---
title: Label Ranking Loss
description: 'Compute the label ranking loss for multilabel data [1].'
canonical: >-
  https://lightning.ai/docs/torchmetrics/stable/classification/label_ranking_loss
---
# Label Ranking Loss {#label-ranking-loss}

## Module Interface {#module-interface}

### `class torchmetrics.classification.MultilabelRankingLoss(num_labels, ignore_index=None, validate_args=True, **kwargs)` {#torchmetrics.classification.MultilabelRankingLoss}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/ranking.py#L302-L431)

Compute the label ranking loss for multilabel data \[1\].

The score is corresponds to the average number of label pairs that are incorrectly ordered given some predictions weighted by the size of the label set and the number of labels not in the label set. The best score is 0.

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)")): A float tensor of shape `(N, C, ...)`. Preds should be a tensor containing probabilities or logits for each observation. If preds has values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element.
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): An int tensor of shape `(N, C, ...)`. Target should be a tensor containing ground truth labels, and therefore only contain {0,1} values (except if ignore\_index is specified).
    

Tip

Additional dimension `...` will be flattened into the batch dimension.

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

*   `mlrl` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A tensor containing the multilabel ranking loss.
    

Parameters:

*   **preds** – Tensor with predictions
    
*   **target** – Tensor with true labels
    
*   **num\_labels** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Integer specifying the number of labels
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    

Example

```python
>>> from torch import rand, randint
>>> from torchmetrics.classification import MultilabelRankingLoss
>>> preds = rand(10, 5)
>>> target = randint(2, (10, 5))
>>> mlrl = MultilabelRankingLoss(num_labels=5)
>>> mlrl(preds, target)
tensor(0.4167)
```

#### `plot(val=None, ax=None)` {#torchmetrics.classification.MultilabelRankingLoss.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/ranking.py#L391-L431)

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 object and Axes object

Raises:

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

```python
>>> from torch import rand, randint
>>> # Example plotting a single value
>>> from torchmetrics.classification import MultilabelRankingLoss
>>> metric = MultilabelRankingLoss(num_labels=3)
>>> metric.update(rand(20, 3), randint(2, (20, 3)))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/label\_ranking\_loss-1.png](/docs/torchmetrics/1.9.0/static/_images/label_ranking_loss-1.png)](/docs/torchmetrics/1.9.0/static/_images/label_ranking_loss-1.png)

```python
>>> from torch import rand, randint
>>> # Example plotting multiple values
>>> from torchmetrics.classification import MultilabelRankingLoss
>>> metric = MultilabelRankingLoss(num_labels=3)
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(rand(20, 3), randint(2, (20, 3))))
>>> fig_, ax_ = metric.plot(values)
```

[![../../\_images/label\_ranking\_loss-2.png](/docs/torchmetrics/1.9.0/static/_images/label_ranking_loss-2.png)](/docs/torchmetrics/1.9.0/static/_images/label_ranking_loss-2.png)

## Functional Interface {#functional-interface}

### `torchmetrics.functional.classification.multilabel_ranking_loss(preds, target, num_labels, ignore_index=None, validate_args=True)` {#torchmetrics.functional.classification.multilabel_ranking_loss}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/ranking.py#L216-L267)

Compute the label ranking loss for multilabel data \[1\].

The score is corresponds to the average number of label pairs that are incorrectly ordered given some predictions weighted by the size of the label set and the number of labels not in the label set. The best score is 0.

Accepts the following input tensors:

*   `preds` (float tensor): `(N, C, ...)`. Preds should be a tensor containing probabilities or logits for each observation. If preds has values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element.
    
*   `target` (int tensor): `(N, C, ...)`. Target should be a tensor containing ground truth labels, and therefore only contain {0,1} values (except if ignore\_index is specified).
    

Additional dimension `...` will be flattened into the batch dimension.

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with true labels
    
*   **num\_labels** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Integer specifying the number of labels
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    

Return type:

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

Example

```python
>>> from torch import rand, randint
>>> from torchmetrics.functional.classification import multilabel_ranking_loss
>>> preds = rand(10, 5)
>>> target = randint(2, (10, 5))
>>> multilabel_ranking_loss(preds, target, num_labels=5)
tensor(0.4167)
```

References

\[1\] Tsoumakas, G., Katakis, I., & Vlahavas, I. (2010). Mining multi-label data. In Data mining and knowledge discovery handbook (pp. 667-685). Springer US.

---

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