## Definition Edit

Given a distance function between elements of a universe set , the **Minkowski distance** is a function defined as

where is a positive integer.

## Examples Edit

- For and , .
- For the difference and (Manhattan distance), .
- For the difference and (Euclidean distance), .

## Normalization Edit

If is normalized, is possible to define the **Minkowski similarity** as

## Examples Edit

- If , and , .

## Variations Edit

- If is a number set, is the difference and we have the Manhattan distance.
- If is a number set, is the difference and we have the Euclidean distance.
- If is a number set, is the difference and we have the Tchebychev distance.
- If , and we have Hamming similarity.

## Aplications Edit

- Comparing vectors in a metric space (usually vectors in ).
- Comparing vectors of boolean features.