Fowlkesmallowsindex

---
name: fowlkesmallowsindex
description: Compute the FowlkesMallowsIndex metric — provided by torchmetrics. Use when the user has predictions and ground-truth and needs to compute FowlkesMallowsIndex, or asks how to score with FowlkesMallowsIndex.
metadata:
  skill_kind: metric
  source_lib: torchmetrics
  import_path: torchmetrics.clustering.FowlkesMallowsIndex
  source: library_introspection
---

# fowlkesmallowsindex

> Metric `FowlkesMallowsIndex` from `torchmetrics` (torchmetrics.clustering.FowlkesMallowsIndex)

## When to invoke this skill

The user has predictions + ground truth and asks to evaluate with FowlkesMallowsIndex, or
mentions `torchmetrics.clustering.FowlkesMallowsIndex` directly, or wants the standard torchmetrics implementation.

## Reference signature

```python
from torchmetrics.clustering import FowlkesMallowsIndex

# FowlkesMallowsIndex(**kwargs: Any) -> None
```

## Library docstring

```
Compute `Fowlkes-Mallows Index`_.

.. math::
    FMI(U,V) = \frac{TP}{\sqrt{(TP + FP) * (TP + FN)}}

Where :math:`TP` is the number of true positives, :math:`FP` is the number of false positives, and :math:`FN` is
the number of false negatives.

As input to ``forward`` and ``update`` the metric accepts the following input:

- ``preds`` (:class:`~torch.Tensor`): single integer tensor with shape ``(N,)`` with predicted cluster labels
- ``target`` (:class:`~torch.Tensor`): single integer tensor with shape ``(N,)`` with ground truth cluster labels

As output of ``forward`` and ``compute`` the metric returns the following output:

- ``fmi`` (:class:`~torch.Tensor`): A tensor with the Fowlkes-Mallows index.

Args:
    kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.

Example::
    >>> import torch
    >>> from torchmetrics.clustering import FowlkesMallowsIndex
    >>> preds = torch.tensor([2, 2, 0, 1, 0])
    >>> target = torch.tensor([2, 2, 1, 1, 0])
    >>> fmi = FowlkesMallowsIndex()
    >>> fmi(preds, target)
    tensor(0.5000)
```

## Quick recipe

```python
import torchmetrics.clustering as _m
score = _m.FowlkesMallowsIndex(y_true, y_pred)
```

## Don'ts

- Don't reimplement when the library version handles edge cases (NaN, ties, empty inputs) better than a hand-rolled formula.
- Always check the library version's argument order — sklearn is `(y_true, y_pred)` while torchmetrics is `(preds, target)`.