeric vector to a standardized or normalized scale, suitable for various indicator types (positive, negative, centered, interval-based, or extreme-based).

Usage

standardize(x, center = TRUE, scale = TRUE)

normalize(x)

rescale(x, type = "+", a = 0, b = 1)

rescale_middle(x, m)

rescale_interval(x, a, b)

rescale_extreme(x, type = "+")

rescale_initial(x, type = "+")

rescale_mean(x)

to_positive(x, type = "minmax")

Arguments

x

Numeric vector to be preprocessed.

center

Logical or numeric scalar, passed to base::scale for centering (for standardize). Default is TRUE.

scale

Logical or numeric scalar, passed to base::scale for scaling (for standardize). Default is TRUE.

type

Character scalar specifying the transformation direction or method:

"+"

Positive direction (larger values are better, for rescale, rescale_extreme and rescale_initial).

"-"

Negative direction (smaller values are better, for rescale rescale_extreme and rescale_initial).

"minmax"

Min-max transformation (for to_positive).

"reciprocal"

Reciprocal transformation (for to_positive).

a

Numeric scalar, lower bound of the output range or optimal interval (for rescale and rescale_interval).

b

Numeric scalar, upper bound of the output range or optimal interval (for rescale and rescale_interval).

m

Numeric scalar, optimal value for centered-type normalization (for rescale_middle).

Value

A numeric vector of the same length as x, transformed as follows:

  • standardize: Standardized values (mean = 0, sd = 1).

  • normalize: L2 norm normalized values (Euclidean norm, unit length).

  • rescale: Min-Max scaled values in [a, b] (default 0, 1).

  • rescale_middle: Centered-type normalized values in 0, 1, where 1 indicates x = m.

  • rescale_interval: Interval-type normalized values in 0, 1, where 1 indicates x in [a, b].

  • rescale_extreme: Extreme-based normalized values using min(x)/x (positive) or x/max(x) (negative).

  • rescale_initial: Initial-based normalized values using x/x[1] or x[1]/x.

  • rescale_mean: Mean-based normalized values using x/mean(x).

  • to_positive: Transformed values converting negative indicators to positive using min-max or reciprocal transformation.

Details

These functions support various preprocessing needs in data analysis:

  • standardize: Applies Z-score standardization (mean = 0, sd = 1), ideal for equalizing variances or normally distributed data.

  • normalize: Scales the vector to unit length by dividing by its L2 (Euclidean) norm, useful for machine learning or similarity calculations.

  • rescale: Performs Min-Max scaling to a specified range (default 0, 1), supporting positive or negative indicators.

  • rescale_middle: Normalizes centered-type indicators, where values closer to an optimal value m are better, mapping to 0, 1.

  • rescale_interval: Normalizes interval-type indicators, where values within [a, b] are optimal, mapping to 0, 1.

  • rescale_extreme: Normalizes using extreme values: min(x)/x for positive indicators or x/max(x) for negative indicators, often used in grey relational analysis.

  • rescale_initial: Normalizes by dividing by the first value (x/x[1] or x[1]/x), commonly used in grey relational analysis.

  • rescale_mean: Normalizes by dividing by the mean (x/mean(x)), commonly used in grey relational analysis.

  • to_positive: Converts negative indicators to positive using either min-max (max(x) - x) or reciprocal (1/x) transformation.

Missing values (NA) are preserved in the output. For rescale_initial and rescale_mean, the initial value or mean must be non-zero, respectively.

Examples

# Standardization
x = c(4, 1, NA, 5, 8)
standardize(x)
#> [1] -0.1732051 -1.2124356         NA  0.1732051  1.2124356

# L2 norm normalization
normalize(x)
#> [1] 0.38851434 0.09712859         NA 0.48564293 0.77702869

# Min-Max normalization (positive direction)
rescale(x)                # Scale to [0, 1]
#> [1] 0.4285714 0.0000000        NA 0.5714286 1.0000000
rescale(x, type = "-", a = 0.002, b = 0.996)  # Reverse scaling
#> [1] 0.570 0.996    NA 0.428 0.002

# Negative-to-positive transformation
to_positive(x)                       # Min-max transformation
#> [1]  4  7 NA  3  0
to_positive(x, type = "reciprocal")  # Reciprocal transformation
#> [1] 0.250 1.000    NA 0.200 0.125

# Centered-type normalization
PH = 6:9
rescale_middle(PH, 7)
#> [1] 0.5 1.0 0.5 0.0

# Interval-type normalization
Temp = c(35.2, 35.8, 36.6, 37.1, 37.8, 38.4)
rescale_interval(Temp, 36, 37)
#> [1] 0.4285714 0.8571429 1.0000000 0.9285714 0.4285714 0.0000000

# Extreme-based normalization
rescale_extreme(x)         # min(x)/x
#> [1] 0.500 0.125    NA 0.625 1.000
rescale_extreme(x, "-")    # x/max(x)
#> [1] 0.250 1.000    NA 0.200 0.125

# Initial-based normalization
rescale_initial(x)
#> [1] 1.00 0.25   NA 1.25 2.00

# Mean-based normalization
rescale_mean(x)
#> [1] 0.8888889 0.2222222        NA 1.1111111 1.7777778