class_docstr: 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)
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code: def __init__(self, **kwargs: Any) -> None:
      super().__init__(**kwargs)
  
      self.add_state("preds", default=[], dist_reduce_fx="cat")
      self.add_state("target", default=[], dist_reduce_fx="cat")
  
file_path: torchmetrics/src/torchmetrics/clustering/fowlkes_mallows_index.py
imports: from typing import Any, List, Optional, Sequence, Union
  from torch import Tensor
  from torchmetrics.functional.clustering import fowlkes_mallows_index
  from torchmetrics.metric import Metric
  from torchmetrics.utilities.data import dim_zero_cat
  from torchmetrics.utilities.imports import _MATPLOTLIB_AVAILABLE
  from torchmetrics.utilities.plot import _AX_TYPE, _PLOT_OUT_TYPE
label_desc: Use image node_id 1 to create a new FowlkesMallowsIndex object from inherited base classes: Metric with example: obj = FowlkesMallowsIndex()