# Xu¶

Xu Index

Xu Index is among the most complicated sum-of-squares based metrics 1. It is calculated based on the Sum-of-Squares Within Clusters (SSW), total number of points, number of clusters, and the dimension of the cluserting problem.

The lower the Xu index, the higher the clustering quality is.

## Attributes¶

• bigger_is_better

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

## Examples¶

>>> from river import cluster
>>> from river import stream
>>> from river import metrics

>>> X = [
...     [1, 2],
...     [1, 4],
...     [1, 0],
...     [4, 2],
...     [4, 4],
...     [4, 0],
...     [-2, 2],
...     [-2, 4],
...     [-2, 0]
... ]

>>> k_means = cluster.KMeans(n_clusters=3, halflife=0.4, sigma=3, seed=0)
>>> metric = metrics.cluster.Xu()

>>> for x, _ in stream.iter_array(X):
...     k_means = k_means.learn_one(x)
...     y_pred = k_means.predict_one(x)
...     metric = metric.update(x, y_pred, k_means.centers)

>>> metric
Xu: -2.73215


## Methods¶

get

Return the current value of the metric.

revert

Revert the metric.

Parameters

• x
• y_pred
• centers
• sample_weight – defaults to 1.0
update

Update the metric.

Parameters

• x
• y_pred
• centers
• 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. Q. Zhao, M. Xu, and P. Franti, "Sum-of-squares based cluster validity index and significance analysis," in Adaptive and Natural Computing Algorithms, M. Kolehmainen, P. Toivanen, and B. Beliczynski, Eds. Berlin, Germany: Springer, 2009, pp. 313–322.