# Q2¶

Q2 index.

Q2 index is presented by Dom 2 as a normalized version of the original Q0 index. This index has a range of $$(0, 1]$$ 1, with greater scores being representing more preferred clustering.

The Q2 index can be calculated as follows 1

$Q2(C, K) = \frac{\frac{1}{n} \sum_{c=1}^{|C|} \log \binom{h(c) + |C| - 1}{|C| - 1} }{Q_0(C, K)}$

where $$C$$ is the target partition, $$K$$ is the hypothesized partition and $$h(k)$$ is the size of cluster $$k$$.

Due to the complexity of the formula, this metric is one order of magnitude slower than its original version (Q0) and most other implemented metrics.

## Parameters¶

• cm – defaults to None

This parameter allows sharing the same confusion matrix between multiple metrics. Sharing a confusion matrix reduces the amount of storage and computation time.

## Attributes¶

• bigger_is_better

Indicate if a high value is better than a low one or not.

• requires_labels

Indicates if labels are required, rather than probabilities.

• sample_correction

• works_with_weights

Indicate whether the model takes into consideration the effect of sample weights

## Examples¶

>>> from river import metrics

>>> y_true = [1, 1, 2, 2, 3, 3]
>>> y_pred = [1, 1, 1, 2, 2, 2]

>>> metric = metrics.Q2()

>>> for yt, yp in zip(y_true, y_pred):
...     print(metric.update(yt, yp).get())
0.0
0.0
0.0
0.4545045563529578
0.39923396953448914
0.3979343306829813

>>> metric
Q2: 0.397934


## Methods¶

binomial_coeff
clone

Return a fresh estimator with the same parameters.

The clone has the same parameters but has not been updated with any data. This works by looking at the parameters from the class signature. Each parameter is either - recursively cloned if it's a River classes. - deep-copied via copy.deepcopy if not. If the calling object is stochastic (i.e. it accepts a seed parameter) and has not been seeded, then the clone will not be idempotent. Indeed, this method's purpose if simply to return a new instance with the same input parameters.

get

Return the current value of the metric.

is_better_than
revert

Revert the metric.

Parameters

• y_true
• y_pred
• sample_weight – defaults to 1.0
• correction – defaults to None
update

Update the metric.

Parameters

• y_true
• y_pred
• sample_weight – defaults to 1.0
works_with

Indicates whether or not a metric can work with a given model.

Parameters

• model (river.base.estimator.Estimator)

## References¶

1. Andrew Rosenberg and Julia Hirschberg (2007). V-Measure: A conditional entropy-based external cluster evaluation measure. Proceedings of the 2007 Joing Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, pp. 410 - 420, Prague, June 2007. URL: https://www.aclweb.org/anthology/D07-1043.pdf.

2. Byron E. Dom. 2001. An information-theoretic external cluster-validity measure. Technical Report RJ10219, IBM, October.