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# Matthews Correlation Coefficient¶

## Module Interface¶

### MatthewsCorrCoef¶

class torchmetrics.MatthewsCorrCoef(task: Optional[Literal['binary', 'multiclass', 'multilabel']] = None, threshold: float = 0.5, num_classes: = None, num_labels: = None, ignore_index: = None, validate_args: bool = True, **kwargs: Any)[source]

Calculates Matthews correlation coefficient . This metric measures the general correlation or quality of a classification.

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 BinaryMatthewsCorrCoef, MulticlassMatthewsCorrCoef and MultilabelMatthewsCorrCoef for the specific details of each argument influence and examples.

Legacy Example:
>>> target = torch.tensor([1, 1, 0, 0])
>>> preds = torch.tensor([0, 1, 0, 0])
>>> matthews_corrcoef(preds, target)
tensor(0.5774)


### BinaryMatthewsCorrCoef¶

class torchmetrics.classification.BinaryMatthewsCorrCoef(threshold=0.5, ignore_index=None, validate_args=True, **kwargs)[source]

Calculates Matthews correlation coefficient for binary tasks. This metric measures the general correlation or quality of a classification.

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

• preds (Tensor): A int tensor 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. Addtionally, we convert to int tensor with thresholding using the value in threshold.

• target (Tensor): An int tensor of shape (N, ...)

Note

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

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

• bmcc (Tensor): A tensor containing the Binary Matthews Correlation Coefficient.

Parameters
Example (preds is int tensor):
>>> from torchmetrics.classification import BinaryMatthewsCorrCoef
>>> target = torch.tensor([1, 1, 0, 0])
>>> preds = torch.tensor([0, 1, 0, 0])
>>> metric = BinaryMatthewsCorrCoef()
>>> metric(preds, target)
tensor(0.5774)

Example (preds is float tensor):
>>> from torchmetrics.classification import BinaryMatthewsCorrCoef
>>> target = torch.tensor([1, 1, 0, 0])
>>> preds = torch.tensor([0.35, 0.85, 0.48, 0.01])
>>> metric = BinaryMatthewsCorrCoef()
>>> metric(preds, target)
tensor(0.5774)


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

### MulticlassMatthewsCorrCoef¶

class torchmetrics.classification.MulticlassMatthewsCorrCoef(num_classes, ignore_index=None, validate_args=True, **kwargs)[source]

Calculates Matthews correlation coefficient for multiclass tasks. This metric measures the general correlation or quality of a classification.

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

• preds (Tensor): 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): An int tensor of shape (N, ...)

Note

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

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

• mcmcc (Tensor): A tensor containing the Multi-class Matthews Correlation Coefficient.

Parameters
Example (pred is integer tensor):
>>> from torchmetrics.classification import MulticlassMatthewsCorrCoef
>>> target = torch.tensor([2, 1, 0, 0])
>>> preds = torch.tensor([2, 1, 0, 1])
>>> metric = MulticlassMatthewsCorrCoef(num_classes=3)
>>> metric(preds, target)
tensor(0.7000)

Example (pred is float tensor):
>>> from torchmetrics.classification import MulticlassMatthewsCorrCoef
>>> 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 = MulticlassMatthewsCorrCoef(num_classes=3)
>>> metric(preds, target)
tensor(0.7000)


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

### MultilabelMatthewsCorrCoef¶

class torchmetrics.classification.MultilabelMatthewsCorrCoef(num_labels, threshold=0.5, ignore_index=None, validate_args=True, **kwargs)[source]

Calculates Matthews correlation coefficient for multilabel tasks. This metric measures the general correlation or quality of a classification.

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

• preds (Tensor): An int 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. Addtionally, we convert to int tensor with thresholding using the value in threshold.

• target (Tensor): An int tensor of shape (N, C, ...)

Note

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

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

• mlmcc (Tensor): A tensor containing the Multi-label Matthews Correlation Coefficient.

Parameters
Example (preds is int tensor):
>>> from torchmetrics.classification import MultilabelMatthewsCorrCoef
>>> target = torch.tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = torch.tensor([[0, 0, 1], [1, 0, 1]])
>>> metric = MultilabelMatthewsCorrCoef(num_labels=3)
>>> metric(preds, target)
tensor(0.3333)

Example (preds is float tensor):
>>> from torchmetrics.classification import MultilabelMatthewsCorrCoef
>>> 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 = MultilabelMatthewsCorrCoef(num_labels=3)
>>> metric(preds, target)
tensor(0.3333)


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

## Functional Interface¶

### matthews_corrcoef¶

torchmetrics.functional.matthews_corrcoef(preds, target, task=None, threshold=0.5, num_classes=None, num_labels=None, ignore_index=None, validate_args=True)[source]

Calculates Matthews correlation coefficient . This metric measures the general correlation or quality of a classification.

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_matthews_corrcoef(), multiclass_matthews_corrcoef() and multilabel_matthews_corrcoef() for the specific details of each argument influence and examples.

Legacy Example:
>>> target = torch.tensor([1, 1, 0, 0])
>>> preds = torch.tensor([0, 1, 0, 0])
tensor(0.5774)

Return type

Tensor

### binary_matthews_corrcoef¶

torchmetrics.functional.classification.binary_matthews_corrcoef(preds, target, threshold=0.5, ignore_index=None, validate_args=True)[source]

Calculates Matthews correlation coefficient for binary tasks. This metric measures the general correlation or quality of a classification.

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, ...)

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

Parameters
Example (preds is int tensor):
>>> from torchmetrics.functional.classification import binary_matthews_corrcoef
>>> target = torch.tensor([1, 1, 0, 0])
>>> preds = torch.tensor([0, 1, 0, 0])
>>> binary_matthews_corrcoef(preds, target)
tensor(0.5774)

Example (preds is float tensor):
>>> from torchmetrics.functional.classification import binary_matthews_corrcoef
>>> target = torch.tensor([1, 1, 0, 0])
>>> preds = torch.tensor([0.35, 0.85, 0.48, 0.01])
>>> binary_matthews_corrcoef(preds, target)
tensor(0.5774)

Return type

Tensor

### multiclass_matthews_corrcoef¶

torchmetrics.functional.classification.multiclass_matthews_corrcoef(preds, target, num_classes, ignore_index=None, validate_args=True)[source]

Calculates Matthews correlation coefficient for multiclass tasks. This metric measures the general correlation or quality of a classification.

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
Example (pred is integer tensor):
>>> from torchmetrics.functional.classification import multiclass_matthews_corrcoef
>>> target = torch.tensor([2, 1, 0, 0])
>>> preds = torch.tensor([2, 1, 0, 1])
>>> multiclass_matthews_corrcoef(preds, target, num_classes=3)
tensor(0.7000)

Example (pred is float tensor):
>>> from torchmetrics.functional.classification import multiclass_matthews_corrcoef
>>> 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_matthews_corrcoef(preds, target, num_classes=3)
tensor(0.7000)

Return type

Tensor

### multilabel_matthews_corrcoef¶

torchmetrics.functional.classification.multilabel_matthews_corrcoef(preds, target, num_labels, threshold=0.5, ignore_index=None, validate_args=True)[source]

Calculates Matthews correlation coefficient for multilabel tasks. This metric measures the general correlation or quality of a classification.

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, ...)

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

Parameters
• num_classes – Integer specifing the number of labels

• threshold (float) – Threshold for transforming probability to binary (0,1) predictions

• 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.

Example (preds is int tensor):
>>> from torchmetrics.functional.classification import multilabel_matthews_corrcoef
>>> target = torch.tensor([[0, 1, 0], [1, 0, 1]])
>>> preds = torch.tensor([[0, 0, 1], [1, 0, 1]])
>>> multilabel_matthews_corrcoef(preds, target, num_labels=3)
tensor(0.3333)

Example (preds is float tensor):
>>> from torchmetrics.functional.classification import multilabel_matthews_corrcoef
>>> 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_matthews_corrcoef(preds, target, num_labels=3)
tensor(0.3333)

Return type

Tensor

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