---
title: Jaccard Index
description: Calculate the Jaccard index for multilabel tasks.
canonical: 'https://lightning.ai/docs/torchmetrics/stable/classification/jaccard_index'
---
# Jaccard Index {#jaccard-index}

## Module Interface {#module-interface}

### `class torchmetrics.JaccardIndex(**kwargs)` {#torchmetrics.JaccardIndex}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/jaccard.py#L434-L485)

Calculate the Jaccard index for multilabel tasks.

The [Jaccard index](https://en.wikipedia.org/wiki/Jaccard_index) (also known as the intersection over union or jaccard similarity coefficient) is an statistic that can be used to determine the similarity and diversity of a sample set. It is defined as the size of the intersection divided by the union of the sample sets:

```math
J(A,B) = \frac{|A\cap B|}{|A\cup B|}
```

This function is a simple wrapper to get the task specific versions of this metric, which is done by setting the `task` argument to either `'binary'`, `'multiclass'` or `'multilabel'`. See the documentation of [`BinaryJaccardIndex`](#torchmetrics.classification.BinaryJaccardIndex "torchmetrics.classification.BinaryJaccardIndex"), [`MulticlassJaccardIndex`](#torchmetrics.classification.MulticlassJaccardIndex "torchmetrics.classification.MulticlassJaccardIndex") and [`MultilabelJaccardIndex`](#torchmetrics.classification.MultilabelJaccardIndex "torchmetrics.classification.MultilabelJaccardIndex") for the specific details of each argument influence and examples.

Legacy Example:

```python
>>> from torch import randint, tensor
>>> target = randint(0, 2, (10, 25, 25))
>>> pred = tensor(target)
>>> pred[2:5, 7:13, 9:15] = 1 - pred[2:5, 7:13, 9:15]
>>> jaccard = JaccardIndex(task="multiclass", num_classes=2)
>>> jaccard(pred, target)
tensor(0.9660)
```

#### `static __new__(cls, task, threshold=0.5, num_classes=None, num_labels=None, average='macro', ignore_index=None, validate_args=True, **kwargs)` {#torchmetrics.JaccardIndex.__new__}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/jaccard.py#L461-L485)

Initialize task metric.

Return type:

[`Metric`](/docs/torchmetrics/1.9.0/api-reference/metric.md#torchmetrics.Metric "torchmetrics.metric.Metric")

### BinaryJaccardIndex {#binaryjaccardindex}

### `class torchmetrics.classification.BinaryJaccardIndex(threshold=0.5, ignore_index=None, validate_args=True, zero_division=0, **kwargs)` {#torchmetrics.classification.BinaryJaccardIndex}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/jaccard.py#L40-L155)

Calculate the Jaccard index for binary tasks.

The [Jaccard index](https://en.wikipedia.org/wiki/Jaccard_index) (also known as the intersection over union or jaccard similarity coefficient) is an statistic that can be used to determine the similarity and diversity of a sample set. It is defined as the size of the intersection divided by the union of the sample sets:

```math
J(A,B) = \frac{|A\cap B|}{|A\cup B|}
```

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 v2.13)")): A int or float tensor of shape `(N, ...)`. If preds is a floating point tensor with values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element. Additionally, we convert to int tensor with thresholding using the value in `threshold`.
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")): An int tensor of shape `(N, ...)`.
    

Tip

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

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

*   `bji` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")): A tensor containing the Binary Jaccard Index.
    

Parameters:

*   **threshold** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Threshold for transforming probability to binary (0,1) predictions
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`int`](https://docs.python.org/3/library/functions.html#int "(in Python v3.14)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/library/functions.html#bool "(in Python v3.14)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    
*   **zero\_division** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Value to replace when there is a division by zero. Should be 0 or 1.
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.14)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Example (preds is int tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.classification import BinaryJaccardIndex
>>> target = tensor([1, 1, 0, 0])
>>> preds = tensor([0, 1, 0, 0])
>>> metric = BinaryJaccardIndex()
>>> metric(preds, target)
tensor(0.5000)
```

Example (preds is float tensor):

```python
>>> from torchmetrics.classification import BinaryJaccardIndex
>>> target = tensor([1, 1, 0, 0])
>>> preds = tensor([0.35, 0.85, 0.48, 0.01])
>>> metric = BinaryJaccardIndex()
>>> metric(preds, target)
tensor(0.5000)
```

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

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/jaccard.py#L115-L155)

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 v2.13)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.14)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")\], [`None`](https://docs.python.org/3/library/constants.html#None "(in Python v3.14)")\]) – 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 v3.14)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.1)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.14)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.1)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.1)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure object and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/library/exceptions.html#ModuleNotFoundError "(in Python v3.14)") – If matplotlib is not installed

```python
>>> # Example plotting a single value
>>> from torch import rand, randint
>>> from torchmetrics.classification import BinaryJaccardIndex
>>> metric = BinaryJaccardIndex()
>>> metric.update(rand(10), randint(2,(10,)))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/jaccard\_index-1.png](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-1.png)](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-1.png)

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

[![../../\_images/jaccard\_index-2.png](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-2.png)](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-2.png)

### MulticlassJaccardIndex {#multiclassjaccardindex}

### `class torchmetrics.classification.MulticlassJaccardIndex(num_classes, average='macro', ignore_index=None, validate_args=True, zero_division=0, **kwargs)` {#torchmetrics.classification.MulticlassJaccardIndex}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/jaccard.py#L158-L292)

Calculate the Jaccard index for multiclass tasks.

The [Jaccard index](https://en.wikipedia.org/wiki/Jaccard_index) (also known as the intersection over union or jaccard similarity coefficient) is an statistic that can be used to determine the similarity and diversity of a sample set. It is defined as the size of the intersection divided by the union of the sample sets:

```math
J(A,B) = \frac{|A\cap B|}{|A\cup B|}
```

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 v2.13)")): A int tensor of shape `(N, ...)` or float tensor of shape `(N, C, ..)`. If preds is a floating point we apply `torch.argmax` along the `C` dimension to automatically convert probabilities/logits into an int tensor.
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")): An int tensor of shape `(N, ...)`.
    

Tip

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

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

*   `mcji` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")): A tensor containing the Multi-class Jaccard Index.
    

Parameters:

*   **num\_classes** ([`int`](https://docs.python.org/3/library/functions.html#int "(in Python v3.14)")) – Integer specifying the number of classes
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`int`](https://docs.python.org/3/library/functions.html#int "(in Python v3.14)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **average** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.14)")\[`'micro'`, `'macro'`, `'weighted'`, `'none'`\]\]) –
    
    Defines the reduction that is applied over labels. Should be one of the following:
    
    *   `micro`: Sum statistics over all labels
        
    *   `macro`: Calculate statistics for each label and average them
        
    *   `weighted`: calculates statistics for each label and computes weighted average using their support
        
    *   `"none"` or `None`: calculates statistic for each label and applies no reduction
        
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/library/functions.html#bool "(in Python v3.14)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    
*   **zero\_division** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Value to replace when there is a division by zero. Should be 0 or 1.
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.14)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Example (pred is integer tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.classification import MulticlassJaccardIndex
>>> target = tensor([2, 1, 0, 0])
>>> preds = tensor([2, 1, 0, 1])
>>> metric = MulticlassJaccardIndex(num_classes=3)
>>> metric(preds, target)
tensor(0.6667)
```

Example (pred is float tensor):

```python
>>> from torchmetrics.classification import MulticlassJaccardIndex
>>> target = tensor([2, 1, 0, 0])
>>> preds = tensor([[0.16, 0.26, 0.58],
...                 [0.22, 0.61, 0.17],
...                 [0.71, 0.09, 0.20],
...                 [0.05, 0.82, 0.13]])
>>> metric = MulticlassJaccardIndex(num_classes=3)
>>> metric(preds, target)
tensor(0.6667)
```

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

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/jaccard.py#L252-L292)

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 v2.13)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.14)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")\], [`None`](https://docs.python.org/3/library/constants.html#None "(in Python v3.14)")\]) – 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 v3.14)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.1)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.14)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.1)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.1)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure object and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/library/exceptions.html#ModuleNotFoundError "(in Python v3.14)") – If matplotlib is not installed

```python
>>> # Example plotting a single value per class
>>> from torch import randint
>>> from torchmetrics.classification import MulticlassJaccardIndex
>>> metric = MulticlassJaccardIndex(num_classes=3, average=None)
>>> metric.update(randint(3, (20,)), randint(3, (20,)))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/jaccard\_index-3.png](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-3.png)](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-3.png)

```python
>>> # Example plotting a multiple values per class
>>> from torch import randint
>>> from torchmetrics.classification import MulticlassJaccardIndex
>>> metric = MulticlassJaccardIndex(num_classes=3, average=None)
>>> values = []
>>> for _ in range(20):
...     values.append(metric(randint(3, (20,)), randint(3, (20,))))
>>> fig_, ax_ = metric.plot(values)
```

[![../../\_images/jaccard\_index-4.png](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-4.png)](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-4.png)

### MultilabelJaccardIndex {#multilabeljaccardindex}

### `class torchmetrics.classification.MultilabelJaccardIndex(num_labels, threshold=0.5, average='macro', ignore_index=None, validate_args=True, zero_division=0, **kwargs)` {#torchmetrics.classification.MultilabelJaccardIndex}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/jaccard.py#L295-L431)

Calculate the Jaccard index for multilabel tasks.

The [Jaccard index](https://en.wikipedia.org/wiki/Jaccard_index) (also known as the intersection over union or jaccard similarity coefficient) is an statistic that can be used to determine the similarity and diversity of a sample set. It is defined as the size of the intersection divided by the union of the sample sets:

```math
J(A,B) = \frac{|A\cap B|}{|A\cup B|}
```

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 v2.13)")): A int tensor or float tensor of shape `(N, C, ...)`. If preds is a floating point tensor with values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element. Additionally, we convert to int tensor with thresholding using the value in `threshold`.
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")): An int tensor of shape `(N, C, ...)`
    

Tip

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

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

*   `mlji` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")): A tensor containing the Multi-label Jaccard Index loss.
    

Parameters:

*   **num\_classes** – Integer specifying the number of labels
    
*   **threshold** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Threshold for transforming probability to binary (0,1) predictions
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`int`](https://docs.python.org/3/library/functions.html#int "(in Python v3.14)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **average** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.14)")\[`'micro'`, `'macro'`, `'weighted'`, `'none'`\]\]) –
    
    Defines the reduction that is applied over labels. Should be one of the following:
    
    *   `micro`: Sum statistics over all labels
        
    *   `macro`: Calculate statistics for each label and average them
        
    *   `weighted`: calculates statistics for each label and computes weighted average using their support
        
    *   `"none"` or `None`: calculates statistic for each label and applies no reduction
        
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/library/functions.html#bool "(in Python v3.14)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    
*   **zero\_division** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Value to replace when there is a division by zero. Should be 0 or 1.
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.14)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Example (preds is int tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.classification import MultilabelJaccardIndex
>>> target = tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = tensor([[0, 0, 1], [1, 0, 1]])
>>> metric = MultilabelJaccardIndex(num_labels=3)
>>> metric(preds, target)
tensor(0.5000)
```

Example (preds is float tensor):

```python
>>> from torchmetrics.classification import MultilabelJaccardIndex
>>> target = tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = tensor([[0.11, 0.22, 0.84], [0.73, 0.33, 0.92]])
>>> metric = MultilabelJaccardIndex(num_labels=3)
>>> metric(preds, target)
tensor(0.5000)
```

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

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/jaccard.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 v2.13)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.14)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")\], [`None`](https://docs.python.org/3/library/constants.html#None "(in Python v3.14)")\]) – 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 v3.14)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.1)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.14)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.1)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.1)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/library/exceptions.html#ModuleNotFoundError "(in Python v3.14)") – If matplotlib is not installed

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

[![../../\_images/jaccard\_index-5.png](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-5.png)](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-5.png)

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

[![../../\_images/jaccard\_index-6.png](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-6.png)](/docs/torchmetrics/1.9.0/static/_images/jaccard_index-6.png)

## Functional Interface {#functional-interface}

### jaccard_index {#jaccard-index}

### `torchmetrics.functional.jaccard_index(preds, target, task, threshold=0.5, num_classes=None, num_labels=None, average='macro', ignore_index=None, validate_args=True, zero_division=0.0)` {#torchmetrics.functional.jaccard_index}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/jaccard.py#L326-L375)

Calculate the Jaccard index.

The [Jaccard index](https://en.wikipedia.org/wiki/Jaccard_index) (also known as the intersection over union or jaccard similarity coefficient) is an statistic that can be used to determine the similarity and diversity of a sample set. It is defined as the size of the intersection divided by the union of the sample sets: :rtype: [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")

```math
J(A,B) = \frac{|A\cap B|}{|A\cup B|}
```

This function is a simple wrapper to get the task specific versions of this metric, which is done by setting the `task` argument to either `'binary'`, `'multiclass'` or `'multilabel'`. See the documentation of [`binary_jaccard_index()`](#torchmetrics.functional.classification.binary_jaccard_index "torchmetrics.functional.classification.binary_jaccard_index"), [`multiclass_jaccard_index()`](#torchmetrics.functional.classification.multiclass_jaccard_index "torchmetrics.functional.classification.multiclass_jaccard_index") and [`multilabel_jaccard_index()`](#torchmetrics.functional.classification.multilabel_jaccard_index "torchmetrics.functional.classification.multilabel_jaccard_index") for the specific details of each argument influence and examples.

Legacy Example:

```python
>>> from torch import randint, tensor
>>> target = randint(0, 2, (10, 25, 25))
>>> pred = tensor(target)
>>> pred[2:5, 7:13, 9:15] = 1 - pred[2:5, 7:13, 9:15]
>>> jaccard_index(pred, target, task="multiclass", num_classes=2)
tensor(0.9660)
```

### binary_jaccard_index {#binary-jaccard-index}

### `torchmetrics.functional.classification.binary_jaccard_index(preds, target, threshold=0.5, ignore_index=None, validate_args=True, zero_division=0.0)` {#torchmetrics.functional.classification.binary_jaccard_index}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/jaccard.py#L100-L157)

Calculate the Jaccard index for binary tasks.

The [Jaccard index](https://en.wikipedia.org/wiki/Jaccard_index) (also known as the intersection over union or jaccard similarity coefficient) is an statistic that can be used to determine the similarity and diversity of a sample set. It is defined as the size of the intersection divided by the union of the sample sets:

```math
J(A,B) = \frac{|A\cap B|}{|A\cup B|}
```

Accepts the following input tensors:

*   `preds` (int or float tensor): `(N, ...)`. If preds is a floating point tensor with values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element. Additionally, we convert to int tensor with thresholding using the value in `threshold`.
    
*   `target` (int tensor): `(N, ...)`
    

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

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")) – Tensor with true labels
    
*   **threshold** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Threshold for transforming probability to binary (0,1) predictions
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`int`](https://docs.python.org/3/library/functions.html#int "(in Python v3.14)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/library/functions.html#bool "(in Python v3.14)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    
*   **zero\_division** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Value to replace when there is a division by zero. Should be 0 or 1.
    

Return type:

[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")

Example (preds is int tensor):

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

Example (preds is float tensor):

```python
>>> from torchmetrics.functional.classification import binary_jaccard_index
>>> target = tensor([1, 1, 0, 0])
>>> preds = tensor([0.35, 0.85, 0.48, 0.01])
>>> binary_jaccard_index(preds, target)
tensor(0.5000)
```

### multiclass_jaccard_index {#multiclass-jaccard-index}

### `torchmetrics.functional.classification.multiclass_jaccard_index(preds, target, num_classes, average='macro', ignore_index=None, validate_args=True, zero_division=0.0)` {#torchmetrics.functional.classification.multiclass_jaccard_index}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/jaccard.py#L171-L240)

Calculate the Jaccard index for multiclass tasks.

The [Jaccard index](https://en.wikipedia.org/wiki/Jaccard_index) (also known as the intersection over union or jaccard similarity coefficient) is an statistic that can be used to determine the similarity and diversity of a sample set. It is defined as the size of the intersection divided by the union of the sample sets:

```math
J(A,B) = \frac{|A\cap B|}{|A\cup B|}
```

Accepts the following input tensors:

*   `preds`: `(N, ...)` (int tensor) or `(N, C, ..)` (float tensor). If preds is a floating point we apply `torch.argmax` along the `C` dimension to automatically convert probabilities/logits into an int tensor.
    
*   `target` (int tensor): `(N, ...)`
    

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

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")) – Tensor with true labels
    
*   **num\_classes** ([`int`](https://docs.python.org/3/library/functions.html#int "(in Python v3.14)")) – Integer specifying the number of classes
    
*   **average** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.14)")\[`'micro'`, `'macro'`, `'weighted'`, `'none'`\]\]) –
    
    Defines the reduction that is applied over labels. Should be one of the following:
    
    *   `micro`: Sum statistics over all labels
        
    *   `macro`: Calculate statistics for each label and average them
        
    *   `weighted`: calculates statistics for each label and computes weighted average using their support
        
    *   `"none"` or `None`: calculates statistic for each label and applies no reduction
        
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`int`](https://docs.python.org/3/library/functions.html#int "(in Python v3.14)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/library/functions.html#bool "(in Python v3.14)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    
*   **zero\_division** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Value to replace when there is a division by zero. Should be 0 or 1.
    

Return type:

[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")

Example (pred is integer tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.functional.classification import multiclass_jaccard_index
>>> target = tensor([2, 1, 0, 0])
>>> preds = tensor([2, 1, 0, 1])
>>> multiclass_jaccard_index(preds, target, num_classes=3)
tensor(0.6667)
```

Example (pred is float tensor):

```python
>>> from torchmetrics.functional.classification import multiclass_jaccard_index
>>> target = tensor([2, 1, 0, 0])
>>> preds = tensor([[0.16, 0.26, 0.58],
...                 [0.22, 0.61, 0.17],
...                 [0.71, 0.09, 0.20],
...                 [0.05, 0.82, 0.13]])
>>> multiclass_jaccard_index(preds, target, num_classes=3)
tensor(0.6667)
```

### multilabel_jaccard_index {#multilabel-jaccard-index}

### `torchmetrics.functional.classification.multilabel_jaccard_index(preds, target, num_labels, threshold=0.5, average='macro', ignore_index=None, validate_args=True, zero_division=0.0)` {#torchmetrics.functional.classification.multilabel_jaccard_index}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/jaccard.py#L255-L323)

Calculate the Jaccard index for multilabel tasks.

The [Jaccard index](https://en.wikipedia.org/wiki/Jaccard_index) (also known as the intersection over union or jaccard similarity coefficient) is an statistic that can be used to determine the similarity and diversity of a sample set. It is defined as the size of the intersection divided by the union of the sample sets:

```math
J(A,B) = \frac{|A\cap B|}{|A\cup B|}
```

Accepts the following input tensors:

*   `preds` (int or float tensor): `(N, C, ...)`. If preds is a floating point tensor with values outside \[0,1\] range we consider the input to be logits and will auto apply sigmoid per element. Additionally, we convert to int tensor with thresholding using the value in `threshold`.
    
*   `target` (int tensor): `(N, C, ...)`
    

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

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")) – Tensor with true labels
    
*   **num\_labels** ([`int`](https://docs.python.org/3/library/functions.html#int "(in Python v3.14)")) – Integer specifying the number of labels
    
*   **threshold** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Threshold for transforming probability to binary (0,1) predictions
    
*   **average** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.14)")\[`'micro'`, `'macro'`, `'weighted'`, `'none'`\]\]) –
    
    Defines the reduction that is applied over labels. Should be one of the following:
    
    *   `micro`: Sum statistics over all labels
        
    *   `macro`: Calculate statistics for each label and average them
        
    *   `weighted`: calculates statistics for each label and computes weighted average using their support
        
    *   `"none"` or `None`: calculates statistic for each label and applies no reduction
        
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.14)")\[[`int`](https://docs.python.org/3/library/functions.html#int "(in Python v3.14)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/library/functions.html#bool "(in Python v3.14)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    
*   **zero\_division** ([`float`](https://docs.python.org/3/library/functions.html#float "(in Python v3.14)")) – Value to replace when there is a division by zero. Should be 0 or 1.
    

Return type:

[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.13)")

Example (preds is int tensor):

```python
>>> from torch import tensor
>>> from torchmetrics.functional.classification import multilabel_jaccard_index
>>> target = tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = tensor([[0, 0, 1], [1, 0, 1]])
>>> multilabel_jaccard_index(preds, target, num_labels=3)
tensor(0.5000)
```

Example (preds is float tensor):

```python
>>> from torchmetrics.functional.classification import multilabel_jaccard_index
>>> target = tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = tensor([[0.11, 0.22, 0.84], [0.73, 0.33, 0.92]])
>>> multilabel_jaccard_index(preds, target, num_labels=3)
tensor(0.5000)
```

---

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