distances.py

'''
    Python3 program to calculate different distances between two vectors
    Author: Sadip Giri (sadipgiri@bennington.edu)
    Date: 10th May, 2019
'''

import numpy as np

def euclidean_dist(vector_1, vector_2):
    '''
        Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. 
        With this distance, Euclidean space becomes a metric space. The associated norm is called the Euclidean norm.
        Euclidean distance is also known as L2 norm.

        Optimization Options (for faster calculation):
            1. don't need to calculate square root since we can compare between squares
            2. instead of squaring: use vector transpose operator:
                -> euclidean_distance(x, y) = (x − y)T (x − y) where, T is transpose
    '''

    # initial distance calculation:
    # return np.sqrt(np.sum(np.square(vector_1 - vector_2)))

    # use vector transpose operator: (x − y)T (x − y) where, T is transpose
    # return np.dot(np.transpose(vector_1 - vector_2), vector_1 - vector_2)

    # just using sum of squares between vectors
    return np.sum(np.square(vector_1 - vector_2))

def manhattan_dist(vector_1, vector_2):
    '''
        The Manhattan distance, also known as Levenshtein distance or L1 norm, is ∑ |xi − yi|
    '''
    return np.sum(np.abs(vector_2 - vector_1))

def cosine_dist(vector_1, vector_2, normalized = 1):
    '''
        Cosine similarity is a measure of similarity between two non-zero vectors of an inner product space that measures the cosine of the angle between them.
        Mathematically, it's dot product between two vectors after normalization (converting two vectors into their respective unit vectors)
    '''
    if normalized == 1:
        return np.dot(vector_1, vector_2)
    return np.dot(vector_1, vector_2)/(magnitude(vector_1) * magnitude(vector_2))

def magnitude(vector):
    return np.sqrt(np.sum(np.square(vector)))

if __name__ == '__main__':
    v1 = np.array([i for i in range(100)])
    v2 = np.array([i*2 for i in range(100)])
    print(euclidean_dist(v1,v2))
    print(manhattan_dist(v1, v2))
    print(cosine_dist(v1, v2, normalized=2))