anomaly_detection.py

#!/usr/bin/env python3
# Auhor Dario Clavijo 2021

import math


def mean(L):
    """mean or average of all values in list"""

    tmp = sum(L) * 1.0
    l = len(L)
    return tmp / l


avg = mean


def stddev(X):
    """standar deviation calculaion of all values in the list"""

    l = len(X)

    def F(X):
        x = mean(X)
        s = 0
        for i in range(0, l):
            s += (X[i] - x) ** 2
        return s

    return math.sqrt((1.0 / l) * F(X))


def MAD(X):
    """Median Absolute deviation calculaion of all values in the list"""

    l = len(X)

    def F(X):
        x = mean(X)
        s = 0
        for i in range(0, l):
            s += abs(X[i] - x)
        return s

    return (1.0 / l) * F(X)


def bounds(X):
    """Upper and lower bounds"""

    SD = stddev(X)
    m = mean(X)
    return m - SD, SD + m


def simple_anonaly_detection(X):
    """A simple check if a value in a list is outside the bounds
    It sould return tuples of (index,value)"""

    B = bounds(X)
    for i in range(0, len(X)):
        if X[i] < B[0] or X[i] > B[1]:
            yield (i, X[i])


def zvalue(X):
    """zvalue calculation"""

    SD = stddev(X)
    m = mean(X)
    for i in range(0, len(X)):
        yield (X[i] - m) / SD


def zvalue_anomaly_detection(X, treshold=[-1, 1]):
    """zvalue anomaly detection
    It sould return tuples of (index,value,score)"""

    Z = list(zvalue(X))
    for i in range(0, len(X)):
        if Z[i] < treshold[0] or Z[i] > treshold[1]:
            yield (i, X[i], Z[i])


def MAD_anomaly_detection(X, treshold=1.5):
    """Median absoute value anomaly detection
    It should return a tuple of (index,value,score)"""

    M = MAD(X)
    m = mean(X)
    for i in range(0, len(X)):
        v = abs(X[i] - m) / M
        if v > treshold:
            yield (i, X[i], v)


def test():
    """
    Expected output:
    Series: [2, 3, 5, 2, 3, 12, 5, 3, 4]
    Mean: 4.333333333333333
    StdDev: 2.9059326290271157
    Bounds: (1.4274007043062173, 7.239265962360449)
    simple anomaly detection: [(5, 12)]
    zvalues: [-0.8029550685469661, -0.45883146774112343, 0.22941573387056186, -0.8029550685469661, -0.45883146774112343, 2.6382809395114606, 0.22941573387056186, -0.45883146774112343, -0.11470786693528078]
    zvalue anomaly detection: [(5, 12, 2.6382809395114606)]
    MAD anomaly detection: [(5, 12, 3.8333333333333344)]
    """
    S = [2, 3, 5, 2, 3, 12, 5, 3, 4]
    print(("Series:", S))
    print(("Mean:", mean(S)))
    print(("StdDev:", stddev(S)))
    print(("Bounds:", bounds(S)))
    print(("simple anomaly detection:", list(simple_anonaly_detection(S))))
    print(("zvalues:", list(zvalue(S))))
    print(("zvalue anomaly detection:", list(zvalue_anomaly_detection(S))))
    print(("MAD anomaly detection:", list(MAD_anomaly_detection(S))))


if __name__ == "__main__":
    test()