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