scipy.spatial.distance.jensenshannon

scipy.spatial.distance.jensenshannon(p, q, base=None)

Compute the Jensen-Shannon distance (metric) between two 1-D probability arrays. This is the square root of the Jensen-Shannon divergence.

The Jensen-Shannon distance between two probability vectors p and q is defined as,

\[\sqrt{\frac{D(p \parallel m) + D(q \parallel m)}{2}}\]

where \(m\) is the pointwise mean of \(p\) and \(q\) and \(D\) is the Kullback-Leibler divergence.

This routine will normalize p and q if they don’t sum to 1.0.

Parameters:

p : (N,) array_like

left probability vector

q : (N,) array_like

right probability vector

base : double, optional

the base of the logarithm used to compute the output if not given, then the routine uses the default base of scipy.stats.entropy.

Returns:

js : double

The Jensen-Shannon distance between p and q

.. versionadded:: 1.2.0

Examples

>>> from scipy.spatial import distance
>>> distance.jensenshannon([1.0, 0.0, 0.0], [0.0, 1.0, 0.0], 2.0)
1.0
>>> distance.jensenshannon([1.0, 0.0], [0.5, 0.5])
0.46450140402245893
>>> distance.jensenshannon([1.0, 0.0, 0.0], [1.0, 0.0, 0.0])
0.0