Minkowski distance is a metric in a normed vector space. Minkowski distance is used for distance similarity of vector. Given two or more vectors, find distance similarity of these vectors.
Mainly, Minkowski distance is applied in machine learning to find out distance similarity.
Examples :
Input : vector1 = 0 2 3 4
vector2 = 2, 4, 3, 7
p = 3
Output : distance1 = 3.5033
Input : vector1 = 1, 4, 7, 12, 23
vector2 = 2, 5, 6, 10, 20
p = 2
Output : distance2 = 4.0
Note : Here distance1 and distance2 are almost same so it will be in same near region.
Python3
# Python3 program to find Minkowski distance# import math libraryfrom math import *from decimal import Decimal# Function distance between two points # and calculate distance value to given# root value(p is root value)def p_root(value, root): root_value = 1 / float(root) return round (Decimal(value) ** Decimal(root_value), 3)def minkowski_distance(x, y, p_value): # pass the p_root function to calculate # all the value of vector parallelly return (p_root(sum(pow(abs(a-b), p_value) for a, b in zip(x, y)), p_value))# Driver Codevector1 = [0, 2, 3, 4]vector2 = [2, 4, 3, 7]p = 3print(minkowski_distance(vector1, vector2, p)) |
Output :
3.503
Time Complexity : O(N)
Auxiliary Space : O(N)
Reference :
https://en.wikipedia.org/wiki/Minkowski_distance
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