GD53¶

Generalized Dunn's index 53 (GD53).

The Generalized Dunn's indices comprise a set of 17 variants of the original Dunn's index devised to address sensitivity to noise in the latter. The formula of this index is given by:

\[ GD_{rs} = \frac{\min_{i \new q} [\delta_r (\omega_i, \omega_j)]}{\max_k [\Delta_s (\omega_k)]}, \]

where \(\delta_r(.)\) is a measure of separation, and \(\Delta_s(.)\) is a measure of compactness, the parameters \(r\) and \(s\) index the measures' formulations. In particular, when employing Euclidean distance, GD43 is formulated using:

\[ \delta_5 (\omega_i, \omega_j) = \frac{CP_1^2 (v_i, \omega_i) + CP_1^2 (v_j, \omega_j)}{n_i + n_j}, \]

and

\[ \Delta_3 (\omega_k) = \frac{2 \times CP_1^2 (v_k, \omega_k)}{n_k}. \]

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.GD53()

>>> 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
GD53: 0.158377

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¶

J. Bezdek and N. Pal, "Some new indexes of cluster validity," IEEE Trans. Syst., Man, Cybern. B, vol. 28, no. 3, pp. 301–315, Jun. 1998. ↩