Added Normalization and Standardization Algorithms (TheAlgorithms#2192)

* Added Standardization and Normalization algorithms with built-in stats

* Implement ndigits for rounding

Co-authored-by: Christian Clauss <[email protected]>

Author: danmurphy1217

machine_learning/data_transformations.py

@@ -0,0 +1,62 @@
+"""
+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:
+    """
+    Returns 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:
+    """
+    Returns 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]