def _fit(self, x, y=None):
"""Fit the PCA using input data.
Parameters
----------
x : array_like
Training data, 2-Dim array like object with shape
(n_patterns, n_features), where each row is a pattern
of n_features columns.
y : CArray or None, optional
Flat array with the label of each pattern.
Can be None if not required by the preprocessing algorithm.
Returns
-------
CPCA
Instance of the trained transformer.
Examples
--------
>>> from secml.array import CArray
>>> from secml.ml.features.reduction import CPCA
>>> array = CArray([[1., 0., 2.], [2., 5., 0.], [0., 1., -9.]])
>>> pca = CPCA().fit(array)
>>> pca.eigenval
CArray(3,)(dense: [8.390159e+00 3.777816e+00 1.909570e-17])
>>> pca.eigenvec
CArray(3, 3)(dense: [[-0.486132 -0.656005 0.57735 ] [-0.325051 0.749005 0.57735 ] [ 0.811183 -0.093 0.57735 ]])
>>> pca.explained_variance
CArray(3,)(dense: [3.519739e+01 7.135946e+00 1.823230e-34])
>>> pca.explained_variance_ratio
CArray(3,)(dense: [8.314343e-01 1.685657e-01 4.306842e-36])
"""
data_carray = CArray(x).todense().atleast_2d()
# Max number of components is the number of patterns available (rows)
n_samples = data_carray.shape[0]
n_features = data_carray.shape[1]
if self.n_components is None:
self.n_components = min(n_samples, n_features)
else:
if self.n_components > n_samples:
raise ValueError(
"maximum number of components is {:}".format(n_samples))
# Centering training data
self._mean = data_carray.mean(axis=0, keepdims=False)
data_carray -= self.mean
# Performing training of PCA (used by KernelPCA too)
return self._svd_train(data_carray)
def _objective_function(self, xc, acc=False):
"""
Parameters
----------
xc: poisoning point
Returns
-------
f_obj: values of objective function (average hinge loss) at x
"""
# index of poisoning point within xc.
# This will be replaced by the input parameter xc
if self._idx is None:
idx = 0
self._xc = xc
self._yc = 1
else:
idx = self._idx
xc = CArray(xc).atleast_2d()
n_samples = xc.shape[0]
if n_samples > 1:
raise TypeError("xc is not a single sample!")
self._xc[idx, :] = xc
clf, tr = self._update_poisoned_clf()
# targeted attacks
y_ts = self._y_target if self._y_target is not None else self.val.Y
y_pred, score = clf.predict(self.val.X, return_decision_function=True)
# TODO: binary loss check
if self._attacker_loss.class_type != 'softmax':
score = CArray(score[:, 1].ravel())
if acc is True:
error = CArray(y_ts != y_pred).ravel() # compute test error
else:
error = self._attacker_loss.loss(y_ts, score)
obj = error.mean()
return obj
