# Minkowski Distance Metric

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A Minkowski Distance Metric is a vector distance metric for Euclidean points.

**AKA:**Ln Distance.**Context:**- It weighs all dimensions equally.

**Example(s):**- L1 Distance, [math]d((0,0),(3,4))= 7[/math].
- L2 Distance(Euclidean Distance), [math]d((0,0),(3,4))= 5[/math].

**Counter-Example(s):**- A Jaccard Distance Measure, for sets = 1 minus Jaccard similarity.
- A Cosine Distance Measure, based on the angle between vectors from the origin to the points in question.
- An Edit Distance Measure, based on the operations to change one object into another.
- A Hamming Distance Measure, based on the number of positions in which bit vectors differ.

**See:**Vector Distance Function, Euclidean Distance.

## References

### 2009

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Minkowski_distance
- The Minkowski distance is a metric on Euclidean space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance.

### 2008

- http://xlinux.nist.gov/dads//HTML/lmdistance.html
- QUOTE: The generalized distance between two points. In a plane with point p
_{1}at (x_{1}, y_{1}) and p_{2}at (x_{2}, y_{2}), it is (|x_{1}- x_{2}|^{m}+ |y_{1}- y_{2}|^{m})^{1/m}.

- QUOTE: The generalized distance between two points. In a plane with point p