Add zero_division for single class prediction in MCC

[cynddl]

Describe the bug

I have found a potential edge case issue with sklearn.metrics.matthews_corrcoef. The example provided in the documentation works as expected:

from sklearn.metrics import matthews_corrcoef
matthews_corrcoef([1, 1, 1, -1], [1, -1, 1, 1])  # returns -1/3 OK

However, edge cases appear when either y or y_true have only one single label.

Steps/Code to Reproduce

from sklearn.metrics import matthews_corrcoef
matthews_corrcoef([1, 1, 1, 1], [1, 1, 1, 1])  # returns 0 instead of 1
matthews_corrcoef([0, 0, 0, 0], [0, 0, 0, 0])  # returns 0 instead of 1

Expected Results

Outputs should be 1, not 0.

Actual Results

Outputs are 0.

Versions

System:
    python: 3.11.9 (main, Apr  2 2024, 08:25:04) [Clang 16.0.6 ]
executable: /tmp/sklearn-test/.venv/bin/python
   machine: macOS-14.2.1-arm64-arm-64bit

Python dependencies:
      sklearn: 1.4.2
          pip: 24.0
   setuptools: 69.5.1
        numpy: 1.26.4
        scipy: 1.13.0
       Cython: None
       pandas: None
   matplotlib: None
       joblib: 1.4.2
threadpoolctl: 3.5.0

Built with OpenMP: True

threadpoolctl info:
       user_api: openmp
   internal_api: openmp
    num_threads: 8
         prefix: libomp
       filepath: /tmp/sklearn-test/.venv/lib/python3.11/site-packages/torch/lib/libomp.dylib
        version: None

       user_api: blas
   internal_api: openblas
    num_threads: 8
         prefix: libopenblas
       filepath: /tmp/sklearn-test/.venv/lib/python3.11/site-packages/numpy/.dylibs/libopenblas64_.0.dylib
        version: 0.3.23.dev
threading_layer: pthreads
   architecture: armv8

       user_api: blas
   internal_api: openblas
    num_threads: 8
         prefix: libopenblas
       filepath: /tmp/sklearn-test/.venv/lib/python3.11/site-packages/scipy/.dylibs/libopenblas.0.dylib
        version: 0.3.26.dev
threading_layer: pthreads
   architecture: neoversen1

       user_api: openmp
   internal_api: openmp
    num_threads: 8
         prefix: libomp
       filepath: /tmp/sklearn-test/.venv/lib/python3.11/site-packages/sklearn/.dylibs/libomp.dylib
        version: None

[hammad7]

From the definition, its actually going into the if condition at last, to avoid division by zero:

def matthews_corrcoef(y_true, y_pred, *, sample_weight=None):
    """Compute the Matthews correlation coefficient (MCC).

    The Matthews correlation coefficient is used in machine learning as a
    measure of the quality of binary and multiclass classifications. It takes
    into account true and false positives and negatives and is generally
    regarded as a balanced measure which can be used even if the classes are of
    very different sizes. The MCC is in essence a correlation coefficient value
    between -1 and +1. A coefficient of +1 represents a perfect prediction, 0
    an average random prediction and -1 an inverse prediction.  The statistic
    is also known as the phi coefficient. [source: Wikipedia]

    Binary and multiclass labels are supported.  Only in the binary case does
    this relate to information about true and false positives and negatives.
    See references below.

    Read more in the :ref:`User Guide <matthews_corrcoef>`.

    Parameters
    ----------
    y_true : array, shape = [n_samples]
        Ground truth (correct) target values.

    y_pred : array, shape = [n_samples]
        Estimated targets as returned by a classifier.

    sample_weight : array-like of shape (n_samples,), default=None
        Sample weights.

        .. versionadded:: 0.18

    Returns
    -------
    mcc : float
        The Matthews correlation coefficient (+1 represents a perfect
        prediction, 0 an average random prediction and -1 and inverse
        prediction).

    References
    ----------
    .. [1] :doi:`Baldi, Brunak, Chauvin, Andersen and Nielsen, (2000). Assessing the
       accuracy of prediction algorithms for classification: an overview.
       <10.1093/bioinformatics/16.5.412>`

    .. [2] `Wikipedia entry for the Matthews Correlation Coefficient
       <https://en.wikipedia.org/wiki/Matthews_correlation_coefficient>`_.

    .. [3] `Gorodkin, (2004). Comparing two K-category assignments by a
        K-category correlation coefficient
        <https://www.sciencedirect.com/science/article/pii/S1476927104000799>`_.

    .. [4] `Jurman, Riccadonna, Furlanello, (2012). A Comparison of MCC and CEN
        Error Measures in MultiClass Prediction
        <https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0041882>`_.

    Examples
    --------
    >>> from sklearn.metrics import matthews_corrcoef
    >>> y_true = [+1, +1, +1, -1]
    >>> y_pred = [+1, -1, +1, +1]
    >>> matthews_corrcoef(y_true, y_pred)
    -0.33...
    """
    y_type, y_true, y_pred = _check_targets(y_true, y_pred)
    check_consistent_length(y_true, y_pred, sample_weight)
    if y_type not in {"binary", "multiclass"}:
        raise ValueError("%s is not supported" % y_type)

    lb = LabelEncoder()
    lb.fit(np.hstack([y_true, y_pred]))
    y_true = lb.transform(y_true)
    y_pred = lb.transform(y_pred)

    C = confusion_matrix(y_true, y_pred, sample_weight=sample_weight)
    t_sum = C.sum(axis=1, dtype=np.float64)
    p_sum = C.sum(axis=0, dtype=np.float64)
    n_correct = np.trace(C, dtype=np.float64)
    n_samples = p_sum.sum()
    cov_ytyp = n_correct * n_samples - np.dot(t_sum, p_sum)
    cov_ypyp = n_samples**2 - np.dot(p_sum, p_sum)
    cov_ytyt = n_samples**2 - np.dot(t_sum, t_sum)

    if cov_ypyp * cov_ytyt == 0:
        return 0.0
    else:
        return cov_ytyp / np.sqrt(cov_ytyt * cov_ypyp)

[glemaitre]

Basically the solution is to provide a zero_division parameter to have a better handling here because this is a corner case: #28509