scipy.spatial.distance.

jensenshannon#

scipy.spatial.distance.jensenshannon(p, q, base=None, *, axis=<object object>, keepdims=False)[source]#

Compute the Jensen-Shannon distance (metric) between two 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

basedouble, 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.

axisint, optional

Axis along which the Jensen-Shannon distances are computed. The default is 0.

Added in version 1.7.0.

Deprecated since version 2.0.0: The default value for axis is changing to -1 in v2.2. That means the distances will be computed along the last axis. For 1-D inputs the result does not change.

keepdimsbool, optional

If this is set to True, the reduced axes are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. Default is False.

Added in version 1.7.0.

Returns:
jsdouble or ndarray

The Jensen-Shannon distances between p and q along the axis.

Notes

Added in version 1.2.0.

Array API Standard Support

jensenshannon has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library

CPU

GPU

NumPy

✅

n/a

CuPy

n/a

✅

PyTorch

✅

✅

JAX

✅

✅

Dask

✅

n/a

See Support for the array API standard for more information.

Examples

>>> from scipy.spatial import distance
>>> import numpy as np
>>> 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
>>> a = np.array([[1, 2, 3, 4],
...               [5, 6, 7, 8],
...               [9, 10, 11, 12]])
>>> b = np.array([[13, 14, 15, 16],
...               [17, 18, 19, 20],
...               [21, 22, 23, 24]])
>>> distance.jensenshannon(a, b, axis=0)
array([0.1954288, 0.1447697, 0.1138377, 0.0927636])
>>> distance.jensenshannon(a, b, axis=1)
array([0.1402339, 0.0399106, 0.0201815])
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