# 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) โ 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¶

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 โ defaults to 1.0
update

Update the metric.

Parameters

• y_true
• y_pred
• sample_weight โ 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). Fowlkesโ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). โA method for comparing two hierarchical clusteringsโ. Journal of the American Statistical Association