# Minkowski distance

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Minkowski distance is a distance/ similarity measurement between two points in the normed vector space (N dimensional real space) and is a generalization of the Euclidean distance and the Manhattan distance.

### Minkowski distance in N-D space

In a N dimensional space, a point is represented as (x1, x2, ..., xN).

Consider two points P1 and P2:

```
P1: (X1, X2, ..., XN)
P2: (Y1, Y2, ..., YN)
```

Then, the Minkowski distance between P1 and P2 is given as:

$$ \sqrt[p]{{(x1-y1)}^p\ +\ {(x2-y2)}^p\ +\ ...\ +\ {(xN-yN)}^p}

$$

### Euclidean distance from Minkowski distance

When **p = 2**, Minkowshi distance is same as Euclidean distance.

### Manhattan distance from Minkowski distance

When **p = 1**, Minkowshi distance is same as Manhattan distance.

### Visualize

Unit circles (**path represents points with same Minkowshi distance**) with various values of p (Minkowski distance):

### Applications

Applications of Minkowshi Distance are:

Euclidean distance and Manhattan distance are same as Minkowshi Distance, hence, the applications of the previous two distance metrics are applications of Minkowshi Distance.