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"""

Normalization.

Wikipedia: https://en.wikipedia.org/wiki/Normalization

Normalization is the process of converting numerical data to a standard range of values.

This range is typically between [0, 1] or [-1, 1]. The equation for normalization is

x_norm = (x - x_min)/(x_max - x_min) where x_norm is the normalized value, x is the

value, x_min is the minimum value within the column or list of data, and x_max is the

maximum value within the column or list of data. Normalization is used to speed up the

training of data and put all of the data on a similar scale. This is useful because

variance in the range of values of a dataset can heavily impact optimization

(particularly Gradient Descent).

Standardization Wikipedia: https://en.wikipedia.org/wiki/Standardization

Standardization is the process of converting numerical data to a normally distributed

range of values. This range will have a mean of 0 and standard deviation of 1. This is

also known as z-score normalization. The equation for standardization is

x_std = (x - mu)/(sigma) where mu is the mean of the column or list of values and sigma

is the standard deviation of the column or list of values.

Choosing between Normalization & Standardization is more of an art of a science, but it

is often recommended to run experiments with both to see which performs better.

Additionally, a few rules of thumb are:

1. gaussian (normal) distributions work better with standardization

2. non-gaussian (non-normal) distributions work better with normalization

3. If a column or list of values has extreme values / outliers, use standardization

"""

from statistics import mean, stdev

def normalization(data: list, ndigits: int = 3) -> list:

"""

Return a normalized list of values.

@params: data, a list of values to normalize

@returns: a list of normalized values (rounded to ndigits decimal places)

@examples:

>>> normalization([2, 7, 10, 20, 30, 50])

[0.0, 0.104, 0.167, 0.375, 0.583, 1.0]

>>> normalization([5, 10, 15, 20, 25])

[0.0, 0.25, 0.5, 0.75, 1.0]

"""

# variables for calculation

x_min = min(data)

x_max = max(data)

# normalize data

return [round((x - x_min) / (x_max - x_min), ndigits) for x in data]

def standardization(data: list, ndigits: int = 3) -> list:

"""

Return a standardized list of values.

@params: data, a list of values to standardize

@returns: a list of standardized values (rounded to ndigits decimal places)

@examples:

>>> standardization([2, 7, 10, 20, 30, 50])

[-0.999, -0.719, -0.551, 0.009, 0.57, 1.69]

>>> standardization([5, 10, 15, 20, 25])

[-1.265, -0.632, 0.0, 0.632, 1.265]

"""

# variables for calculation

mu = mean(data)

sigma = stdev(data)

# standardize data

return [round((x - mu) / (sigma), ndigits) for x in data]

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