import numpy as np
from .base import BaseThresholder
from .thresh_utility import cut, gen_kde
[docs]
class FGD(BaseThresholder):
"""FGD class for Fixed Gradient Descent thresholder.
Use the fixed gradient descent to evaluate a non-parametric means
to threshold scores generated by the decision_scores where outliers
are set to any value beyond where the first derivative of the kde
with respect to the decision scores passes the mean of the first
and second inflection points. See :cite:`qi2021fgd` for details.
Parameters
----------
fallback : str ('ignore', 'warn', 'raise'), optional (default='warn')
The action to take for thresholders when their criterion are
not met. In these cases when set to 'ignore' on eval and fit
all train data is set to inliers and the threshold is set to
max of the train scores + eps. Passing 'warn' will do the same as
'ignore' but also produce a warning. If 'raise', the thresholder
raises a ValueError.
random_state : int, optional (default=1234)
Random seed for the random number generators of the thresholders. Can also
be set to None.
Attributes
----------
thresh_ : threshold value that separates inliers from outliers
dscores_ : 1D array of decomposed decision scores
Notes
-----
A probability distribution of the decision scores is generated using
kernel density estimation. The first derivative of the pdf is
calculated, and the threshold is set as the middle point between the
first and second inflection points starting from the left side of the
data range.
"""
def __init__(self, fallback="warn", random_state=1234):
super().__init__(fallback=fallback)
self.random_state = random_state
np.random.seed(random_state)
[docs]
def eval(self, decision):
"""Outlier/inlier evaluation process for decision scores.
Parameters
----------
decision : np.array or list of shape (n_samples)
or np.array of shape (n_samples, n_detectors)
which are the decision scores from a
outlier detection.
Returns
-------
outlier_labels : numpy array of shape (n_samples,)
For each observation, tells whether or not
it should be considered as an outlier according to the
fitted model. 0 stands for inliers and 1 for outliers.
"""
decision = self._data_setup(decision)
# Generate KDE
val, dat_range = gen_kde(decision, 0, 1, len(decision) * 3)
# Calculate the first derivative of the KDE with respect
# to the data range
deriv = np.gradient(val, dat_range[1] - dat_range[0])
count = 0
ind = []
# Find the first two inflection points
for i in range(len(deriv) - 1):
if (deriv[i] > 0) & (deriv[i + 1] <= 0):
count += 1
ind.append(i)
if count == 2:
break
eps = np.finfo(decision.dtype).eps
limit = (dat_range[ind[0]] + dat_range[ind[1]]) / 2 if len(ind) > 1 else 1.0 + eps
self._check_threshold(limit)
self.thresh_ = limit
return cut(decision, limit)