---
title: Fowlkes-Mallows Index
description: Compute Fowlkes-Mallows Index.
canonical: 'https://lightning.ai/docs/torchmetrics/stable/clustering/fowlkes_mallows_index'
---
# Fowlkes-Mallows Index {#fowlkes-mallows-index}

## Module Interface {#module-interface}

### `class torchmetrics.clustering.FowlkesMallowsIndex(**kwargs)` {#torchmetrics.clustering.FowlkesMallowsIndex}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/clustering/fowlkes_mallows_index.py#L29-L122)

Compute [Fowlkes-Mallows Index](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.fowlkes_mallows_score.html#sklearn.metrics.fowlkes_mallows_score).

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

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

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

*   `preds` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): single integer tensor with shape `(N,)` with predicted cluster labels
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): single integer tensor with shape `(N,)` with ground truth cluster labels
    

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

*   `fmi` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A tensor with the Fowlkes-Mallows index.
    

Parameters:

**kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.15)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.

Example::

```python
>>> 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)
```

#### `plot(val=None, ax=None)` {#torchmetrics.clustering.FowlkesMallowsIndex.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/clustering/fowlkes_mallows_index.py#L84-L122)

Plot a single or multiple values from the metric.

Parameters:

*   **val** (`Union`\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – Either a single result from calling metric.forward or metric.compute or a list of these results. If no value is provided, will automatically call metric.compute and plot that result.
    
*   **ax** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.2)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(in Python v3.15)") – If matplotlib is not installed

```python
>>> # Example plotting a single value
>>> import torch
>>> from torchmetrics.clustering import FowlkesMallowsIndex
>>> metric = FowlkesMallowsIndex()
>>> metric.update(torch.randint(0, 4, (10,)), torch.randint(0, 4, (10,)))
>>> fig_, ax_ = metric.plot(metric.compute())
```

[![../../\_images/fowlkes\_mallows\_index-1.png](/docs/torchmetrics/1.9.0/static/_images/fowlkes_mallows_index-1.png)](/docs/torchmetrics/1.9.0/static/_images/fowlkes_mallows_index-1.png)

```python
>>> # Example plotting multiple values
>>> import torch
>>> from torchmetrics.clustering import FowlkesMallowsIndex
>>> metric = FowlkesMallowsIndex()
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(torch.randint(0, 4, (10,)), torch.randint(0, 4, (10,))))
>>> fig_, ax_ = metric.plot(values)
```

[![../../\_images/fowlkes\_mallows\_index-2.png](/docs/torchmetrics/1.9.0/static/_images/fowlkes_mallows_index-2.png)](/docs/torchmetrics/1.9.0/static/_images/fowlkes_mallows_index-2.png)

## Functional Interface {#functional-interface}

### `torchmetrics.functional.clustering.fowlkes_mallows_index(preds, target)` {#torchmetrics.functional.clustering.fowlkes_mallows_index}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/clustering/fowlkes_mallows_index.py#L57-L77)

Compute Fowlkes-Mallows index between two clusterings.

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – predicted cluster labels
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – ground truth cluster labels
    

Return type:

[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")

Returns:

Scalar tensor with Fowlkes-Mallows index

Example

```python
>>> import torch
>>> from torchmetrics.functional.clustering import fowlkes_mallows_index
>>> preds = torch.tensor([2, 2, 0, 1, 0])
>>> target = torch.tensor([2, 2, 1, 1, 0])
>>> fowlkes_mallows_index(preds, target)
tensor(0.5000)
```

---

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- Parent: [Clustering](/docs/torchmetrics/1.9.0/clustering.md)