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68 lines
2.8 KiB
Python
68 lines
2.8 KiB
Python
"""
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Normalization.
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Wikipedia: https://en.wikipedia.org/wiki/Normalization
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Normalization is the process of converting numerical data to a standard range of values.
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This range is typically between [0, 1] or [-1, 1]. The equation for normalization is
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x_norm = (x - x_min)/(x_max - x_min) where x_norm is the normalized value, x is the
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value, x_min is the minimum value within the column or list of data, and x_max is the
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maximum value within the column or list of data. Normalization is used to speed up the
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training of data and put all of the data on a similar scale. This is useful because
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variance in the range of values of a dataset can heavily impact optimization
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(particularly Gradient Descent).
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Standardization Wikipedia: https://en.wikipedia.org/wiki/Standardization
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Standardization is the process of converting numerical data to a normally distributed
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range of values. This range will have a mean of 0 and standard deviation of 1. This is
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also known as z-score normalization. The equation for standardization is
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x_std = (x - mu)/(sigma) where mu is the mean of the column or list of values and sigma
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is the standard deviation of the column or list of values.
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Choosing between Normalization & Standardization is more of an art of a science, but it
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is often recommended to run experiments with both to see which performs better.
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Additionally, a few rules of thumb are:
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1. gaussian (normal) distributions work better with standardization
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2. non-gaussian (non-normal) distributions work better with normalization
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3. If a column or list of values has extreme values / outliers, use standardization
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"""
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from statistics import mean, stdev
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def normalization(data: list, ndigits: int = 3) -> list:
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"""
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Return a normalized list of values.
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@params: data, a list of values to normalize
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@returns: a list of normalized values (rounded to ndigits decimal places)
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@examples:
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>>> normalization([2, 7, 10, 20, 30, 50])
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[0.0, 0.104, 0.167, 0.375, 0.583, 1.0]
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>>> normalization([5, 10, 15, 20, 25])
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[0.0, 0.25, 0.5, 0.75, 1.0]
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"""
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# variables for calculation
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x_min = min(data)
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x_max = max(data)
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# normalize data
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return [round((x - x_min) / (x_max - x_min), ndigits) for x in data]
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def standardization(data: list, ndigits: int = 3) -> list:
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"""
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Return a standardized list of values.
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@params: data, a list of values to standardize
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@returns: a list of standardized values (rounded to ndigits decimal places)
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@examples:
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>>> standardization([2, 7, 10, 20, 30, 50])
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[-0.999, -0.719, -0.551, 0.009, 0.57, 1.69]
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>>> standardization([5, 10, 15, 20, 25])
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[-1.265, -0.632, 0.0, 0.632, 1.265]
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"""
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# variables for calculation
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mu = mean(data)
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sigma = stdev(data)
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# standardize data
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return [round((x - mu) / (sigma), ndigits) for x in data]
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