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jaccard(u, v, w=None)

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 $k < n$ .

Notes

When both u and v lead to a :None:None:`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 , and this paper .

versionchanged

Previously, when :None:None:`u` and :None:None:`v` lead to a :None:None:`0/0` division, the function would return NaN. This was changed to return 0 instead.

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.

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

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
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.spatial.distance.jaccard

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GitHub : /scipy/spatial/distance.py#735
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