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# Matthews Correlation Coefficient¶

## Module Interface¶

### MatthewsCorrCoef¶

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

Matthews correlation coefficient.

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.

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

In the binary case it is defined as:

where TP, TN, FP and FN are respectively the true postitives, true negatives, false positives and false negatives. Also works in the case of multi-label or multi-class input.

Note

This metric produces a multi-dimensional output, so it can not be directly logged.

Forward accepts

• preds (float or long tensor): (N, ...) or (N, C, ...) where C is the number of classes

• target (long tensor): (N, ...)

If preds and target are the same shape and preds is a float tensor, we use the self.threshold argument to convert into integer labels. This is the case for binary and multi-label probabilities.

If preds has an extra dimension as in the case of multi-class scores we perform an argmax on dim=1.

Parameters

Example

>>> from torchmetrics import MatthewsCorrCoef
>>> target = torch.tensor([1, 1, 0, 0])
>>> preds = torch.tensor([0, 1, 0, 0])
>>> matthews_corrcoef = MatthewsCorrCoef(num_classes=2)
>>> matthews_corrcoef(preds, target)
tensor(0.5774)


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

compute()[source]

Computes matthews correlation coefficient.

Return type

Tensor

update(preds, target)[source]

Update state with predictions and targets.

Parameters
Return type

None

### 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.

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
• 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

• normalize

Normalization mode for confusion matrix. Choose from:

• None or 'none': no normalization (default)

• 'true': normalization over the targets (most commonly used)

• 'pred': normalization over the predictions

• 'all': normalization over the whole matrix

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

• kwargs (Any) – Additional keyword arguments, see Advanced metric settings for more info.

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.

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
• num_classes (int) – Integer specifing the number of classes

• ignore_index (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation

• normalize

Normalization mode for confusion matrix. Choose from:

• None or 'none': no normalization (default)

• 'true': normalization over the targets (most commonly used)

• 'pred': normalization over the predictions

• 'all': normalization over the whole matrix

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

• kwargs (Any) – Additional keyword arguments, see Advanced metric settings for more info.

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.

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

• normalize

Normalization mode for confusion matrix. Choose from:

• None or 'none': no normalization (default)

• 'true': normalization over the targets (most commonly used)

• 'pred': normalization over the predictions

• 'all': normalization over the whole matrix

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

• kwargs (Any) – Additional keyword arguments, see Advanced metric settings for more info.

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, num_classes, threshold=0.5, task=None, num_labels=None, ignore_index=None, validate_args=True)[source]

Matthews correlation coefficient.

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.

Calculates Matthews correlation coefficient that measures the general correlation or quality of a classification. In the binary case it is defined as:

where TP, TN, FP and FN are respectively the true postitives, true negatives, false positives and false negatives. Also works in the case of multi-label or multi-class input.

Parameters
• preds (Tensor) – (float or long tensor), Either a (N, ...) tensor with labels or (N, C, ...) where C is the number of classes, tensor with labels/probabilities

• target (Tensor) – target (long tensor), tensor with shape (N, ...) with ground true labels

• num_classes (int) – Number of classes in the dataset.

• threshold (float) – Threshold value for binary or multi-label probabilities.

Example

>>> from torchmetrics.functional import matthews_corrcoef
>>> target = torch.tensor([1, 1, 0, 0])
>>> preds = torch.tensor([0, 1, 0, 0])
>>> matthews_corrcoef(preds, target, num_classes=2)
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
• 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

• normalize

Normalization mode for confusion matrix. Choose from:

• None or 'none': no normalization (default)

• 'true': normalization over the targets (most commonly used)

• 'pred': normalization over the predictions

• 'all': normalization over the whole matrix

• 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 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
• num_classes (int) – Integer specifing the number of classes

• ignore_index (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation

• normalize

Normalization mode for confusion matrix. Choose from:

• None or 'none': no normalization (default)

• 'true': normalization over the targets (most commonly used)

• 'pred': normalization over the predictions

• 'all': normalization over the whole matrix

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

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

• normalize

Normalization mode for confusion matrix. Choose from:

• None or 'none': no normalization (default)

• 'true': normalization over the targets (most commonly used)

• 'pred': normalization over the predictions

• 'all': normalization over the whole matrix

• 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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