Hamming Distance¶

Module Interface¶

HammingDistance¶

class torchmetrics.HammingDistance(threshold=0.5, **kwargs)[source]

Hamming distance.

Note

From v0.10 an 'binary_*', 'multiclass_*', 'multilabel_*' version now exist of each classification metric. Moving forward we recommend using these versions. This base metric will still work as it did prior to v0.10 until v0.11. From v0.11 the task argument introduced in this metric will be required and the general order of arguments may change, such that this metric will just function as an single entrypoint to calling the three specialized versions.

Computes the average Hamming distance (also known as Hamming loss) between targets and predictions:

$\text{Hamming distance} = \frac{1}{N \cdot L}\sum_i^N \sum_l^L 1(y_{il} \neq \hat{y_{il}})$

Where $y$ is a tensor of target values, $\hat{y}$ is a tensor of predictions, and $\bullet_{il}$ refers to the $l$ -th label of the $i$ -th sample of that tensor.

This is the same as 1-accuracy for binary data, while for all other types of inputs it treats each possible label separately - meaning that, for example, multi-class data is treated as if it were multi-label.

Accepts all input types listed in Input types.

Parameters

threshold¶ (float) – Threshold for transforming probability or logit predictions to binary (0,1) predictions, in the case of binary or multi-label inputs. Default value of 0.5 corresponds to input being probabilities.
kwargs¶ (Any) – Additional keyword arguments, see Advanced metric settings for more info.

Raises

ValueError – If threshold is not between 0 and 1.

Example

>>> from torchmetrics import HammingDistance
>>> target = torch.tensor([[0, 1], [1, 1]])
>>> preds = torch.tensor([[0, 1], [0, 1]])
>>> hamming_distance = HammingDistance()
>>> hamming_distance(preds, target)
tensor(0.2500)

Initializes internal Module state, shared by both nn.Module and ScriptModule.

compute()[source]

Computes hamming distance based on inputs passed in to update previously.

Return type: Tensor

update(preds, target)[source]

Update state with predictions and targets.

See Input types for more information on input types.

Parameters

preds¶ (Tensor) – Predictions from model (probabilities, logits or labels)
target¶ (Tensor) – Ground truth labels

Return type

None

BinaryHammingDistance¶

class torchmetrics.classification.BinaryHammingDistance(threshold=0.5, multidim_average='global', ignore_index=None, validate_args=True, **kwargs)[source]

Computes the average Hamming distance (also known as Hamming loss) for binary tasks:

$\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})$

Where $y$ is a tensor of target values, $\hat{y}$ is a tensor of predictions, and $\bullet_{il}$ refers to the $l$ -th label of the $i$ -th sample of that tensor.

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. Addtionally, we convert to int tensor with thresholding using the value in threshold.
target (int tensor): (N, ...)

The influence of the additional dimension ... (if present) will be determined by the multidim_average argument.

Parameters

threshold¶ (float) – Threshold for transforming probability to binary {0,1} predictions
multidim_average¶ (Literal[‘global’, ‘samplewise’]) –
Defines how additionally dimensions ... should be handled. Should be one of the following:
- global: Additional dimensions are flatted along the batch dimension
- samplewise: Statistic will be calculated independently for each sample on the N axis. The statistics in this case are calculated over the additional dimensions.
ignore_index¶ (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation
validate_args¶ (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

Returns

If multidim_average is set to global, the metric returns a scalar value. If multidim_average is set to samplewise, the metric returns (N,) vector consisting of a scalar value per sample.

Example (preds is int tensor):

>>> from torchmetrics.classification import BinaryHammingDistance
>>> target = torch.tensor([0, 1, 0, 1, 0, 1])
>>> preds = torch.tensor([0, 0, 1, 1, 0, 1])
>>> metric = BinaryHammingDistance()
>>> metric(preds, target)
tensor(0.3333)

Example (preds is float tensor):

>>> from torchmetrics.classification import BinaryHammingDistance
>>> target = torch.tensor([0, 1, 0, 1, 0, 1])
>>> preds = torch.tensor([0.11, 0.22, 0.84, 0.73, 0.33, 0.92])
>>> metric = BinaryHammingDistance()
>>> metric(preds, target)
tensor(0.3333)

Example (multidim tensors):

>>> from torchmetrics.classification import BinaryHammingDistance
>>> target = torch.tensor([[[0, 1], [1, 0], [0, 1]], [[1, 1], [0, 0], [1, 0]]])
>>> preds = torch.tensor(
...     [
...         [[0.59, 0.91], [0.91, 0.99], [0.63, 0.04]],
...         [[0.38, 0.04], [0.86, 0.780], [0.45, 0.37]],
...     ]
... )
>>> metric = BinaryHammingDistance(multidim_average='samplewise')
>>> metric(preds, target)
tensor([0.6667, 0.8333])

Initializes internal Module state, shared by both nn.Module and ScriptModule.

compute()[source]

Computes the final statistics.

Return type

Tensor

Returns

The metric returns a tensor of shape (..., 5), where the last dimension corresponds to [tp, fp, tn, fn, sup] (sup stands for support and equals tp + fn). The shape depends on the multidim_average parameter:

If multidim_average is set to global, the shape will be (5,)
If multidim_average is set to samplewise, the shape will be (N, 5)

MulticlassHammingDistance¶

class torchmetrics.classification.MulticlassHammingDistance(num_classes, top_k=1, average='macro', multidim_average='global', ignore_index=None, validate_args=True, **kwargs)[source]

Computes the average Hamming distance (also known as Hamming loss) for multiclass tasks:

$\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})$

Where $y$ is a tensor of target values, $\hat{y}$ is a tensor of predictions, and $\bullet_{il}$ refers to the $l$ -th label of the $i$ -th sample of that tensor.

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, ...)

The influence of the additional dimension ... (if present) will be determined by the multidim_average argument.

Parameters

num_classes¶ (int) – Integer specifing the number of classes
average¶ (Optional[Literal[‘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
top_k¶ (int) – Number of highest probability or logit score predictions considered to find the correct label. Only works when preds contain probabilities/logits.
multidim_average¶ (Literal[‘global’, ‘samplewise’]) –
Defines how additionally dimensions ... should be handled. Should be one of the following:
- global: Additional dimensions are flatted along the batch dimension
- samplewise: Statistic will be calculated independently for each sample on the N axis. The statistics in this case are calculated over the additional dimensions.
ignore_index¶ (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation
validate_args¶ (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

Returns

If multidim_average is set to global:
- If average='micro'/'macro'/'weighted', the output will be a scalar tensor
- If average=None/'none', the shape will be (C,)
If multidim_average is set to samplewise:
- If average='micro'/'macro'/'weighted', the shape will be (N,)
- If average=None/'none', the shape will be (N, C)

Return type

The returned shape depends on the average and multidim_average arguments

Example (preds is int tensor):

>>> from torchmetrics.classification import MulticlassHammingDistance
>>> target = torch.tensor([2, 1, 0, 0])
>>> preds = torch.tensor([2, 1, 0, 1])
>>> metric = MulticlassHammingDistance(num_classes=3)
>>> metric(preds, target)
tensor(0.1667)
>>> metric = MulticlassHammingDistance(num_classes=3, average=None)
>>> metric(preds, target)
tensor([0.5000, 0.0000, 0.0000])

Example (preds is float tensor):

>>> from torchmetrics.classification import MulticlassHammingDistance
>>> target = torch.tensor([2, 1, 0, 0])
>>> preds = torch.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 = MulticlassHammingDistance(num_classes=3)
>>> metric(preds, target)
tensor(0.1667)
>>> metric = MulticlassHammingDistance(num_classes=3, average=None)
>>> metric(preds, target)
tensor([0.5000, 0.0000, 0.0000])

Example (multidim tensors):

>>> from torchmetrics.classification import MulticlassHammingDistance
>>> target = torch.tensor([[[0, 1], [2, 1], [0, 2]], [[1, 1], [2, 0], [1, 2]]])
>>> preds = torch.tensor([[[0, 2], [2, 0], [0, 1]], [[2, 2], [2, 1], [1, 0]]])
>>> metric = MulticlassHammingDistance(num_classes=3, multidim_average='samplewise')
>>> metric(preds, target)
tensor([0.5000, 0.7222])
>>> metric = MulticlassHammingDistance(num_classes=3, multidim_average='samplewise', average=None)
>>> metric(preds, target)
tensor([[0.0000, 1.0000, 0.5000],
        [1.0000, 0.6667, 0.5000]])

Initializes internal Module state, shared by both nn.Module and ScriptModule.

compute()[source]

Computes the final statistics.

Return type

Tensor

Returns

The metric returns a tensor of shape (..., 5), where the last dimension corresponds to [tp, fp, tn, fn, sup] (sup stands for support and equals tp + fn). The shape depends on average and multidim_average parameters:

If multidim_average is set to global
If average='micro'/'macro'/'weighted', the shape will be (5,)
If average=None/'none', the shape will be (C, 5)
If multidim_average is set to samplewise
If average='micro'/'macro'/'weighted', the shape will be (N, 5)
If average=None/'none', the shape will be (N, C, 5)

MultilabelHammingDistance¶

class torchmetrics.classification.MultilabelHammingDistance(num_labels, threshold=0.5, average='macro', multidim_average='global', ignore_index=None, validate_args=True, **kwargs)[source]

Computes the average Hamming distance (also known as Hamming loss) for multilabel tasks:

$\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})$

Where $y$ is a tensor of target values, $\hat{y}$ is a tensor of predictions, and $\bullet_{il}$ refers to the $l$ -th label of the $i$ -th sample of that tensor.

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. Addtionally, we convert to int tensor with thresholding using the value in threshold.
target (int tensor): (N, C, ...)

The influence of the additional dimension ... (if present) will be determined by the multidim_average argument.

Parameters

num_labels¶ (int) – Integer specifing the number of labels
threshold¶ (float) – Threshold for transforming probability to binary (0,1) predictions
average¶ (Optional[Literal[‘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
multidim_average¶ (Literal[‘global’, ‘samplewise’]) –
Defines how additionally dimensions ... should be handled. Should be one of the following:
- global: Additional dimensions are flatted along the batch dimension
- samplewise: Statistic will be calculated independently for each sample on the N axis. The statistics in this case are calculated over the additional dimensions.
ignore_index¶ (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation
validate_args¶ (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

Returns

If multidim_average is set to global:
- If average='micro'/'macro'/'weighted', the output will be a scalar tensor
- If average=None/'none', the shape will be (C,)
If multidim_average is set to samplewise:
- If average='micro'/'macro'/'weighted', the shape will be (N,)
- If average=None/'none', the shape will be (N, C)

Return type

The returned shape depends on the average and multidim_average arguments

Example (preds is int tensor):

>>> from torchmetrics.classification import MultilabelHammingDistance
>>> target = torch.tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = torch.tensor([[0, 0, 1], [1, 0, 1]])
>>> metric = MultilabelHammingDistance(num_labels=3)
>>> metric(preds, target)
tensor(0.3333)
>>> metric = MultilabelHammingDistance(num_labels=3, average=None)
>>> metric(preds, target)
tensor([0.0000, 0.5000, 0.5000])

Example (preds is float tensor):

>>> from torchmetrics.classification import MultilabelHammingDistance
>>> target = torch.tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = torch.tensor([[0.11, 0.22, 0.84], [0.73, 0.33, 0.92]])
>>> metric = MultilabelHammingDistance(num_labels=3)
>>> metric(preds, target)
tensor(0.3333)
>>> metric = MultilabelHammingDistance(num_labels=3, average=None)
>>> metric(preds, target)
tensor([0.0000, 0.5000, 0.5000])

Example (multidim tensors):

>>> from torchmetrics.classification import MultilabelHammingDistance
>>> target = torch.tensor([[[0, 1], [1, 0], [0, 1]], [[1, 1], [0, 0], [1, 0]]])
>>> preds = torch.tensor(
...     [
...         [[0.59, 0.91], [0.91, 0.99], [0.63, 0.04]],
...         [[0.38, 0.04], [0.86, 0.780], [0.45, 0.37]],
...     ]
... )
>>> metric = MultilabelHammingDistance(num_labels=3, multidim_average='samplewise')
>>> metric(preds, target)
tensor([0.6667, 0.8333])
>>> metric = MultilabelHammingDistance(num_labels=3, multidim_average='samplewise', average=None)
>>> metric(preds, target)
tensor([[0.5000, 0.5000, 1.0000],
        [1.0000, 1.0000, 0.5000]])

Initializes internal Module state, shared by both nn.Module and ScriptModule.

compute()[source]

Computes the final statistics.

Return type

Tensor

Returns

The metric returns a tensor of shape (..., 5), where the last dimension corresponds to [tp, fp, tn, fn, sup] (sup stands for support and equals tp + fn). The shape depends on average and multidim_average parameters:

If multidim_average is set to global
If average='micro'/'macro'/'weighted', the shape will be (5,)
If average=None/'none', the shape will be (C, 5)
If multidim_average is set to samplewise
If average='micro'/'macro'/'weighted', the shape will be (N, 5)
If average=None/'none', the shape will be (N, C, 5)

Functional Interface¶

hamming_distance¶

torchmetrics.functional.hamming_distance(preds, target, threshold=0.5, task=None, num_classes=None, num_labels=None, average='macro', top_k=1, multidim_average='global', ignore_index=None, validate_args=True)[source]

Hamming distance.

Note

From v0.10 an 'binary_*', 'multiclass_*', 'multilabel_*' version now exist of each classification metric. Moving forward we recommend using these versions. This base metric will still work as it did prior to v0.10 until v0.11. From v0.11 the task argument introduced in this metric will be required and the general order of arguments may change, such that this metric will just function as an single entrypoint to calling the three specialized versions.

Computes the average Hamming distance (also known as Hamming loss) between targets and predictions:

$\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})$

Where $y$ is a tensor of target values, $\hat{y}$ is a tensor of predictions, and $\bullet_{il}$ refers to the $l$ -th label of the $i$ -th sample of that tensor.

This is the same as 1-accuracy for binary data, while for all other types of inputs it treats each possible label separately - meaning that, for example, multi-class data is treated as if it were multi-label.

Accepts all input types listed in Input types.

Parameters

preds¶ (Tensor) – Predictions from model (probabilities, logits or labels)
target¶ (Tensor) – Ground truth
threshold¶ (float) – Threshold for transforming probability or logit predictions to binary (0,1) predictions, in the case of binary or multi-label inputs. Default value of 0.5 corresponds to input being probabilities.

Example

>>> from torchmetrics.functional import hamming_distance
>>> target = torch.tensor([[0, 1], [1, 1]])
>>> preds = torch.tensor([[0, 1], [0, 1]])
>>> hamming_distance(preds, target)
tensor(0.2500)

Return type: Tensor

binary_hamming_distance¶

torchmetrics.functional.classification.binary_hamming_distance(preds, target, threshold=0.5, multidim_average='global', ignore_index=None, validate_args=True)[source]

Computes the average Hamming distance (also known as Hamming loss) for binary tasks:

$\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})$

Where $y$ is a tensor of target values, $\hat{y}$ is a tensor of predictions, and $\bullet_{il}$ refers to the $l$ -th label of the $i$ -th sample of that tensor.

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. Addtionally, we convert to int tensor with thresholding using the value in threshold.
target (int tensor): (N, ...)

The influence of the additional dimension ... (if present) will be determined by the multidim_average argument.

Parameters

preds¶ (Tensor) – Tensor with predictions
target¶ (Tensor) – Tensor with true labels
threshold¶ (float) – Threshold for transforming probability to binary {0,1} predictions
multidim_average¶ (Literal[‘global’, ‘samplewise’]) –
Defines how additionally dimensions ... should be handled. Should be one of the following:
- global: Additional dimensions are flatted along the batch dimension
- samplewise: Statistic will be calculated independently for each sample on the N axis. The statistics in this case are calculated over the additional dimensions.
ignore_index¶ (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation
validate_args¶ (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

Return type

Tensor

Returns

If multidim_average is set to global, the metric returns a scalar value. If multidim_average is set to samplewise, the metric returns (N,) vector consisting of a scalar value per sample.

Example (preds is int tensor):

>>> from torchmetrics.functional.classification import binary_hamming_distance
>>> target = torch.tensor([0, 1, 0, 1, 0, 1])
>>> preds = torch.tensor([0, 0, 1, 1, 0, 1])
>>> binary_hamming_distance(preds, target)
tensor(0.3333)

Example (preds is float tensor):

>>> from torchmetrics.functional.classification import binary_hamming_distance
>>> target = torch.tensor([0, 1, 0, 1, 0, 1])
>>> preds = torch.tensor([0.11, 0.22, 0.84, 0.73, 0.33, 0.92])
>>> binary_hamming_distance(preds, target)
tensor(0.3333)

Example (multidim tensors):

>>> from torchmetrics.functional.classification import binary_hamming_distance
>>> target = torch.tensor([[[0, 1], [1, 0], [0, 1]], [[1, 1], [0, 0], [1, 0]]])
>>> preds = torch.tensor(
...     [
...         [[0.59, 0.91], [0.91, 0.99], [0.63, 0.04]],
...         [[0.38, 0.04], [0.86, 0.780], [0.45, 0.37]],
...     ]
... )
>>> binary_hamming_distance(preds, target, multidim_average='samplewise')
tensor([0.6667, 0.8333])

multiclass_hamming_distance¶

torchmetrics.functional.classification.multiclass_hamming_distance(preds, target, num_classes, average='macro', top_k=1, multidim_average='global', ignore_index=None, validate_args=True)[source]

Computes the average Hamming distance (also known as Hamming loss) for multiclass tasks:

$\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})$

Where $y$ is a tensor of target values, $\hat{y}$ is a tensor of predictions, and $\bullet_{il}$ refers to the $l$ -th label of the $i$ -th sample of that tensor.

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, ...)

The influence of the additional dimension ... (if present) will be determined by the multidim_average argument.

Parameters

preds¶ (Tensor) – Tensor with predictions
target¶ (Tensor) – Tensor with true labels
num_classes¶ (int) – Integer specifing the number of classes
average¶ (Optional[Literal[‘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
top_k¶ (int) – Number of highest probability or logit score predictions considered to find the correct label. Only works when preds contain probabilities/logits.
multidim_average¶ (Literal[‘global’, ‘samplewise’]) –
Defines how additionally dimensions ... should be handled. Should be one of the following:
- global: Additional dimensions are flatted along the batch dimension
- samplewise: Statistic will be calculated independently for each sample on the N axis. The statistics in this case are calculated over the additional dimensions.
ignore_index¶ (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation
validate_args¶ (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

Returns

If multidim_average is set to global:
- If average='micro'/'macro'/'weighted', the output will be a scalar tensor
- If average=None/'none', the shape will be (C,)
If multidim_average is set to samplewise:
- If average='micro'/'macro'/'weighted', the shape will be (N,)
- If average=None/'none', the shape will be (N, C)

Return type

The returned shape depends on the average and multidim_average arguments

Example (preds is int tensor):

>>> from torchmetrics.functional.classification import multiclass_hamming_distance
>>> target = torch.tensor([2, 1, 0, 0])
>>> preds = torch.tensor([2, 1, 0, 1])
>>> multiclass_hamming_distance(preds, target, num_classes=3)
tensor(0.1667)
>>> multiclass_hamming_distance(preds, target, num_classes=3, average=None)
tensor([0.5000, 0.0000, 0.0000])

Example (preds is float tensor):

>>> from torchmetrics.functional.classification import multiclass_hamming_distance
>>> target = torch.tensor([2, 1, 0, 0])
>>> preds = torch.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_hamming_distance(preds, target, num_classes=3)
tensor(0.1667)
>>> multiclass_hamming_distance(preds, target, num_classes=3, average=None)
tensor([0.5000, 0.0000, 0.0000])

Example (multidim tensors):

>>> from torchmetrics.functional.classification import multiclass_hamming_distance
>>> target = torch.tensor([[[0, 1], [2, 1], [0, 2]], [[1, 1], [2, 0], [1, 2]]])
>>> preds = torch.tensor([[[0, 2], [2, 0], [0, 1]], [[2, 2], [2, 1], [1, 0]]])
>>> multiclass_hamming_distance(preds, target, num_classes=3, multidim_average='samplewise')
tensor([0.5000, 0.7222])
>>> multiclass_hamming_distance(preds, target, num_classes=3, multidim_average='samplewise', average=None)
tensor([[0.0000, 1.0000, 0.5000],
        [1.0000, 0.6667, 0.5000]])

multilabel_hamming_distance¶

torchmetrics.functional.classification.multilabel_hamming_distance(preds, target, num_labels, threshold=0.5, average='macro', multidim_average='global', ignore_index=None, validate_args=True)[source]

Computes the average Hamming distance (also known as Hamming loss) for multilabel tasks:

$\text{Hamming distance} = \frac{1}{N \cdot L} \sum_i^N \sum_l^L 1(y_{il} \neq \hat{y}_{il})$

Where $y$ is a tensor of target values, $\hat{y}$ is a tensor of predictions, and $\bullet_{il}$ refers to the $l$ -th label of the $i$ -th sample of that tensor.

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. Addtionally, we convert to int tensor with thresholding using the value in threshold.
target (int tensor): (N, C, ...)

The influence of the additional dimension ... (if present) will be determined by the multidim_average argument.

Parameters

preds¶ (Tensor) – Tensor with predictions
target¶ (Tensor) – Tensor with true labels
num_labels¶ (int) – Integer specifing the number of labels
threshold¶ (float) – Threshold for transforming probability to binary (0,1) predictions
average¶ (Optional[Literal[‘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
multidim_average¶ (Literal[‘global’, ‘samplewise’]) –
Defines how additionally dimensions ... should be handled. Should be one of the following:
- global: Additional dimensions are flatted along the batch dimension
- samplewise: Statistic will be calculated independently for each sample on the N axis. The statistics in this case are calculated over the additional dimensions.
ignore_index¶ (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation
validate_args¶ (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

Returns

If multidim_average is set to global:
- If average='micro'/'macro'/'weighted', the output will be a scalar tensor
- If average=None/'none', the shape will be (C,)
If multidim_average is set to samplewise:
- If average='micro'/'macro'/'weighted', the shape will be (N,)
- If average=None/'none', the shape will be (N, C)

Return type

The returned shape depends on the average and multidim_average arguments

Example (preds is int tensor):

>>> from torchmetrics.functional.classification import multilabel_hamming_distance
>>> target = torch.tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = torch.tensor([[0, 0, 1], [1, 0, 1]])
>>> multilabel_hamming_distance(preds, target, num_labels=3)
tensor(0.3333)
>>> multilabel_hamming_distance(preds, target, num_labels=3, average=None)
tensor([0.0000, 0.5000, 0.5000])

Example (preds is float tensor):

>>> from torchmetrics.functional.classification import multilabel_hamming_distance
>>> target = torch.tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = torch.tensor([[0.11, 0.22, 0.84], [0.73, 0.33, 0.92]])
>>> multilabel_hamming_distance(preds, target, num_labels=3)
tensor(0.3333)
>>> multilabel_hamming_distance(preds, target, num_labels=3, average=None)
tensor([0.0000, 0.5000, 0.5000])

Example (multidim tensors):

>>> from torchmetrics.functional.classification import multilabel_hamming_distance
>>> target = torch.tensor([[[0, 1], [1, 0], [0, 1]], [[1, 1], [0, 0], [1, 0]]])
>>> preds = torch.tensor(
...     [
...         [[0.59, 0.91], [0.91, 0.99], [0.63, 0.04]],
...         [[0.38, 0.04], [0.86, 0.780], [0.45, 0.37]],
...     ]
... )
>>> multilabel_hamming_distance(preds, target, num_labels=3, multidim_average='samplewise')
tensor([0.6667, 0.8333])
>>> multilabel_hamming_distance(preds, target, num_labels=3, multidim_average='samplewise', average=None)
tensor([[0.5000, 0.5000, 1.0000],
        [1.0000, 1.0000, 0.5000]])