# FowlkesMallows¶

Fowlkes-Mallows Index.

The Fowlkes-Mallows Index 1 2 is an external evaluation method that is used to determine the similarity between two clusterings, and also a metric to measure confusion matrices. The measure of similarity could be either between two hierarchical clusterings or a clustering and a benchmark classification. A higher value for the Fowlkes-Mallows index indicates a greater similarity between the clusters and the benchmark classifications.

The Fowlkes-Mallows Index, for two cluster algorithms, is defined as:

$FM = \sqrt{PPV \times TPR} = \sqrt{\frac{TP}{TP+FP} \times \frac{TP}{TP+FN}}$

where

• TP, FP, FN are respectively the number of true positives, false positives and false negatives;

• TPR is the True Positive Rate (or Sensitivity/Recall), PPV is the Positive Predictive Rate (or Precision).

## Parameters¶

• cm (river.metrics.confusion.ConfusionMatrix) – 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.

• works_with_weights

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

## Examples¶

>>> from river import metrics

>>> y_true = [0, 0, 0, 1, 1, 1]
>>> y_pred = [0, 0, 1, 1, 2, 2]

>>> metric = metrics.FowlkesMallows()

>>> for yt, yp in zip(y_true, y_pred):
...     print(metric.update(yt, yp))
FowlkesMallows: 0.00%
FowlkesMallows: 100.00%
FowlkesMallows: 57.74%
FowlkesMallows: 40.82%
FowlkesMallows: 35.36%
FowlkesMallows: 47.14%


## Methods¶

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
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. Wikipedia contributors. (2020, December 22). Fowlkes–Mallows index. In Wikipedia, The Free Encyclopedia, from https://en.wikipedia.org/w/index.php?title=Fowlkes%E2%80%93Mallows_index&oldid=995714222

2. E. B. Fowkles and C. L. Mallows (1983). “A method for comparing two hierarchical clusterings”. Journal of the American Statistical Association