[data mining] task 1: distance calculation

subject

Given two tuples （22,1,42,10） and （20,0,36,8） The object of expression

（a） Calculate the Euclidean distance between these two objects ;

（b） Calculate the Manhattan distance between the two objects ;

（c） Use q=3, Calculate the Minkowski distance between the two objects

（d） Calculates the supremum distance between two objects

Create objects

a = (22, 1, 42, 10)
b = (20, 0, 36, 8)

Euclidean distance

import numpy as np


def euclidean(x, y):
    return np.sqrt(sum((x[i] - y[i]) ** 2 for i in range(len(x))))

euclidean(a, b)

6.708203932499369

Manhattan distance

def manhattan(x, y):
    return sum(np.abs(x[i] - y[i]) for i in range(len(x)))

manhattan(a, b)

11

Minkowski distance

def minkowski(x, y, p):
    return sum(np.abs(x[i] - y[i]) ** p for i in range(len(x))) ** (1 / p)

minkowski(a, b, 3)

6.153449493663682

Supremum distance

def Supremum(x, y):
    return np.abs(max(x) - max(y))

Supremum(a, b)

6