Minkowski Distance Metric

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]\displaystyle{ d((0,0),(3,4))= 7 }[/math].
  • L2 Distance(Euclidean Distance), [math]\displaystyle{ 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.

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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 p₁ at (x₁, y₁) and p₂ at (x₂, y₂), it is (|x₁ - x₂|^m + |y₁ - y₂|^m)^1/m.

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