# scipy.spatial.distance.jaccard

scipy.spatial.distance.jaccard(u, v, w=None)

  Compute the Jaccard-Needham dissimilarity between two boolean 1-D arrays.

  The Jaccard-Needham dissimilarity between 1-D boolean arrays u and v, is defined as

  \[\frac{c_{TF} + c_{FT}} {c_{TT} + c_{FT} + c_{TF}}\]

  where \(c_{ij}\) is the number of occurrences of \(\mathtt{u[k]} = i\) and \(\mathtt{v[k]} = j\) for \(k < n\).

  Parameters:
    u(N,) array_like, bool

      Input array.

    v(N,) array_like, bool

      Input array.

    w(N,) array_like, optional

      The weights for each value in u and v. Default is None, which gives each value a weight of 1.0

  Returns:
    jaccard double

      The Jaccard distance between vectors u and v.

  Notes

  When both u and v lead to a 0/0 division i.e. there is no overlap between the items in the vectors the returned distance is 0. See the Wikipedia page on the Jaccard index [1], and this paper [2].

  Changed in version 1.2.0: Previously, when u and v lead to a 0/0 division, the function would return NaN. This was changed to return 0 instead.

  References

  [1]

  https://en.wikipedia.org/wiki/Jaccard_index

  [2]

  S. Kosub, “A note on the triangle inequality for the Jaccard distance”, 2016, arXiv:1612.02696

  Examples

      >>> from scipy.spatial import distance
      >>> distance.jaccard([1, 0, 0], [0, 1, 0])
      1.0
      >>> distance.jaccard([1, 0, 0], [1, 1, 0])
      0.5
      >>> distance.jaccard([1, 0, 0], [1, 2, 0])
      0.5
      >>> distance.jaccard([1, 0, 0], [1, 1, 1])
      0.66666666666666663