Feature Scaling — feature

Scale features in a datasets.

Usage

feature_rescale(x, x_min = NULL, x_max = NULL)

feature_derescale(x_rescaled, x_min, x_max)

feature_norm(x, x_norm = NULL)

feature_denorm(x_norm_std, x_norm = NULL)

feature_standardize(x, x_mean = NULL, x_sd = NULL)

feature_destandardize(x_std, x_mean = NULL, x_sd = NULL)

Arguments

x: Numeric values
x_min: Minimum non-normalized numeric value
x_max: Maximum non-normalized numeric value
x_rescaled: Rescaled values of x.
x_norm: Euclidean norm of x
x_norm_std: Euclidean vector of normalized x values.
x_mean: Mean of x values
x_sd: Standard Deviation of x values
x_std: Z-transformed x values

Value

A numeric vector.

Details

The following functions provide a means to either scale features or to descale the features and return them to normal. These functions are ideal for working with optimizers.

Feature Scale	Feature Descale
feature_rescale	feature_derescale
feature_norm	feature_denorm
feature_standardize	feature_destandardize

Feature Rescaling

Convert the original data $x$ to $x_{scaled}$:

$$x[scaled] = (x-x[min])/(x[max]-x[min])$$

To move from the rescaled value $x_{scaled}$ to the original value $x$ use:

$$x = x[scaled] * (x[max] - x[min]) + x[min]$$

Feature Standardization

Convert the original data $x$ to $x_{std}$:

$$x[std] = (x-avg[x])/(sigma[x])$$

To move from the standardized value $x_{std}$ to the original value $x$ use:

$$x = x[std] * sigma[x] + avg[x]$$

Feature Normalization

Convert the original data $x$ to $x_{norm}$:

$$x[norm] = (x)/||x||$$

To move from the normalized value $x_{norm}$ to the original value $x$ use:

$$x = x[norm] * ||x||$$

Author

James Balamuta

Examples


# Rescaling Features
temperatures = c(94.2, 88.1, 32, 0)

temp_min = min(temperatures)
temp_max = max(temperatures)

temperatures_norm   = feature_rescale(temp_min, temp_max)
temperatures_denorm = feature_derescale(temperatures_norm, temp_min, temp_max)

all.equal(temperatures, temperatures_denorm)
#> [1] "Numeric: lengths (4, 1) differ"
 
# Norming Features
x = 1:10

x_norm = sqrt(sum(x^2))

x_norm_std = feature_norm(x, x_norm)

x_recover = feature_denorm(x_norm_std, x_norm)
all.equal(x, x_recover)
#> [1] TRUE

# Standardizing Features
x      = 1:10

x_mean = mean(x)
x_sd   = sd(x)

x_std  = feature_standardize(x, x_mean, x_sd)
x_recovery = feature_destandardize(x, x_mean, x_sd)

all.equal(x, x_recovery)
#> [1] "Mean relative difference: 3.02765"