r"""
.. _sec-randindex:
Rand index
====================================================================================================
Description
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The Rand index measures the similarity between two segmentations.
Formally, for a signal :math:`\{y_t\}_t` and a segmentation :math:`\mathcal{S}`, denote by :math:`A` the associated membership matrix:
.. math::
\mathcal{A}_{ij} &= 1 \text{ if both samples } y_i \text{ and } y_j \text{ are in the same segment according to } \mathcal{S} \\
&= 0 \quad\text{otherwise}
Let :math:`\hat{\mathcal{S}}` be the estimated segmentation and :math:`\hat{A}`, the associated membership matrix.
Then the Rand index is equal to
.. math::
\frac{\sum_{i<j} \mathbb{1}(A_{ij} = \hat{A}_{ij})}{T(T-1)/2}
where :math:`T` is the number of samples.
It has a value between 0 and 1: 0 indicates that the two segmentations do not agree on any pair of points and 1 indicates that the two segmentations are exactly the same.
.. figure:: /images/randindex.png
:scale: 50 %
:alt: Schematic view of the RandIndex metric
Schematic example: true segmentation in gray, estimated segmentation in dashed lines and their associated membership matrices. Rand index is equal to 1 minus the gray area.
Usage
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Start with the usual imports and create two segmentations to compare.
.. code-block:: python
from ruptures.metrics import randindex
bkps1, bkps2 = [100, 200, 500], [105, 115, 350, 400, 500]
print(randindex(bkps1, bkps2))
Code explanation
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.. autofunction:: ruptures.metrics.randindex.randindex
"""
from ruptures.metrics import hamming
[docs]def randindex(bkps1, bkps2):
"""Rand index for two partitions. The result is scaled to be within 0 and 1.
Args:
bkps1 (list): list of the last index of each regime.
bkps2 (list): list of the last index of each regime.
Returns:
float: Rand index
"""
return 1 - hamming(bkps1, bkps2)