Data Transformations

machine_learning/data_transformations.py

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+"""
+    Normalization Wikipedia: https://en.wikipedia.org/wiki/Normalization
+    Standardization Wikipedia: https://en.wikipedia.org/wiki/Standardization
+
+    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 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
+"""
+
+
+def normalization(data : list) -> list:
+    """
+    Returns a normalized list of values
+    @params: data, a list of values to normalize
+    @returns: a list of normalized values (rounded to 3 decimals)
+    @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), 3) for x in data]
+
+
+def standardization(data : list) -> list:
+    """
+    Returns a standardized list of values
+    @params: data, a list of values to standardize
+    @returns: a list of standardized values (rounded to 3 decimals)
+    @examples:
+    >>> standardization([2, 7, 10, 20, 30, 50])
+    [-1.095, -0.788, -0.604, 0.01, 0.624, 1.852]
+
+    >>> standardization([5, 10, 15, 20, 25])
+    [-1.414, -0.707, 0.0, 0.707, 1.414]
+    """
+    # variables for calculation
+    mu = mean(data)
+    sigma = stdDeviation(data)
+
+    # standardize data
+    return [round((x - mu) / (sigma), 3) for x in data]
+
+
+def mean(data : list) -> float:
+    """
+    Helper function that returns the mean of a list of values
+    @params: data, a list of values
+    @returns: a float representing the mean (rounded to 3 decimals)
+    @examples:
+    >>> mean([2, 7, 10, 20, 30, 50])
+    19.833
+
+    >>> mean([5, 10, 15, 20, 25])
+    15.0
+    """
+    return round(sum(data) / len(data), 3)
+
+
+def stdDeviation(data : list) -> float:
+    """
+    Helper function that returns the standard deviation of a list of values
+    @params: data, a list of values
+    @returns: a float representing the standard deviation (rounded to 3 values)
+    @examples:
+    >>> stdDeviation([2, 7, 10, 20, 30, 50])
+    16.293
+
+    >>> stdDeviation([5, 10, 15, 20, 25])
+    7.071
+    """
+    x_mean = mean(data)
+    sum_squared_diff = sum([(x - x_mean)**2 for x in data])
+    return round(((sum_squared_diff) / len(data))**.5, 3)