# feature_scaling: Feature Scaling In jjb: Balamuta Miscellaneous

## Description

Scale features in a datasets.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 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

## 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

## Value

A numeric vector.

## Feature Rescaling

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}

## Feature Standardization

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}

## Feature Normalization

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

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 # 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) 

jjb documentation built on Jan. 8, 2020, 5:07 p.m.