Add MCC loss

kakumarabhishek · kakumarabhishek · commit cc21cefda226 · 2026-03-19T03:27:20.000-07:00
Add implementation of Matthews Correlation Coefficient (MCC)-based loss
Add tests for MCC loss
Add entry for MCC loss in documentation

Signed-off-by: Kumar Abhishek &lt;7644965+kakumarabhishek@users.noreply.github.com&gt;
diff --git a/docs/source/losses.rst b/docs/source/losses.rst
@@ -98,6 +98,11 @@ Segmentation Losses
 .. autoclass:: NACLLoss
     :members:
 
+`MCCLoss`
+~~~~~~~~~
+.. autoclass:: MCCLoss
+    :members:
+
 Registration Losses
 -------------------
 
diff --git a/monai/losses/__init__.py b/monai/losses/__init__.py
@@ -35,6 +35,7 @@
 from .focal_loss import FocalLoss
 from .giou_loss import BoxGIoULoss, giou
 from .hausdorff_loss import HausdorffDTLoss, LogHausdorffDTLoss
+from .mcc_loss import MCCLoss
 from .image_dissimilarity import GlobalMutualInformationLoss, LocalNormalizedCrossCorrelationLoss
 from .multi_scale import MultiScaleLoss
 from .nacl_loss import NACLLoss
diff --git a/monai/losses/mcc_loss.py b/monai/losses/mcc_loss.py
@@ -0,0 +1,188 @@
+# Copyright (c) MONAI Consortium
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#     http://www.apache.org/licenses/LICENSE-2.0
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import annotations
+
+import warnings
+from collections.abc import Callable
+
+import torch
+from torch.nn.modules.loss import _Loss
+
+from monai.networks import one_hot
+from monai.utils import LossReduction
+
+
+class MCCLoss(_Loss):
+    """
+    Compute the Matthews Correlation Coefficient (MCC) loss between two tensors.
+
+    Unlike Dice and Tversky losses which only use TP, FP, and FN, the MCC loss considers all four entries
+    of the confusion matrix (TP, TN, FP, FN), making it effective for class-imbalanced segmentation tasks
+    where background dominates the image. The loss is computed as ``1 - MCC`` where
+    ``MCC = (TP * TN - FP * FN) / sqrt((TP+FP)(TP+FN)(TN+FP)(TN+FN))``.
+
+    The soft confusion matrix entries are computed as:
+
+        - ``TP = sum(input * target)``
+        - ``TN = sum((1 - input) * (1 - target))``
+        - ``FP = sum(input * (1 - target))``
+        - ``FN = sum((1 - input) * target)``
+
+    The data `input` (BNHW[D] where N is number of classes) is compared with ground truth `target` (BNHW[D]).
+
+    Note that axis N of `input` is expected to be logits or probabilities for each class, if passing logits as input,
+    must set `sigmoid=True` or `softmax=True`, or specifying `other_act`. And the same axis of `target`
+    can be 1 or N (one-hot format).
+
+    The original paper:
+
+        Abhishek, K. and Hamarneh, G. (2021) Matthews Correlation Coefficient Loss for Deep Convolutional
+        Networks: Application to Skin Lesion Segmentation. IEEE ISBI, pp. 225-229.
+        (https://doi.org/10.1109/ISBI48211.2021.9433782)
+
+    """
+
+    def __init__(
+        self,
+        include_background: bool = True,
+        to_onehot_y: bool = False,
+        sigmoid: bool = False,
+        softmax: bool = False,
+        other_act: Callable | None = None,
+        reduction: LossReduction | str = LossReduction.MEAN,
+        smooth_nr: float = 0.0,
+        smooth_dr: float = 1e-5,
+        batch: bool = False,
+    ) -> None:
+        """
+        Args:
+            include_background: if False, channel index 0 (background category) is excluded from the calculation.
+                if the non-background segmentations are small compared to the total image size they can get
+                overwhelmed by the signal from the background so excluding it in such cases helps convergence.
+            to_onehot_y: whether to convert the ``target`` into the one-hot format,
+                using the number of classes inferred from `input` (``input.shape[1]``). Defaults to False.
+            sigmoid: if True, apply a sigmoid function to the prediction.
+            softmax: if True, apply a softmax function to the prediction.
+            other_act: callable function to execute other activation layers, Defaults to ``None``. for example:
+                ``other_act = torch.tanh``.
+            reduction: {``"none"``, ``"mean"``, ``"sum"``}
+                Specifies the reduction to apply to the output. Defaults to ``"mean"``.
+
+                - ``"none"``: no reduction will be applied.
+                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
+                - ``"sum"``: the output will be summed.
+
+            smooth_nr: a small constant added to the numerator to avoid zero.
+            smooth_dr: a small constant added to the denominator to avoid nan.
+            batch: whether to sum the confusion matrix entries over the batch dimension before computing MCC.
+                Defaults to False, MCC is computed independently for each item in the batch
+                before any `reduction`.
+
+        Raises:
+            TypeError: When ``other_act`` is not an ``Optional[Callable]``.
+            ValueError: When more than 1 of [``sigmoid=True``, ``softmax=True``, ``other_act is not None``].
+                Incompatible values.
+
+        """
+        super().__init__(reduction=LossReduction(reduction).value)
+        if other_act is not None and not callable(other_act):
+            raise TypeError(f"other_act must be None or callable but is {type(other_act).__name__}.")
+        if int(sigmoid) + int(softmax) + int(other_act is not None) > 1:
+            raise ValueError("Incompatible values: more than 1 of [sigmoid=True, softmax=True, other_act is not None].")
+        self.include_background = include_background
+        self.to_onehot_y = to_onehot_y
+        self.sigmoid = sigmoid
+        self.softmax = softmax
+        self.other_act = other_act
+        self.smooth_nr = float(smooth_nr)
+        self.smooth_dr = float(smooth_dr)
+        self.batch = batch
+
+    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
+        """
+        Args:
+            input: the shape should be BNH[WD], where N is the number of classes.
+            target: the shape should be BNH[WD] or B1H[WD], where N is the number of classes.
+
+        Raises:
+            AssertionError: When input and target (after one hot transform if set)
+                have different shapes.
+            ValueError: When ``self.reduction`` is not one of ["mean", "sum", "none"].
+
+        Example:
+            >>> from monai.losses.mcc_loss import MCCLoss
+            >>> import torch
+            >>> B, C, H, W = 7, 1, 3, 2
+            >>> input = torch.rand(B, C, H, W)
+            >>> target = torch.randint(low=0, high=2, size=(B, C, H, W)).float()
+            >>> self = MCCLoss(reduction='none')
+            >>> loss = self(input, target)
+        """
+        if self.sigmoid:
+            input = torch.sigmoid(input)
+
+        n_pred_ch = input.shape[1]
+        if self.softmax:
+            if n_pred_ch == 1:
+                warnings.warn("single channel prediction, `softmax=True` ignored.")
+            else:
+                input = torch.softmax(input, 1)
+
+        if self.other_act is not None:
+            input = self.other_act(input)
+
+        if self.to_onehot_y:
+            if n_pred_ch == 1:
+                warnings.warn("single channel prediction, `to_onehot_y=True` ignored.")
+            else:
+                target = one_hot(target, num_classes=n_pred_ch)
+
+        if not self.include_background:
+            if n_pred_ch == 1:
+                warnings.warn("single channel prediction, `include_background=False` ignored.")
+            else:
+                target = target[:, 1:]
+                input = input[:, 1:]
+
+        if target.shape != input.shape:
+            raise AssertionError(f"ground truth has differing shape ({target.shape}) from input ({input.shape})")
+
+        # reducing only spatial dimensions (not batch nor channels)
+        reduce_axis: list[int] = torch.arange(2, len(input.shape)).tolist()
+        if self.batch:
+            reduce_axis = [0] + reduce_axis
+
+        # Soft confusion matrix entries (Eq. 5 in the paper).
+        tp = torch.sum(input * target, dim=reduce_axis)
+        tn = torch.sum((1.0 - input) * (1.0 - target), dim=reduce_axis)
+        fp = torch.sum(input * (1.0 - target), dim=reduce_axis)
+        fn = torch.sum((1.0 - input) * target, dim=reduce_axis)
+
+        # MCC (Eq. 3) and loss (Eq. 4).
+        numerator = tp * tn - fp * fn + self.smooth_nr
+        denominator = torch.sqrt((tp + fp) * (tp + fn) * (tn + fp) * (tn + fn) + self.smooth_dr)
+
+        mcc = numerator / denominator
+        score: torch.Tensor = 1.0 - mcc
+
+        # When fp = fn = 0, prediction is perfect but the denominator product
+        # tends to 0 when tp = 0 or tn = 0, giving mcc ~ 0 instead of 1.
+        perfect = (fp == 0) & (fn == 0)
+        score = torch.where(perfect, torch.zeros_like(score), score)
+
+        if self.reduction == LossReduction.SUM.value:
+            return torch.sum(score)
+        if self.reduction == LossReduction.NONE.value:
+            return score
+        if self.reduction == LossReduction.MEAN.value:
+            return torch.mean(score)
+        raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')
diff --git a/tests/losses/test_mcc_loss.py b/tests/losses/test_mcc_loss.py
@@ -0,0 +1,154 @@
+# Copyright (c) MONAI Consortium
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#     http://www.apache.org/licenses/LICENSE-2.0
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import annotations
+
+import unittest
+
+import numpy as np
+import torch
+from parameterized import parameterized
+
+from monai.losses import MCCLoss
+from tests.test_utils import test_script_save
+
+TEST_CASES = [
+    [  # shape: (1, 1, 2, 2), (1, 1, 2, 2), sigmoid
+        {"include_background": True, "sigmoid": True},
+        {"input": torch.tensor([[[[1.0, -1.0], [-1.0, 1.0]]]]), "target": torch.tensor([[[[1.0, 0.0], [1.0, 1.0]]]])},
+        0.733197,
+    ],
+    [  # shape: (2, 1, 2, 2), (2, 1, 2, 2), sigmoid
+        {"include_background": True, "sigmoid": True},
+        {
+            "input": torch.tensor([[[[1.0, -1.0], [-1.0, 1.0]]], [[[1.0, -1.0], [-1.0, 1.0]]]]),
+            "target": torch.tensor([[[[1.0, 1.0], [1.0, 1.0]]], [[[1.0, 0.0], [1.0, 0.0]]]]),
+        },
+        1.0,
+    ],
+    [  # shape: (1, 1, 2, 2), (1, 1, 2, 2), perfect prediction
+        {"include_background": True},
+        {"input": torch.tensor([[[[1.0, 0.0], [0.0, 1.0]]]]), "target": torch.tensor([[[[1.0, 0.0], [0.0, 1.0]]]])},
+        0.0,
+    ],
+    [  # shape: (1, 1, 2, 2), (1, 1, 2, 2), worst case (inverted)
+        {"include_background": True},
+        {"input": torch.tensor([[[[0.0, 1.0], [1.0, 0.0]]]]), "target": torch.tensor([[[[1.0, 0.0], [0.0, 1.0]]]])},
+        2.0,
+    ],
+    [  # shape: (2, 2, 3), (2, 1, 3), multi-class, exclude background, one-hot
+        {"include_background": False, "to_onehot_y": True},
+        {
+            "input": torch.tensor([[[1.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 1.0], [0.0, 1.0, 0.0]]]),
+            "target": torch.tensor([[[0.0, 0.0, 1.0]], [[0.0, 1.0, 0.0]]]),
+        },
+        0.0,
+    ],
+    [  # shape: (2, 2, 3), (2, 1, 3), multi-class, sigmoid, one-hot
+        {"include_background": True, "to_onehot_y": True, "sigmoid": True},
+        {
+            "input": torch.tensor([[[-1.0, 0.0, 1.0], [1.0, 0.0, -1.0]], [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]]),
+            "target": torch.tensor([[[1.0, 0.0, 0.0]], [[1.0, 1.0, 0.0]]]),
+        },
+        0.836617,
+    ],
+    [  # shape: (2, 2, 3), (2, 1, 3), multi-class, sigmoid, one-hot, batch=True
+        {"include_background": True, "to_onehot_y": True, "sigmoid": True, "batch": True},
+        {
+            "input": torch.tensor([[[-1.0, 0.0, 1.0], [1.0, 0.0, -1.0]], [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]]),
+            "target": torch.tensor([[[1.0, 0.0, 0.0]], [[1.0, 1.0, 0.0]]]),
+        },
+        0.845961,
+    ],
+    [  # shape: (2, 2, 3), (2, 1, 3), multi-class, sigmoid, one-hot, reduction=sum
+        {"include_background": True, "to_onehot_y": True, "sigmoid": True, "reduction": "sum"},
+        {
+            "input": torch.tensor([[[-1.0, 0.0, 1.0], [1.0, 0.0, -1.0]], [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]]),
+            "target": torch.tensor([[[1.0, 0.0, 0.0]], [[1.0, 1.0, 0.0]]]),
+        },
+        3.346468,
+    ],
+    [  # shape: (2, 2, 3), (2, 1, 3), multi-class, softmax, one-hot
+        {"include_background": True, "to_onehot_y": True, "softmax": True},
+        {
+            "input": torch.tensor([[[-1.0, 0.0, 1.0], [1.0, 0.0, -1.0]], [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]]),
+            "target": torch.tensor([[[1.0, 0.0, 0.0]], [[1.0, 1.0, 0.0]]]),
+        },
+        0.730736,
+    ],
+    [  # shape: (2, 2, 3), (2, 1, 3), multi-class, softmax, one-hot, reduction=none
+        {"include_background": True, "to_onehot_y": True, "softmax": True, "reduction": "none"},
+        {
+            "input": torch.tensor([[[-1.0, 0.0, 1.0], [1.0, 0.0, -1.0]], [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]]),
+            "target": torch.tensor([[[1.0, 0.0, 0.0]], [[1.0, 1.0, 0.0]]]),
+        },
+        [[0.461472, 0.461472], [1.0, 1.0]],
+    ],
+    [  # shape: (1, 1, 3, 3), (1, 1, 3, 3), all-ones perfect prediction
+        {"include_background": True},
+        {"input": torch.ones(1, 1, 3, 3), "target": torch.ones(1, 1, 3, 3)},
+        0.0,
+    ],
+    [  # shape: (1, 1, 3, 3), (1, 1, 3, 3), all-zeros perfect prediction
+        {"include_background": True},
+        {"input": torch.zeros(1, 1, 3, 3), "target": torch.zeros(1, 1, 3, 3)},
+        0.0,
+    ],
+    [  # shape: (2, 1, 2, 2), (2, 1, 2, 2), other_act=torch.tanh
+        {"include_background": True, "other_act": torch.tanh},
+        {
+            "input": torch.tensor([[[[1.0, -1.0], [-1.0, 1.0]]], [[[1.0, -1.0], [-1.0, 1.0]]]]),
+            "target": torch.tensor([[[[1.0, 1.0], [1.0, 1.0]]], [[[1.0, 0.0], [1.0, 0.0]]]]),
+        },
+        1.0,
+    ],
+]
+
+
+class TestMCCLoss(unittest.TestCase):
+    @parameterized.expand(TEST_CASES)
+    def test_shape(self, input_param, input_data, expected_val):
+        result = MCCLoss(**input_param).forward(**input_data)
+        np.testing.assert_allclose(result.detach().cpu().numpy(), expected_val, rtol=1e-4)
+
+    def test_ill_shape(self):
+        loss = MCCLoss()
+        with self.assertRaisesRegex(AssertionError, ""):
+            loss.forward(torch.ones((2, 2, 3)), torch.ones((4, 5, 6)))
+        chn_input = torch.ones((1, 1, 3))
+        chn_target = torch.ones((1, 1, 3))
+        with self.assertRaisesRegex(ValueError, ""):
+            MCCLoss(reduction="unknown")(chn_input, chn_target)
+        with self.assertRaisesRegex(ValueError, ""):
+            MCCLoss(reduction=None)(chn_input, chn_target)
+
+    def test_ill_opts(self):
+        with self.assertRaisesRegex(ValueError, ""):
+            MCCLoss(sigmoid=True, softmax=True)
+        with self.assertRaisesRegex(TypeError, ""):
+            MCCLoss(other_act="tanh")
+
+    @parameterized.expand([(False, False, False), (False, True, False), (False, False, True)])
+    def test_input_warnings(self, include_background, softmax, to_onehot_y):
+        chn_input = torch.ones((1, 1, 3))
+        chn_target = torch.ones((1, 1, 3))
+        with self.assertWarns(Warning):
+            loss = MCCLoss(include_background=include_background, softmax=softmax, to_onehot_y=to_onehot_y)
+            loss.forward(chn_input, chn_target)
+
+    def test_script(self):
+        loss = MCCLoss()
+        test_input = torch.ones(2, 1, 8, 8)
+        test_script_save(loss, test_input, test_input)
+
+
+if __name__ == "__main__":
+    unittest.main()
