import numpy as np
from robpy.preprocessing.utils import wrapping_transformation
from robpy.covariance.base import RobustCovariance
[docs]
class WrappingCovariance(RobustCovariance):
def __init__(
self,
b: float = 1.5,
c: float = 4.0,
q1: float = 1.540793,
q2: float = 0.8622731,
store_precision: bool = True,
assume_centered: bool = False,
):
"""
Covariance estimator based on the wrapping function proposed in Raymaekers, J., &
Rousseeuw, P. J. (2021).
The wrapping transformation is defined as follows:
.. math::
\\Psi_{b, c}(z) =
\\begin{cases}
z & \\text{if } \\ 0 \\leq |z| < b, \\\\
q_1 \\tanh\\left(q_2 (c - |z|)\\right) \\mathrm{sign}(z) & \\text{if } \\ b \\leq |z|
\\leq c,\\\\
0 & \\text{if } \\ c < |z|.
\\end{cases}
The data is first scaled using the median and the MAD before applying the transformation.
Next, the robust covariance of X is computed from the classical covariance on the
transformed data:
.. math::
Cov(Median(X) + MAD(X) * \\Psi_{b, c}(X - Median(X) / MAD(X)))
Args:
b (float, optional):
Lower cutoff. Defaults to 1.5.
c (float, optional):
Upper cutoff. Defaults to 4.0.
q1 (float, optional):
Transformation parameter (see formula). Defaults to 1.540793.
q2 (float, optional):
Transformation parameter (see formula). Defaults to 0.8622731.
store_precision (bool, optional):
Whether to store the precision matrix. Defaults to True.
assume_centered (bool, optional):
Whether the data is already centered. Defaults to False.
References:
- Raymaekers, J., & Rousseeuw, P. J. (2021). Fast robust correlation for
high-dimensional data. Technometrics, 63(2), 184-198.
"""
super().__init__(store_precision=store_precision, assume_centered=assume_centered)
self.b = b
self.c = c
self.q1 = q1
self.q2 = q2
[docs]
def calculate_covariance(self, X: np.ndarray) -> np.ndarray:
"""
Calculate the covariance matrix of the data X after applying the wrapping transformation.
Args:
X (np.ndarray): Data to calculate the covariance matrix of, must have shape (n, p).
Returns:
np.ndarray: Robust covariance matrix of X.
"""
X_transformed = wrapping_transformation(
X, b=self.b, c=self.c, q1=self.q1, q2=self.q2, rescale=True
)
self.correlation_ = np.corrcoef(X_transformed, rowvar=False)
return np.cov(X_transformed, rowvar=False)