168 lines
6.2 KiB
Python
168 lines
6.2 KiB
Python
# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
|
|
# Gael Varoquaux <gael.varoquaux@normalesup.org>
|
|
# Virgile Fritsch <virgile.fritsch@inria.fr>
|
|
#
|
|
# License: BSD 3 clause
|
|
|
|
import itertools
|
|
|
|
import numpy as np
|
|
|
|
from sklearn.utils._testing import assert_array_almost_equal
|
|
from sklearn.utils._testing import assert_raise_message
|
|
from sklearn.utils._testing import assert_warns_message
|
|
|
|
from sklearn import datasets
|
|
from sklearn.covariance import empirical_covariance, MinCovDet
|
|
from sklearn.covariance import fast_mcd
|
|
|
|
X = datasets.load_iris().data
|
|
X_1d = X[:, 0]
|
|
n_samples, n_features = X.shape
|
|
|
|
|
|
def test_mcd():
|
|
# Tests the FastMCD algorithm implementation
|
|
# Small data set
|
|
# test without outliers (random independent normal data)
|
|
launch_mcd_on_dataset(100, 5, 0, 0.01, 0.1, 80)
|
|
# test with a contaminated data set (medium contamination)
|
|
launch_mcd_on_dataset(100, 5, 20, 0.01, 0.01, 70)
|
|
# test with a contaminated data set (strong contamination)
|
|
launch_mcd_on_dataset(100, 5, 40, 0.1, 0.1, 50)
|
|
|
|
# Medium data set
|
|
launch_mcd_on_dataset(1000, 5, 450, 0.1, 0.1, 540)
|
|
|
|
# Large data set
|
|
launch_mcd_on_dataset(1700, 5, 800, 0.1, 0.1, 870)
|
|
|
|
# 1D data set
|
|
launch_mcd_on_dataset(500, 1, 100, 0.001, 0.001, 350)
|
|
|
|
|
|
def test_fast_mcd_on_invalid_input():
|
|
X = np.arange(100)
|
|
assert_raise_message(ValueError, 'Expected 2D array, got 1D array instead',
|
|
fast_mcd, X)
|
|
|
|
|
|
def test_mcd_class_on_invalid_input():
|
|
X = np.arange(100)
|
|
mcd = MinCovDet()
|
|
assert_raise_message(ValueError, 'Expected 2D array, got 1D array instead',
|
|
mcd.fit, X)
|
|
|
|
|
|
def launch_mcd_on_dataset(n_samples, n_features, n_outliers, tol_loc, tol_cov,
|
|
tol_support):
|
|
|
|
rand_gen = np.random.RandomState(0)
|
|
data = rand_gen.randn(n_samples, n_features)
|
|
# add some outliers
|
|
outliers_index = rand_gen.permutation(n_samples)[:n_outliers]
|
|
outliers_offset = 10. * \
|
|
(rand_gen.randint(2, size=(n_outliers, n_features)) - 0.5)
|
|
data[outliers_index] += outliers_offset
|
|
inliers_mask = np.ones(n_samples).astype(bool)
|
|
inliers_mask[outliers_index] = False
|
|
|
|
pure_data = data[inliers_mask]
|
|
# compute MCD by fitting an object
|
|
mcd_fit = MinCovDet(random_state=rand_gen).fit(data)
|
|
T = mcd_fit.location_
|
|
S = mcd_fit.covariance_
|
|
H = mcd_fit.support_
|
|
# compare with the estimates learnt from the inliers
|
|
error_location = np.mean((pure_data.mean(0) - T) ** 2)
|
|
assert(error_location < tol_loc)
|
|
error_cov = np.mean((empirical_covariance(pure_data) - S) ** 2)
|
|
assert(error_cov < tol_cov)
|
|
assert(np.sum(H) >= tol_support)
|
|
assert_array_almost_equal(mcd_fit.mahalanobis(data), mcd_fit.dist_)
|
|
|
|
|
|
def test_mcd_issue1127():
|
|
# Check that the code does not break with X.shape = (3, 1)
|
|
# (i.e. n_support = n_samples)
|
|
rnd = np.random.RandomState(0)
|
|
X = rnd.normal(size=(3, 1))
|
|
mcd = MinCovDet()
|
|
mcd.fit(X)
|
|
|
|
|
|
def test_mcd_issue3367():
|
|
# Check that MCD completes when the covariance matrix is singular
|
|
# i.e. one of the rows and columns are all zeros
|
|
rand_gen = np.random.RandomState(0)
|
|
|
|
# Think of these as the values for X and Y -> 10 values between -5 and 5
|
|
data_values = np.linspace(-5, 5, 10).tolist()
|
|
# Get the cartesian product of all possible coordinate pairs from above set
|
|
data = np.array(list(itertools.product(data_values, data_values)))
|
|
|
|
# Add a third column that's all zeros to make our data a set of point
|
|
# within a plane, which means that the covariance matrix will be singular
|
|
data = np.hstack((data, np.zeros((data.shape[0], 1))))
|
|
|
|
# The below line of code should raise an exception if the covariance matrix
|
|
# is singular. As a further test, since we have points in XYZ, the
|
|
# principle components (Eigenvectors) of these directly relate to the
|
|
# geometry of the points. Since it's a plane, we should be able to test
|
|
# that the Eigenvector that corresponds to the smallest Eigenvalue is the
|
|
# plane normal, specifically [0, 0, 1], since everything is in the XY plane
|
|
# (as I've set it up above). To do this one would start by:
|
|
#
|
|
# evals, evecs = np.linalg.eigh(mcd_fit.covariance_)
|
|
# normal = evecs[:, np.argmin(evals)]
|
|
#
|
|
# After which we need to assert that our `normal` is equal to [0, 0, 1].
|
|
# Do note that there is floating point error associated with this, so it's
|
|
# best to subtract the two and then compare some small tolerance (e.g.
|
|
# 1e-12).
|
|
MinCovDet(random_state=rand_gen).fit(data)
|
|
|
|
|
|
def test_mcd_support_covariance_is_zero():
|
|
# Check that MCD returns a ValueError with informative message when the
|
|
# covariance of the support data is equal to 0.
|
|
X_1 = np.array([0.5, 0.1, 0.1, 0.1, 0.957, 0.1, 0.1, 0.1, 0.4285, 0.1])
|
|
X_1 = X_1.reshape(-1, 1)
|
|
X_2 = np.array([0.5, 0.3, 0.3, 0.3, 0.957, 0.3, 0.3, 0.3, 0.4285, 0.3])
|
|
X_2 = X_2.reshape(-1, 1)
|
|
msg = ('The covariance matrix of the support data is equal to 0, try to '
|
|
'increase support_fraction')
|
|
for X in [X_1, X_2]:
|
|
assert_raise_message(ValueError, msg, MinCovDet().fit, X)
|
|
|
|
|
|
def test_mcd_increasing_det_warning():
|
|
# Check that a warning is raised if we observe increasing determinants
|
|
# during the c_step. In theory the sequence of determinants should be
|
|
# decreasing. Increasing determinants are likely due to ill-conditioned
|
|
# covariance matrices that result in poor precision matrices.
|
|
|
|
X = [[5.1, 3.5, 1.4, 0.2],
|
|
[4.9, 3.0, 1.4, 0.2],
|
|
[4.7, 3.2, 1.3, 0.2],
|
|
[4.6, 3.1, 1.5, 0.2],
|
|
[5.0, 3.6, 1.4, 0.2],
|
|
[4.6, 3.4, 1.4, 0.3],
|
|
[5.0, 3.4, 1.5, 0.2],
|
|
[4.4, 2.9, 1.4, 0.2],
|
|
[4.9, 3.1, 1.5, 0.1],
|
|
[5.4, 3.7, 1.5, 0.2],
|
|
[4.8, 3.4, 1.6, 0.2],
|
|
[4.8, 3.0, 1.4, 0.1],
|
|
[4.3, 3.0, 1.1, 0.1],
|
|
[5.1, 3.5, 1.4, 0.3],
|
|
[5.7, 3.8, 1.7, 0.3],
|
|
[5.4, 3.4, 1.7, 0.2],
|
|
[4.6, 3.6, 1.0, 0.2],
|
|
[5.0, 3.0, 1.6, 0.2],
|
|
[5.2, 3.5, 1.5, 0.2]]
|
|
|
|
mcd = MinCovDet(random_state=1)
|
|
assert_warns_message(RuntimeWarning,
|
|
"Determinant has increased",
|
|
mcd.fit, X)
|