def test_lda_numeric_consistency_float32_float64():
for (solver, shrinkage) in solver_shrinkage:
clf_32 = LinearDiscriminantAnalysis(solver=solver, shrinkage=shrinkage)
clf_32.fit(X.astype(np.float32), y.astype(np.float32))
clf_64 = LinearDiscriminantAnalysis(solver=solver, shrinkage=shrinkage)
clf_64.fit(X.astype(np.float64), y.astype(np.float64))
# Check value consistency between types
rtol = 1e-6
assert_allclose(clf_32.coef_, clf_64.coef_, rtol=rtol)
def test_raises_value_error_on_same_number_of_classes_and_samples(solver):
"""
Tests that if the number of samples equals the number
of classes, a ValueError is raised.
"""
X = np.array([[0.5, 0.6], [0.6, 0.5]])
y = np.array(["a", "b"])
clf = LinearDiscriminantAnalysis(solver=solver)
with pytest.raises(ValueError, match="The number of samples must be more"):
clf.fit(X, y)
def test_lda_transform():
# Test LDA transform.
clf = LinearDiscriminantAnalysis(solver="svd", n_components=1)
X_transformed = clf.fit(X, y).transform(X)
assert X_transformed.shape[1] == 1
clf = LinearDiscriminantAnalysis(solver="eigen", n_components=1)
X_transformed = clf.fit(X, y).transform(X)
assert X_transformed.shape[1] == 1
clf = LinearDiscriminantAnalysis(solver="lsqr", n_components=1)
clf.fit(X, y)
msg = "transform not implemented for 'lsqr'"
assert_raise_message(NotImplementedError, msg, clf.transform, X)
def test_lda_priors():
# Test priors (negative priors)
priors = np.array([0.5, -0.5])
clf = LinearDiscriminantAnalysis(priors=priors)
msg = "priors must be non-negative"
assert_raise_message(ValueError, msg, clf.fit, X, y)
# Test that priors passed as a list are correctly handled (run to see if
# failure)
clf = LinearDiscriminantAnalysis(priors=[0.5, 0.5])
clf.fit(X, y)
# Test that priors always sum to 1
priors = np.array([0.5, 0.6])
prior_norm = np.array([0.45, 0.55])
clf = LinearDiscriminantAnalysis(priors=priors)
assert_warns(UserWarning, clf.fit, X, y)
assert_array_almost_equal(clf.priors_, prior_norm, 2)
def test_lda_predict():
# Test LDA classification.
# This checks that LDA implements fit and predict and returns correct
# values for simple toy data.
for test_case in solver_shrinkage:
solver, shrinkage = test_case
clf = LinearDiscriminantAnalysis(solver=solver, shrinkage=shrinkage)
y_pred = clf.fit(X, y).predict(X)
assert_array_equal(y_pred, y, 'solver %s' % solver)
# Assert that it works with 1D data
y_pred1 = clf.fit(X1, y).predict(X1)
assert_array_equal(y_pred1, y, 'solver %s' % solver)
# Test probability estimates
y_proba_pred1 = clf.predict_proba(X1)
assert_array_equal((y_proba_pred1[:, 1] > 0.5) + 1, y,
'solver %s' % solver)
y_log_proba_pred1 = clf.predict_log_proba(X1)
assert_array_almost_equal(np.exp(y_log_proba_pred1), y_proba_pred1, 8,
'solver %s' % solver)
# Primarily test for commit 2f34950 -- "reuse" of priors
y_pred3 = clf.fit(X, y3).predict(X)
# LDA shouldn't be able to separate those
assert np.any(y_pred3 != y3), 'solver %s' % solver
# Test invalid shrinkages
clf = LinearDiscriminantAnalysis(solver="lsqr", shrinkage=-0.2231)
assert_raises(ValueError, clf.fit, X, y)
clf = LinearDiscriminantAnalysis(solver="eigen", shrinkage="dummy")
assert_raises(ValueError, clf.fit, X, y)
clf = LinearDiscriminantAnalysis(solver="svd", shrinkage="auto")
assert_raises(NotImplementedError, clf.fit, X, y)
# Test unknown solver
clf = LinearDiscriminantAnalysis(solver="dummy")
assert_raises(ValueError, clf.fit, X, y)
def test_lda_explained_variance_ratio():
# Test if the sum of the normalized eigen vectors values equals 1,
# Also tests whether the explained_variance_ratio_ formed by the
# eigen solver is the same as the explained_variance_ratio_ formed
# by the svd solver
state = np.random.RandomState(0)
X = state.normal(loc=0, scale=100, size=(40, 20))
y = state.randint(0, 3, size=(40, ))
clf_lda_eigen = LinearDiscriminantAnalysis(solver="eigen")
clf_lda_eigen.fit(X, y)
assert_almost_equal(clf_lda_eigen.explained_variance_ratio_.sum(), 1.0, 3)
assert clf_lda_eigen.explained_variance_ratio_.shape == (2, ), (
"Unexpected length for explained_variance_ratio_")
clf_lda_svd = LinearDiscriminantAnalysis(solver="svd")
clf_lda_svd.fit(X, y)
assert_almost_equal(clf_lda_svd.explained_variance_ratio_.sum(), 1.0, 3)
assert clf_lda_svd.explained_variance_ratio_.shape == (2, ), (
"Unexpected length for explained_variance_ratio_")
assert_array_almost_equal(clf_lda_svd.explained_variance_ratio_,
clf_lda_eigen.explained_variance_ratio_)
def test_lda_scaling():
# Test if classification works correctly with differently scaled features.
n = 100
rng = np.random.RandomState(1234)
# use uniform distribution of features to make sure there is absolutely no
# overlap between classes.
x1 = rng.uniform(-1, 1, (n, 3)) + [-10, 0, 0]
x2 = rng.uniform(-1, 1, (n, 3)) + [10, 0, 0]
x = np.vstack((x1, x2)) * [1, 100, 10000]
y = [-1] * n + [1] * n
for solver in ('svd', 'lsqr', 'eigen'):
clf = LinearDiscriminantAnalysis(solver=solver)
# should be able to separate the data perfectly
assert clf.fit(x, y).score(x,
y) == 1.0, ('using covariance: %s' % solver)
def test_lda_coefs():
# Test if the coefficients of the solvers are approximately the same.
n_features = 2
n_classes = 2
n_samples = 1000
X, y = make_blobs(n_samples=n_samples,
n_features=n_features,
centers=n_classes,
random_state=11)
clf_lda_svd = LinearDiscriminantAnalysis(solver="svd")
clf_lda_lsqr = LinearDiscriminantAnalysis(solver="lsqr")
clf_lda_eigen = LinearDiscriminantAnalysis(solver="eigen")
clf_lda_svd.fit(X, y)
clf_lda_lsqr.fit(X, y)
clf_lda_eigen.fit(X, y)
assert_array_almost_equal(clf_lda_svd.coef_, clf_lda_lsqr.coef_, 1)
assert_array_almost_equal(clf_lda_svd.coef_, clf_lda_eigen.coef_, 1)
assert_array_almost_equal(clf_lda_eigen.coef_, clf_lda_lsqr.coef_, 1)
from mrex import datasets
from mrex.decomposition import PCA
from mrex.discriminant_analysis import LinearDiscriminantAnalysis
iris = datasets.load_iris()
X = iris.data
y = iris.target
target_names = iris.target_names
pca = PCA(n_components=2)
X_r = pca.fit(X).transform(X)
lda = LinearDiscriminantAnalysis(n_components=2)
X_r2 = lda.fit(X, y).transform(X)
# Percentage of variance explained for each components
print('explained variance ratio (first two components): %s' %
str(pca.explained_variance_ratio_))
plt.figure()
colors = ['navy', 'turquoise', 'darkorange']
lw = 2
for color, i, target_name in zip(colors, [0, 1, 2], target_names):
plt.scatter(X_r[y == i, 0],
X_r[y == i, 1],
color=color,
alpha=.8,
lw=lw,
def test_lda_dtype_match(data_type, expected_type):
for (solver, shrinkage) in solver_shrinkage:
clf = LinearDiscriminantAnalysis(solver=solver, shrinkage=shrinkage)
clf.fit(X.astype(data_type), y.astype(data_type))
assert clf.coef_.dtype == expected_type
plot_ellipse(splot, lda.means_[0], lda.covariance_, 'red')
plot_ellipse(splot, lda.means_[1], lda.covariance_, 'blue')
def plot_qda_cov(qda, splot):
plot_ellipse(splot, qda.means_[0], qda.covariance_[0], 'red')
plot_ellipse(splot, qda.means_[1], qda.covariance_[1], 'blue')
plt.figure(figsize=(10, 8), facecolor='white')
plt.suptitle('Linear Discriminant Analysis vs Quadratic Discriminant Analysis',
y=0.98,
fontsize=15)
for i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):
# Linear Discriminant Analysis
lda = LinearDiscriminantAnalysis(solver="svd", store_covariance=True)
y_pred = lda.fit(X, y).predict(X)
splot = plot_data(lda, X, y, y_pred, fig_index=2 * i + 1)
plot_lda_cov(lda, splot)
plt.axis('tight')
# Quadratic Discriminant Analysis
qda = QuadraticDiscriminantAnalysis(store_covariance=True)
y_pred = qda.fit(X, y).predict(X)
splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)
plot_qda_cov(qda, splot)
plt.axis('tight')
plt.tight_layout()
plt.subplots_adjust(top=0.92)
plt.show()