feature_scaling: Feature Scaling
In jjb: Balamuta Miscellaneous

Description Usage Arguments Details Value Feature Rescaling Feature Standardization Feature Normalization Author(s) Examples

Scale features in a datasets.

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)

`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

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

A numeric vector.

Convert the original data x to x_{scaled}:

x_{scaled} = \frac{(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}

Convert the original data x to x_{std}:

x_{std} = \frac{(x-\bar{x})}{σ_{x}}

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

x = x_{std} σ_{x} + \bar{x}

Convert the original data x to x_{norm}:

x_{norm} = \frac{x}{≤ft\| x \right\|}

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

x = x_{norm} ≤ft\| x \right\|

James Balamuta

# 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)
 
# 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)

# 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)