import numpy as np
from robpy.preprocessing.utils import wrapping_transformation
from robpy.covariance.base import RobustCovariance
[docs]
class WrappingCovariance(RobustCovariance):
"""Covariance estimator based on the wrapping function proposed in
Jakob Raymaekers & Peter J. Rousseeuw (2021)
The wrapping transformation is defined as follows:
.. math::
\\Psi_{b, c}(z) =
\\begin{cases}
z & if \\ 0 \\leq |z| < b \\\\
q_1 \\tanh\\left(q_2 (c - |z|)\\right) \\mathrm{sign}(z) & if \\ b \\leq |z| \\leq c \\\\
0 & if \\ c < |z|
\\end{cases}
Data is first scaled using median and MAD before applying the transformation.
The (standard) covariance is subsequently estimated on the rescaled data
Cov(X) = Cov(Median(X) + MAD(X) * phi(X - Median(X) / MAD(X)))
References:
- Jakob Raymaekers & Peter J. Rousseeuw (2021)
Fast Robust Correlation for High-Dimensional Data,
Technometrics, 63:2, 184-198, DOI: 10.1080/00401706.2019.1677270
"""
def __init__(
self,
b: float = 1.5,
c: float = 4.0,
q1: float = 1.540793,
q2: float = 0.8622731,
rescale: bool = True,
store_precision: bool = True,
assume_centered: bool = False,
):
"""
Args:
X: data to be transformed, must have shape (N, D)
b: lower cutoff
c: upper cutoff
q1, q2: transformation parameters (see formula)
rescale: whether to rescale the wrapped data so the robust location and scale
of the transformed data are the same as the original data
"""
super().__init__(store_precision=store_precision, assume_centered=assume_centered)
self.b = b
self.c = c
self.q1 = q1
self.q2 = q2
self.rescale = rescale
[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: data to calculate the covariance matrix of, must have shape (N, D)
Returns:
robust covariance matrix of X
"""
X_transformed = wrapping_transformation(
X, b=self.b, c=self.c, q1=self.q1, q2=self.q2, rescale=self.rescale
)
self.correlation_ = np.corrcoef(X_transformed, rowvar=False)
return np.cov(X_transformed, rowvar=False)