SciPy

scipy.spatial.distance.jaccard

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

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.

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