Repository: aeon-toolkit/aeon (python)

Issue:
[ENH] Implement Yeo-Johnson Series Transformer
### Describe the feature or idea you want to propose

a long time ago I experimented with the Yeo-Johnson regressor transform.

https://ieeexplore.ieee.org/document/1716845

Yeo-Johnson is an extension of Box-Cox that allows xero and negative regressor values. We have an implementation of Box Cox, it would be nice to include Yeo-Johnson 


### Describe your proposed solution

either extend Box Cox once it is moved into series tranformers, or implement a new BaseSeriesTransformer

### Describe alternatives you've considered, if relevant

_No response_

### Additional context

_No response_

Pull request description:
[ENH] Add Yeo Johnson Transform
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#### Reference Issues/PRs

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Fixes #1475

#### What does this implement/fix? Explain your changes.

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I have added the basic YeoJohnson Transform to the series transform section. This uses the scipy implementation to compute the transform, but implements the aeon interface on top of this.

#### Does your contribution introduce a new dependency? If yes, which one?

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No new dependencies

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N/A

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Patch:
diff --git a/aeon/transformations/series/_yeojohnson.py b/aeon/transformations/series/_yeojohnson.py
new file mode 100644
index 00000000..edc046bb
--- /dev/null
+++ b/aeon/transformations/series/_yeojohnson.py
@@ -0,0 +1,143 @@
+"""Implemenents Yeo-Johnson Transformation."""
+
+__maintainer__ = []
+__all__ = ["YeoJohnsonTransformer"]
+
+import numpy as np
+from numba import njit
+from scipy.stats import yeojohnson_normmax
+
+from aeon.transformations.series.base import BaseSeriesTransformer
+
+
+class YeoJohnsonTransformer(BaseSeriesTransformer):
+    r"""Yeo-Johnson power transform.
+
+    Yeo-Johnson transformation is related to the BoxCox transformation, and is
+    a power transformation that is used to make data more normally distributed
+    and stabilize its variance based on the hyperparameter lambda. [1]_
+
+    The YeoJohnsonTransformer solves for the lambda parameter used in the
+    Yeo-Johnson transformation using maximum likelihood estimation,
+    on input data provided to `fit`.
+
+    The Yeo-Johnson transformation is defined as :math:`\[
+        \phi(\lambda,y) =
+        \begin{cases}
+        log(y+1) & \text{if $\lambda=0, y\geq0$} \\
+        \frac{(y+1)^\lambda - 1}{\lambda} & \text{if $\lambda\neq0, y\geq0$} \\
+        -log(1-y) & \text{if $\lambda=2, y<0$} \\
+        -\frac{(1-y)^{2-\lambda}-1)}{2-\lambda} & \text{if $\lambda\neq2, y<0$}
+        \end{cases}
+    \]`.
+
+    Parameters
+    ----------
+    bounds : tuple
+        Lower and upper bounds used to restrict the feasible range
+        when solving for the value of lambda.
+    lambda_ : float
+        The Yeo-Johnson lambda parameter. If not supplied, it is solved for based
+        on the data provided in `fit`.
+
+    See Also
+    --------
+    aeon.transformations.boxcox.BoxCoxTransformer :
+        Transform input data by using the Box-Cox power transform. Used to
+        make data more normally distributed and stabilize its variance based
+        on the hyperparameter lambda.
+    aeon.transformations.boxcox.LogTransformer :
+        Transform input data using natural log. Can help normalize data and
+        compress variance of the series.
+    aeon.transformations.exponent.ExponentTransformer :
+        Transform input data by raising it to an exponent. Can help compress
+        variance of series if a fractional exponent is supplied.
+    aeon.transformations.exponent.SqrtTransformer :
+        Transform input data by taking its square root. Can help compress
+        variance of input series.
+
+    References
+    ----------
+    .. [1] Yeo and R.A. Johnson, “A New Family of Power Transformations to
+        Improve Normality or Symmetry”, Biometrika 87.4 (2000).
+
+    Examples
+    --------
+    >>> from aeon.transformations.series._yeojohnson import YeoJohnsonTransformer
+    >>> from aeon.datasets import load_airline
+    >>> y = load_airline()
+    >>> transformer = YeoJohnsonTransformer()
+    >>> y_hat = transformer.fit_transform(y)
+    """
+
+    # tag values specific to SeriesTransformers
+    _tags = {
+        "capability:univariate": True,
+        "capability:multivariate": False,
+    }
+
+    def __init__(self, lmbda=None, bounds=None):
+        self.bounds = bounds
+        self.lmbda = lmbda
+        super().__init__(axis=1)
+
+    def _fit(self, X, y=None):
+        """
+        Fit transformer to X and y.
+
+        private _fit containing the core logic, called from fit
+
+        Parameters
+        ----------
+        X : 2D np.ndarray (n x 1)
+            Data to be transformed
+        y : ignored argument for interface compatibility
+            Additional data, e.g., labels for transformation
+
+        Returns
+        -------
+        self: a fitted instance of the estimator
+        """
+        if self.lmbda is None:
+            X = X.flatten()
+            self._lambda = yeojohnson_normmax(X, brack=self.bounds)
+        else:
+            self._lambda = self.lmbda
+        return self
+
+    def _transform(self, X, y=None):
+        """Transform X and return a transformed version.
+
+        private _transform containing the core logic, called from transform
+
+        Parameters
+        ----------
+        X : 2D np.ndarray (1 x n_timepoints)
+            Data to be transformed
+        y : ignored argument for interface compatibility
+            Additional data, e.g., labels for transformation
+
+        Returns
+        -------
+        Xt : 2D np.ndarray
+            transformed version of X
+        """
+        return _yeo_johnson_transform(X, self._lambda)
+
+
+@njit(fastmath=True, cache=True)
+def _yeo_johnson_transform(X, lmbda):
+    X_shape = X.shape
+    Xt = X.flatten()
+    X_gte_0 = Xt >= 0
+    X_lt_0 = Xt < 0
+    if lmbda != 0:
+        Xt[X_gte_0] = (np.power(Xt[X_gte_0] + 1, lmbda) - 1) / lmbda
+    elif lmbda == 0:
+        Xt[X_gte_0] = np.log(Xt[X_gte_0] + 1)
+    if lmbda != 2:
+        Xt[X_lt_0] = -(np.power(-Xt[X_lt_0] + 1, 2 - lmbda) - 1) / (2 - lmbda)
+    elif lmbda == 2:
+        Xt[X_lt_0] = -np.log(-Xt[X_lt_0] + 1)
+    Xt = Xt.reshape(X_shape)
+    return Xt
diff --git a/docs/api_reference/transformations.rst b/docs/api_reference/transformations.rst
index d1c01552..d471923f 100644
--- a/docs/api_reference/transformations.rst
+++ b/docs/api_reference/transformations.rst
@@ -189,6 +189,7 @@ Series transforms
     StatsModelsPACF
     BKFilter
     BoxCoxTransformer
+    YeoJohnsonTransformer
     Dobin
     ScaledLogitSeriesTransformer
     SIVSeriesTransformer


Test patch:
diff --git a/aeon/transformations/series/tests/test_yeojohnson.py b/aeon/transformations/series/tests/test_yeojohnson.py
new file mode 100644
index 00000000..ddbf3e2f
--- /dev/null
+++ b/aeon/transformations/series/tests/test_yeojohnson.py
@@ -0,0 +1,21 @@
+"""Tests for YeoJohnsonTransformer."""
+
+__maintainer__ = []
+__all__ = []
+
+import numpy as np
+from scipy.stats import yeojohnson
+
+from aeon.datasets import load_airline
+from aeon.transformations.series._yeojohnson import YeoJohnsonTransformer
+
+
+def test_yeojohnson_against_scipy():
+    y = load_airline()
+
+    t = YeoJohnsonTransformer()
+    actual = t.fit_transform(y)
+
+    excepted, expected_lambda = yeojohnson(y.values)
+    np.testing.assert_almost_equal(actual, excepted, decimal=12)
+    assert t._lambda == expected_lambda