Vehicle-Anti-Theft-Face-Rec.../venv/Lib/site-packages/sklearn/svm/tests/test_svm.py

1290 lines
46 KiB
Python

"""
Testing for Support Vector Machine module (sklearn.svm)
TODO: remove hard coded numerical results when possible
"""
import numpy as np
import itertools
import pytest
from numpy.testing import assert_array_equal, assert_array_almost_equal
from numpy.testing import assert_almost_equal
from numpy.testing import assert_allclose
from scipy import sparse
from sklearn import svm, linear_model, datasets, metrics, base
from sklearn.svm import LinearSVC
from sklearn.svm import LinearSVR
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_classification, make_blobs
from sklearn.metrics import f1_score
from sklearn.metrics.pairwise import rbf_kernel
from sklearn.utils import check_random_state
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import assert_raise_message
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._testing import assert_no_warnings
from sklearn.utils.validation import _num_samples
from sklearn.utils import shuffle
from sklearn.exceptions import ConvergenceWarning
from sklearn.exceptions import NotFittedError, UndefinedMetricWarning
from sklearn.multiclass import OneVsRestClassifier
# mypy error: Module 'sklearn.svm' has no attribute '_libsvm'
from sklearn.svm import _libsvm # type: ignore
# toy sample
X = [[-2, -1], [-1, -1], [-1, -2], [1, 1], [1, 2], [2, 1]]
Y = [1, 1, 1, 2, 2, 2]
T = [[-1, -1], [2, 2], [3, 2]]
true_result = [1, 2, 2]
# also load the iris dataset
iris = datasets.load_iris()
rng = check_random_state(42)
perm = rng.permutation(iris.target.size)
iris.data = iris.data[perm]
iris.target = iris.target[perm]
def test_libsvm_parameters():
# Test parameters on classes that make use of libsvm.
clf = svm.SVC(kernel='linear').fit(X, Y)
assert_array_equal(clf.dual_coef_, [[-0.25, .25]])
assert_array_equal(clf.support_, [1, 3])
assert_array_equal(clf.support_vectors_, (X[1], X[3]))
assert_array_equal(clf.intercept_, [0.])
assert_array_equal(clf.predict(X), Y)
def test_libsvm_iris():
# Check consistency on dataset iris.
# shuffle the dataset so that labels are not ordered
for k in ('linear', 'rbf'):
clf = svm.SVC(kernel=k).fit(iris.data, iris.target)
assert np.mean(clf.predict(iris.data) == iris.target) > 0.9
assert hasattr(clf, "coef_") == (k == 'linear')
assert_array_equal(clf.classes_, np.sort(clf.classes_))
# check also the low-level API
model = _libsvm.fit(iris.data, iris.target.astype(np.float64))
pred = _libsvm.predict(iris.data, *model)
assert np.mean(pred == iris.target) > .95
model = _libsvm.fit(iris.data, iris.target.astype(np.float64),
kernel='linear')
pred = _libsvm.predict(iris.data, *model, kernel='linear')
assert np.mean(pred == iris.target) > .95
pred = _libsvm.cross_validation(iris.data,
iris.target.astype(np.float64), 5,
kernel='linear',
random_seed=0)
assert np.mean(pred == iris.target) > .95
# If random_seed >= 0, the libsvm rng is seeded (by calling `srand`), hence
# we should get deterministic results (assuming that there is no other
# thread calling this wrapper calling `srand` concurrently).
pred2 = _libsvm.cross_validation(iris.data,
iris.target.astype(np.float64), 5,
kernel='linear',
random_seed=0)
assert_array_equal(pred, pred2)
def test_precomputed():
# SVC with a precomputed kernel.
# We test it with a toy dataset and with iris.
clf = svm.SVC(kernel='precomputed')
# Gram matrix for train data (square matrix)
# (we use just a linear kernel)
K = np.dot(X, np.array(X).T)
clf.fit(K, Y)
# Gram matrix for test data (rectangular matrix)
KT = np.dot(T, np.array(X).T)
pred = clf.predict(KT)
with pytest.raises(ValueError):
clf.predict(KT.T)
assert_array_equal(clf.dual_coef_, [[-0.25, .25]])
assert_array_equal(clf.support_, [1, 3])
assert_array_equal(clf.intercept_, [0])
assert_array_almost_equal(clf.support_, [1, 3])
assert_array_equal(pred, true_result)
# Gram matrix for test data but compute KT[i,j]
# for support vectors j only.
KT = np.zeros_like(KT)
for i in range(len(T)):
for j in clf.support_:
KT[i, j] = np.dot(T[i], X[j])
pred = clf.predict(KT)
assert_array_equal(pred, true_result)
# same as before, but using a callable function instead of the kernel
# matrix. kernel is just a linear kernel
kfunc = lambda x, y: np.dot(x, y.T)
clf = svm.SVC(kernel=kfunc)
clf.fit(np.array(X), Y)
pred = clf.predict(T)
assert_array_equal(clf.dual_coef_, [[-0.25, .25]])
assert_array_equal(clf.intercept_, [0])
assert_array_almost_equal(clf.support_, [1, 3])
assert_array_equal(pred, true_result)
# test a precomputed kernel with the iris dataset
# and check parameters against a linear SVC
clf = svm.SVC(kernel='precomputed')
clf2 = svm.SVC(kernel='linear')
K = np.dot(iris.data, iris.data.T)
clf.fit(K, iris.target)
clf2.fit(iris.data, iris.target)
pred = clf.predict(K)
assert_array_almost_equal(clf.support_, clf2.support_)
assert_array_almost_equal(clf.dual_coef_, clf2.dual_coef_)
assert_array_almost_equal(clf.intercept_, clf2.intercept_)
assert_almost_equal(np.mean(pred == iris.target), .99, decimal=2)
# Gram matrix for test data but compute KT[i,j]
# for support vectors j only.
K = np.zeros_like(K)
for i in range(len(iris.data)):
for j in clf.support_:
K[i, j] = np.dot(iris.data[i], iris.data[j])
pred = clf.predict(K)
assert_almost_equal(np.mean(pred == iris.target), .99, decimal=2)
clf = svm.SVC(kernel=kfunc)
clf.fit(iris.data, iris.target)
assert_almost_equal(np.mean(pred == iris.target), .99, decimal=2)
def test_svr():
# Test Support Vector Regression
diabetes = datasets.load_diabetes()
for clf in (svm.NuSVR(kernel='linear', nu=.4, C=1.0),
svm.NuSVR(kernel='linear', nu=.4, C=10.),
svm.SVR(kernel='linear', C=10.),
svm.LinearSVR(C=10.),
svm.LinearSVR(C=10.)):
clf.fit(diabetes.data, diabetes.target)
assert clf.score(diabetes.data, diabetes.target) > 0.02
# non-regression test; previously, BaseLibSVM would check that
# len(np.unique(y)) < 2, which must only be done for SVC
svm.SVR().fit(diabetes.data, np.ones(len(diabetes.data)))
svm.LinearSVR().fit(diabetes.data, np.ones(len(diabetes.data)))
def test_linearsvr():
# check that SVR(kernel='linear') and LinearSVC() give
# comparable results
diabetes = datasets.load_diabetes()
lsvr = svm.LinearSVR(C=1e3).fit(diabetes.data, diabetes.target)
score1 = lsvr.score(diabetes.data, diabetes.target)
svr = svm.SVR(kernel='linear', C=1e3).fit(diabetes.data, diabetes.target)
score2 = svr.score(diabetes.data, diabetes.target)
assert_allclose(np.linalg.norm(lsvr.coef_),
np.linalg.norm(svr.coef_), 1, 0.0001)
assert_almost_equal(score1, score2, 2)
def test_linearsvr_fit_sampleweight():
# check correct result when sample_weight is 1
# check that SVR(kernel='linear') and LinearSVC() give
# comparable results
diabetes = datasets.load_diabetes()
n_samples = len(diabetes.target)
unit_weight = np.ones(n_samples)
lsvr = svm.LinearSVR(C=1e3, tol=1e-12, max_iter=10000).fit(
diabetes.data, diabetes.target, sample_weight=unit_weight)
score1 = lsvr.score(diabetes.data, diabetes.target)
lsvr_no_weight = svm.LinearSVR(C=1e3, tol=1e-12, max_iter=10000).fit(
diabetes.data, diabetes.target)
score2 = lsvr_no_weight.score(diabetes.data, diabetes.target)
assert_allclose(np.linalg.norm(lsvr.coef_),
np.linalg.norm(lsvr_no_weight.coef_), 1, 0.0001)
assert_almost_equal(score1, score2, 2)
# check that fit(X) = fit([X1, X2, X3],sample_weight = [n1, n2, n3]) where
# X = X1 repeated n1 times, X2 repeated n2 times and so forth
random_state = check_random_state(0)
random_weight = random_state.randint(0, 10, n_samples)
lsvr_unflat = svm.LinearSVR(C=1e3, tol=1e-12, max_iter=10000).fit(
diabetes.data, diabetes.target, sample_weight=random_weight)
score3 = lsvr_unflat.score(diabetes.data, diabetes.target,
sample_weight=random_weight)
X_flat = np.repeat(diabetes.data, random_weight, axis=0)
y_flat = np.repeat(diabetes.target, random_weight, axis=0)
lsvr_flat = svm.LinearSVR(C=1e3, tol=1e-12, max_iter=10000).fit(
X_flat, y_flat)
score4 = lsvr_flat.score(X_flat, y_flat)
assert_almost_equal(score3, score4, 2)
def test_svr_errors():
X = [[0.0], [1.0]]
y = [0.0, 0.5]
# Bad kernel
clf = svm.SVR(kernel=lambda x, y: np.array([[1.0]]))
clf.fit(X, y)
with pytest.raises(ValueError):
clf.predict(X)
def test_oneclass():
# Test OneClassSVM
clf = svm.OneClassSVM()
clf.fit(X)
pred = clf.predict(T)
assert_array_equal(pred, [1, -1, -1])
assert pred.dtype == np.dtype('intp')
assert_array_almost_equal(clf.intercept_, [-1.218], decimal=3)
assert_array_almost_equal(clf.dual_coef_,
[[0.750, 0.750, 0.750, 0.750]],
decimal=3)
with pytest.raises(AttributeError):
(lambda: clf.coef_)()
def test_oneclass_decision_function():
# Test OneClassSVM decision function
clf = svm.OneClassSVM()
rnd = check_random_state(2)
# Generate train data
X = 0.3 * rnd.randn(100, 2)
X_train = np.r_[X + 2, X - 2]
# Generate some regular novel observations
X = 0.3 * rnd.randn(20, 2)
X_test = np.r_[X + 2, X - 2]
# Generate some abnormal novel observations
X_outliers = rnd.uniform(low=-4, high=4, size=(20, 2))
# fit the model
clf = svm.OneClassSVM(nu=0.1, kernel="rbf", gamma=0.1)
clf.fit(X_train)
# predict things
y_pred_test = clf.predict(X_test)
assert np.mean(y_pred_test == 1) > .9
y_pred_outliers = clf.predict(X_outliers)
assert np.mean(y_pred_outliers == -1) > .9
dec_func_test = clf.decision_function(X_test)
assert_array_equal((dec_func_test > 0).ravel(), y_pred_test == 1)
dec_func_outliers = clf.decision_function(X_outliers)
assert_array_equal((dec_func_outliers > 0).ravel(), y_pred_outliers == 1)
def test_oneclass_score_samples():
X_train = [[1, 1], [1, 2], [2, 1]]
clf = svm.OneClassSVM(gamma=1).fit(X_train)
assert_array_equal(clf.score_samples([[2., 2.]]),
clf.decision_function([[2., 2.]]) + clf.offset_)
def test_tweak_params():
# Make sure some tweaking of parameters works.
# We change clf.dual_coef_ at run time and expect .predict() to change
# accordingly. Notice that this is not trivial since it involves a lot
# of C/Python copying in the libsvm bindings.
# The success of this test ensures that the mapping between libsvm and
# the python classifier is complete.
clf = svm.SVC(kernel='linear', C=1.0)
clf.fit(X, Y)
assert_array_equal(clf.dual_coef_, [[-.25, .25]])
assert_array_equal(clf.predict([[-.1, -.1]]), [1])
clf._dual_coef_ = np.array([[.0, 1.]])
assert_array_equal(clf.predict([[-.1, -.1]]), [2])
def test_probability():
# Predict probabilities using SVC
# This uses cross validation, so we use a slightly bigger testing set.
for clf in (svm.SVC(probability=True, random_state=0, C=1.0),
svm.NuSVC(probability=True, random_state=0)):
clf.fit(iris.data, iris.target)
prob_predict = clf.predict_proba(iris.data)
assert_array_almost_equal(
np.sum(prob_predict, 1), np.ones(iris.data.shape[0]))
assert np.mean(np.argmax(prob_predict, 1)
== clf.predict(iris.data)) > 0.9
assert_almost_equal(clf.predict_proba(iris.data),
np.exp(clf.predict_log_proba(iris.data)), 8)
def test_decision_function():
# Test decision_function
# Sanity check, test that decision_function implemented in python
# returns the same as the one in libsvm
# multi class:
clf = svm.SVC(kernel='linear', C=0.1,
decision_function_shape='ovo').fit(iris.data, iris.target)
dec = np.dot(iris.data, clf.coef_.T) + clf.intercept_
assert_array_almost_equal(dec, clf.decision_function(iris.data))
# binary:
clf.fit(X, Y)
dec = np.dot(X, clf.coef_.T) + clf.intercept_
prediction = clf.predict(X)
assert_array_almost_equal(dec.ravel(), clf.decision_function(X))
assert_array_almost_equal(
prediction,
clf.classes_[(clf.decision_function(X) > 0).astype(np.int)])
expected = np.array([-1., -0.66, -1., 0.66, 1., 1.])
assert_array_almost_equal(clf.decision_function(X), expected, 2)
# kernel binary:
clf = svm.SVC(kernel='rbf', gamma=1, decision_function_shape='ovo')
clf.fit(X, Y)
rbfs = rbf_kernel(X, clf.support_vectors_, gamma=clf.gamma)
dec = np.dot(rbfs, clf.dual_coef_.T) + clf.intercept_
assert_array_almost_equal(dec.ravel(), clf.decision_function(X))
@pytest.mark.parametrize('SVM', (svm.SVC, svm.NuSVC))
def test_decision_function_shape(SVM):
# check that decision_function_shape='ovr' or 'ovo' gives
# correct shape and is consistent with predict
clf = SVM(kernel='linear',
decision_function_shape='ovr').fit(iris.data, iris.target)
dec = clf.decision_function(iris.data)
assert dec.shape == (len(iris.data), 3)
assert_array_equal(clf.predict(iris.data), np.argmax(dec, axis=1))
# with five classes:
X, y = make_blobs(n_samples=80, centers=5, random_state=0)
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)
clf = SVM(kernel='linear',
decision_function_shape='ovr').fit(X_train, y_train)
dec = clf.decision_function(X_test)
assert dec.shape == (len(X_test), 5)
assert_array_equal(clf.predict(X_test), np.argmax(dec, axis=1))
# check shape of ovo_decition_function=True
clf = SVM(kernel='linear',
decision_function_shape='ovo').fit(X_train, y_train)
dec = clf.decision_function(X_train)
assert dec.shape == (len(X_train), 10)
with pytest.raises(ValueError, match="must be either 'ovr' or 'ovo'"):
SVM(decision_function_shape='bad').fit(X_train, y_train)
def test_svr_predict():
# Test SVR's decision_function
# Sanity check, test that predict implemented in python
# returns the same as the one in libsvm
X = iris.data
y = iris.target
# linear kernel
reg = svm.SVR(kernel='linear', C=0.1).fit(X, y)
dec = np.dot(X, reg.coef_.T) + reg.intercept_
assert_array_almost_equal(dec.ravel(), reg.predict(X).ravel())
# rbf kernel
reg = svm.SVR(kernel='rbf', gamma=1).fit(X, y)
rbfs = rbf_kernel(X, reg.support_vectors_, gamma=reg.gamma)
dec = np.dot(rbfs, reg.dual_coef_.T) + reg.intercept_
assert_array_almost_equal(dec.ravel(), reg.predict(X).ravel())
def test_weight():
# Test class weights
clf = svm.SVC(class_weight={1: 0.1})
# we give a small weights to class 1
clf.fit(X, Y)
# so all predicted values belong to class 2
assert_array_almost_equal(clf.predict(X), [2] * 6)
X_, y_ = make_classification(n_samples=200, n_features=10,
weights=[0.833, 0.167], random_state=2)
for clf in (linear_model.LogisticRegression(),
svm.LinearSVC(random_state=0), svm.SVC()):
clf.set_params(class_weight={0: .1, 1: 10})
clf.fit(X_[:100], y_[:100])
y_pred = clf.predict(X_[100:])
assert f1_score(y_[100:], y_pred) > .3
@pytest.mark.parametrize("estimator", [svm.SVC(C=1e-2), svm.NuSVC()])
def test_svm_classifier_sided_sample_weight(estimator):
# fit a linear SVM and check that giving more weight to opposed samples
# in the space will flip the decision toward these samples.
X = [[-2, 0], [-1, -1], [0, -2], [0, 2], [1, 1], [2, 0]]
estimator.set_params(kernel='linear')
# check that with unit weights, a sample is supposed to be predicted on
# the boundary
sample_weight = [1] * 6
estimator.fit(X, Y, sample_weight=sample_weight)
y_pred = estimator.decision_function([[-1., 1.]])
assert y_pred == pytest.approx(0)
# give more weights to opposed samples
sample_weight = [10., .1, .1, .1, .1, 10]
estimator.fit(X, Y, sample_weight=sample_weight)
y_pred = estimator.decision_function([[-1., 1.]])
assert y_pred < 0
sample_weight = [1., .1, 10., 10., .1, .1]
estimator.fit(X, Y, sample_weight=sample_weight)
y_pred = estimator.decision_function([[-1., 1.]])
assert y_pred > 0
@pytest.mark.parametrize(
"estimator",
[svm.SVR(C=1e-2), svm.NuSVR(C=1e-2)]
)
def test_svm_regressor_sided_sample_weight(estimator):
# similar test to test_svm_classifier_sided_sample_weight but for
# SVM regressors
X = [[-2, 0], [-1, -1], [0, -2], [0, 2], [1, 1], [2, 0]]
estimator.set_params(kernel='linear')
# check that with unit weights, a sample is supposed to be predicted on
# the boundary
sample_weight = [1] * 6
estimator.fit(X, Y, sample_weight=sample_weight)
y_pred = estimator.predict([[-1., 1.]])
assert y_pred == pytest.approx(1.5)
# give more weights to opposed samples
sample_weight = [10., .1, .1, .1, .1, 10]
estimator.fit(X, Y, sample_weight=sample_weight)
y_pred = estimator.predict([[-1., 1.]])
assert y_pred < 1.5
sample_weight = [1., .1, 10., 10., .1, .1]
estimator.fit(X, Y, sample_weight=sample_weight)
y_pred = estimator.predict([[-1., 1.]])
assert y_pred > 1.5
def test_svm_equivalence_sample_weight_C():
# test that rescaling all samples is the same as changing C
clf = svm.SVC()
clf.fit(X, Y)
dual_coef_no_weight = clf.dual_coef_
clf.set_params(C=100)
clf.fit(X, Y, sample_weight=np.repeat(0.01, len(X)))
assert_allclose(dual_coef_no_weight, clf.dual_coef_)
@pytest.mark.parametrize(
"Estimator, err_msg",
[(svm.SVC,
'Invalid input - all samples have zero or negative weights.'),
(svm.NuSVC, '(negative dimensions are not allowed|nu is infeasible)'),
(svm.SVR,
'Invalid input - all samples have zero or negative weights.'),
(svm.NuSVR,
'Invalid input - all samples have zero or negative weights.'),
(svm.OneClassSVM,
'Invalid input - all samples have zero or negative weights.')
],
ids=['SVC', 'NuSVC', 'SVR', 'NuSVR', 'OneClassSVM']
)
@pytest.mark.parametrize(
"sample_weight",
[[0] * len(Y), [-0.3] * len(Y)],
ids=['weights-are-zero', 'weights-are-negative']
)
def test_negative_sample_weights_mask_all_samples(Estimator,
err_msg, sample_weight):
est = Estimator(kernel='linear')
with pytest.raises(ValueError, match=err_msg):
est.fit(X, Y, sample_weight=sample_weight)
@pytest.mark.parametrize(
"Classifier, err_msg",
[(svm.SVC,
'Invalid input - all samples with positive weights have the same label'),
(svm.NuSVC, 'specified nu is infeasible')],
ids=['SVC', 'NuSVC']
)
@pytest.mark.parametrize(
"sample_weight",
[[0, -0.5, 0, 1, 1, 1],
[1, 1, 1, 0, -0.1, -0.3]],
ids=['mask-label-1', 'mask-label-2']
)
def test_negative_weights_svc_leave_just_one_label(Classifier,
err_msg,
sample_weight):
clf = Classifier(kernel='linear')
with pytest.raises(ValueError, match=err_msg):
clf.fit(X, Y, sample_weight=sample_weight)
@pytest.mark.parametrize(
"Classifier, model",
[(svm.SVC, {'when-left': [0.3998, 0.4], 'when-right': [0.4, 0.3999]}),
(svm.NuSVC, {'when-left': [0.3333, 0.3333],
'when-right': [0.3333, 0.3333]})],
ids=['SVC', 'NuSVC']
)
@pytest.mark.parametrize(
"sample_weight, mask_side",
[([1, -0.5, 1, 1, 1, 1], 'when-left'),
([1, 1, 1, 0, 1, 1], 'when-right')],
ids=['partial-mask-label-1', 'partial-mask-label-2']
)
def test_negative_weights_svc_leave_two_labels(Classifier, model,
sample_weight, mask_side):
clf = Classifier(kernel='linear')
clf.fit(X, Y, sample_weight=sample_weight)
assert_allclose(clf.coef_, [model[mask_side]], rtol=1e-3)
@pytest.mark.parametrize(
"Estimator",
[svm.SVC, svm.NuSVC, svm.NuSVR],
ids=['SVC', 'NuSVC', 'NuSVR']
)
@pytest.mark.parametrize(
"sample_weight",
[[1, -0.5, 1, 1, 1, 1], [1, 1, 1, 0, 1, 1]],
ids=['partial-mask-label-1', 'partial-mask-label-2']
)
def test_negative_weight_equal_coeffs(Estimator, sample_weight):
# model generates equal coefficients
est = Estimator(kernel='linear')
est.fit(X, Y, sample_weight=sample_weight)
coef = np.abs(est.coef_).ravel()
assert coef[0] == pytest.approx(coef[1], rel=1e-3)
@ignore_warnings(category=UndefinedMetricWarning)
def test_auto_weight():
# Test class weights for imbalanced data
from sklearn.linear_model import LogisticRegression
# We take as dataset the two-dimensional projection of iris so
# that it is not separable and remove half of predictors from
# class 1.
# We add one to the targets as a non-regression test:
# class_weight="balanced"
# used to work only when the labels where a range [0..K).
from sklearn.utils import compute_class_weight
X, y = iris.data[:, :2], iris.target + 1
unbalanced = np.delete(np.arange(y.size), np.where(y > 2)[0][::2])
classes = np.unique(y[unbalanced])
class_weights = compute_class_weight('balanced', classes=classes,
y=y[unbalanced])
assert np.argmax(class_weights) == 2
for clf in (svm.SVC(kernel='linear'), svm.LinearSVC(random_state=0),
LogisticRegression()):
# check that score is better when class='balanced' is set.
y_pred = clf.fit(X[unbalanced], y[unbalanced]).predict(X)
clf.set_params(class_weight='balanced')
y_pred_balanced = clf.fit(X[unbalanced], y[unbalanced],).predict(X)
assert (metrics.f1_score(y, y_pred, average='macro')
<= metrics.f1_score(y, y_pred_balanced,
average='macro'))
def test_bad_input():
# Test that it gives proper exception on deficient input
# impossible value of C
with pytest.raises(ValueError):
svm.SVC(C=-1).fit(X, Y)
# impossible value of nu
clf = svm.NuSVC(nu=0.0)
with pytest.raises(ValueError):
clf.fit(X, Y)
Y2 = Y[:-1] # wrong dimensions for labels
with pytest.raises(ValueError):
clf.fit(X, Y2)
# Test with arrays that are non-contiguous.
for clf in (svm.SVC(), svm.LinearSVC(random_state=0)):
Xf = np.asfortranarray(X)
assert not Xf.flags['C_CONTIGUOUS']
yf = np.ascontiguousarray(np.tile(Y, (2, 1)).T)
yf = yf[:, -1]
assert not yf.flags['F_CONTIGUOUS']
assert not yf.flags['C_CONTIGUOUS']
clf.fit(Xf, yf)
assert_array_equal(clf.predict(T), true_result)
# error for precomputed kernelsx
clf = svm.SVC(kernel='precomputed')
with pytest.raises(ValueError):
clf.fit(X, Y)
# predict with sparse input when trained with dense
clf = svm.SVC().fit(X, Y)
with pytest.raises(ValueError):
clf.predict(sparse.lil_matrix(X))
Xt = np.array(X).T
clf.fit(np.dot(X, Xt), Y)
with pytest.raises(ValueError):
clf.predict(X)
clf = svm.SVC()
clf.fit(X, Y)
with pytest.raises(ValueError):
clf.predict(Xt)
@pytest.mark.parametrize(
'Estimator, data',
[(svm.SVC, datasets.load_iris(return_X_y=True)),
(svm.NuSVC, datasets.load_iris(return_X_y=True)),
(svm.SVR, datasets.load_diabetes(return_X_y=True)),
(svm.NuSVR, datasets.load_diabetes(return_X_y=True)),
(svm.OneClassSVM, datasets.load_iris(return_X_y=True))]
)
def test_svm_gamma_error(Estimator, data):
X, y = data
est = Estimator(gamma='auto_deprecated')
err_msg = "When 'gamma' is a string, it should be either 'scale' or 'auto'"
with pytest.raises(ValueError, match=err_msg):
est.fit(X, y)
def test_unicode_kernel():
# Test that a unicode kernel name does not cause a TypeError
clf = svm.SVC(kernel='linear', probability=True)
clf.fit(X, Y)
clf.predict_proba(T)
_libsvm.cross_validation(iris.data,
iris.target.astype(np.float64), 5,
kernel='linear',
random_seed=0)
def test_sparse_precomputed():
clf = svm.SVC(kernel='precomputed')
sparse_gram = sparse.csr_matrix([[1, 0], [0, 1]])
with pytest.raises(TypeError, match="Sparse precomputed"):
clf.fit(sparse_gram, [0, 1])
def test_sparse_fit_support_vectors_empty():
# Regression test for #14893
X_train = sparse.csr_matrix([[0, 1, 0, 0],
[0, 0, 0, 1],
[0, 0, 1, 0],
[0, 0, 0, 1]])
y_train = np.array([0.04, 0.04, 0.10, 0.16])
model = svm.SVR(kernel='linear')
model.fit(X_train, y_train)
assert not model.support_vectors_.data.size
assert not model.dual_coef_.data.size
def test_linearsvc_parameters():
# Test possible parameter combinations in LinearSVC
# Generate list of possible parameter combinations
losses = ['hinge', 'squared_hinge', 'logistic_regression', 'foo']
penalties, duals = ['l1', 'l2', 'bar'], [True, False]
X, y = make_classification(n_samples=5, n_features=5)
for loss, penalty, dual in itertools.product(losses, penalties, duals):
clf = svm.LinearSVC(penalty=penalty, loss=loss, dual=dual)
if ((loss, penalty) == ('hinge', 'l1') or
(loss, penalty, dual) == ('hinge', 'l2', False) or
(penalty, dual) == ('l1', True) or
loss == 'foo' or penalty == 'bar'):
with pytest.raises(ValueError, match="Unsupported set of "
"arguments.*penalty='%s.*loss='%s.*dual=%s"
% (penalty, loss, dual)):
clf.fit(X, y)
else:
clf.fit(X, y)
# Incorrect loss value - test if explicit error message is raised
with pytest.raises(ValueError, match=".*loss='l3' is not supported.*"):
svm.LinearSVC(loss="l3").fit(X, y)
def test_linear_svx_uppercase_loss_penality_raises_error():
# Check if Upper case notation raises error at _fit_liblinear
# which is called by fit
X, y = [[0.0], [1.0]], [0, 1]
assert_raise_message(ValueError, "loss='SQuared_hinge' is not supported",
svm.LinearSVC(loss="SQuared_hinge").fit, X, y)
assert_raise_message(ValueError,
("The combination of penalty='L2'"
" and loss='squared_hinge' is not supported"),
svm.LinearSVC(penalty="L2").fit, X, y)
def test_linearsvc():
# Test basic routines using LinearSVC
clf = svm.LinearSVC(random_state=0).fit(X, Y)
# by default should have intercept
assert clf.fit_intercept
assert_array_equal(clf.predict(T), true_result)
assert_array_almost_equal(clf.intercept_, [0], decimal=3)
# the same with l1 penalty
clf = svm.LinearSVC(penalty='l1', loss='squared_hinge', dual=False,
random_state=0).fit(X, Y)
assert_array_equal(clf.predict(T), true_result)
# l2 penalty with dual formulation
clf = svm.LinearSVC(penalty='l2', dual=True, random_state=0).fit(X, Y)
assert_array_equal(clf.predict(T), true_result)
# l2 penalty, l1 loss
clf = svm.LinearSVC(penalty='l2', loss='hinge', dual=True, random_state=0)
clf.fit(X, Y)
assert_array_equal(clf.predict(T), true_result)
# test also decision function
dec = clf.decision_function(T)
res = (dec > 0).astype(np.int) + 1
assert_array_equal(res, true_result)
def test_linearsvc_crammer_singer():
# Test LinearSVC with crammer_singer multi-class svm
ovr_clf = svm.LinearSVC(random_state=0).fit(iris.data, iris.target)
cs_clf = svm.LinearSVC(multi_class='crammer_singer', random_state=0)
cs_clf.fit(iris.data, iris.target)
# similar prediction for ovr and crammer-singer:
assert (ovr_clf.predict(iris.data) ==
cs_clf.predict(iris.data)).mean() > .9
# classifiers shouldn't be the same
assert (ovr_clf.coef_ != cs_clf.coef_).all()
# test decision function
assert_array_equal(cs_clf.predict(iris.data),
np.argmax(cs_clf.decision_function(iris.data), axis=1))
dec_func = np.dot(iris.data, cs_clf.coef_.T) + cs_clf.intercept_
assert_array_almost_equal(dec_func, cs_clf.decision_function(iris.data))
def test_linearsvc_fit_sampleweight():
# check correct result when sample_weight is 1
n_samples = len(X)
unit_weight = np.ones(n_samples)
clf = svm.LinearSVC(random_state=0).fit(X, Y)
clf_unitweight = svm.LinearSVC(random_state=0, tol=1e-12, max_iter=1000).\
fit(X, Y, sample_weight=unit_weight)
# check if same as sample_weight=None
assert_array_equal(clf_unitweight.predict(T), clf.predict(T))
assert_allclose(clf.coef_, clf_unitweight.coef_, 1, 0.0001)
# check that fit(X) = fit([X1, X2, X3],sample_weight = [n1, n2, n3]) where
# X = X1 repeated n1 times, X2 repeated n2 times and so forth
random_state = check_random_state(0)
random_weight = random_state.randint(0, 10, n_samples)
lsvc_unflat = svm.LinearSVC(random_state=0, tol=1e-12, max_iter=1000).\
fit(X, Y, sample_weight=random_weight)
pred1 = lsvc_unflat.predict(T)
X_flat = np.repeat(X, random_weight, axis=0)
y_flat = np.repeat(Y, random_weight, axis=0)
lsvc_flat = svm.LinearSVC(random_state=0, tol=1e-12, max_iter=1000).fit(
X_flat, y_flat)
pred2 = lsvc_flat.predict(T)
assert_array_equal(pred1, pred2)
assert_allclose(lsvc_unflat.coef_, lsvc_flat.coef_, 1, 0.0001)
def test_crammer_singer_binary():
# Test Crammer-Singer formulation in the binary case
X, y = make_classification(n_classes=2, random_state=0)
for fit_intercept in (True, False):
acc = svm.LinearSVC(fit_intercept=fit_intercept,
multi_class="crammer_singer",
random_state=0).fit(X, y).score(X, y)
assert acc > 0.9
def test_linearsvc_iris():
# Test that LinearSVC gives plausible predictions on the iris dataset
# Also, test symbolic class names (classes_).
target = iris.target_names[iris.target]
clf = svm.LinearSVC(random_state=0).fit(iris.data, target)
assert set(clf.classes_) == set(iris.target_names)
assert np.mean(clf.predict(iris.data) == target) > 0.8
dec = clf.decision_function(iris.data)
pred = iris.target_names[np.argmax(dec, 1)]
assert_array_equal(pred, clf.predict(iris.data))
def test_dense_liblinear_intercept_handling(classifier=svm.LinearSVC):
# Test that dense liblinear honours intercept_scaling param
X = [[2, 1],
[3, 1],
[1, 3],
[2, 3]]
y = [0, 0, 1, 1]
clf = classifier(fit_intercept=True, penalty='l1', loss='squared_hinge',
dual=False, C=4, tol=1e-7, random_state=0)
assert clf.intercept_scaling == 1, clf.intercept_scaling
assert clf.fit_intercept
# when intercept_scaling is low the intercept value is highly "penalized"
# by regularization
clf.intercept_scaling = 1
clf.fit(X, y)
assert_almost_equal(clf.intercept_, 0, decimal=5)
# when intercept_scaling is sufficiently high, the intercept value
# is not affected by regularization
clf.intercept_scaling = 100
clf.fit(X, y)
intercept1 = clf.intercept_
assert intercept1 < -1
# when intercept_scaling is sufficiently high, the intercept value
# doesn't depend on intercept_scaling value
clf.intercept_scaling = 1000
clf.fit(X, y)
intercept2 = clf.intercept_
assert_array_almost_equal(intercept1, intercept2, decimal=2)
def test_liblinear_set_coef():
# multi-class case
clf = svm.LinearSVC().fit(iris.data, iris.target)
values = clf.decision_function(iris.data)
clf.coef_ = clf.coef_.copy()
clf.intercept_ = clf.intercept_.copy()
values2 = clf.decision_function(iris.data)
assert_array_almost_equal(values, values2)
# binary-class case
X = [[2, 1],
[3, 1],
[1, 3],
[2, 3]]
y = [0, 0, 1, 1]
clf = svm.LinearSVC().fit(X, y)
values = clf.decision_function(X)
clf.coef_ = clf.coef_.copy()
clf.intercept_ = clf.intercept_.copy()
values2 = clf.decision_function(X)
assert_array_equal(values, values2)
def test_immutable_coef_property():
# Check that primal coef modification are not silently ignored
svms = [
svm.SVC(kernel='linear').fit(iris.data, iris.target),
svm.NuSVC(kernel='linear').fit(iris.data, iris.target),
svm.SVR(kernel='linear').fit(iris.data, iris.target),
svm.NuSVR(kernel='linear').fit(iris.data, iris.target),
svm.OneClassSVM(kernel='linear').fit(iris.data),
]
for clf in svms:
with pytest.raises(AttributeError):
clf.__setattr__('coef_', np.arange(3))
with pytest.raises((RuntimeError, ValueError)):
clf.coef_.__setitem__((0, 0), 0)
def test_linearsvc_verbose():
# stdout: redirect
import os
stdout = os.dup(1) # save original stdout
os.dup2(os.pipe()[1], 1) # replace it
# actual call
clf = svm.LinearSVC(verbose=1)
clf.fit(X, Y)
# stdout: restore
os.dup2(stdout, 1) # restore original stdout
def test_svc_clone_with_callable_kernel():
# create SVM with callable linear kernel, check that results are the same
# as with built-in linear kernel
svm_callable = svm.SVC(kernel=lambda x, y: np.dot(x, y.T),
probability=True, random_state=0,
decision_function_shape='ovr')
# clone for checking clonability with lambda functions..
svm_cloned = base.clone(svm_callable)
svm_cloned.fit(iris.data, iris.target)
svm_builtin = svm.SVC(kernel='linear', probability=True, random_state=0,
decision_function_shape='ovr')
svm_builtin.fit(iris.data, iris.target)
assert_array_almost_equal(svm_cloned.dual_coef_,
svm_builtin.dual_coef_)
assert_array_almost_equal(svm_cloned.intercept_,
svm_builtin.intercept_)
assert_array_equal(svm_cloned.predict(iris.data),
svm_builtin.predict(iris.data))
assert_array_almost_equal(svm_cloned.predict_proba(iris.data),
svm_builtin.predict_proba(iris.data),
decimal=4)
assert_array_almost_equal(svm_cloned.decision_function(iris.data),
svm_builtin.decision_function(iris.data))
def test_svc_bad_kernel():
svc = svm.SVC(kernel=lambda x, y: x)
with pytest.raises(ValueError):
svc.fit(X, Y)
def test_timeout():
a = svm.SVC(kernel=lambda x, y: np.dot(x, y.T), probability=True,
random_state=0, max_iter=1)
assert_warns(ConvergenceWarning, a.fit, np.array(X), Y)
def test_unfitted():
X = "foo!" # input validation not required when SVM not fitted
clf = svm.SVC()
with pytest.raises(Exception, match=r".*\bSVC\b.*\bnot\b.*\bfitted\b"):
clf.predict(X)
clf = svm.NuSVR()
with pytest.raises(Exception, match=r".*\bNuSVR\b.*\bnot\b.*\bfitted\b"):
clf.predict(X)
# ignore convergence warnings from max_iter=1
@ignore_warnings
def test_consistent_proba():
a = svm.SVC(probability=True, max_iter=1, random_state=0)
proba_1 = a.fit(X, Y).predict_proba(X)
a = svm.SVC(probability=True, max_iter=1, random_state=0)
proba_2 = a.fit(X, Y).predict_proba(X)
assert_array_almost_equal(proba_1, proba_2)
def test_linear_svm_convergence_warnings():
# Test that warnings are raised if model does not converge
lsvc = svm.LinearSVC(random_state=0, max_iter=2)
assert_warns(ConvergenceWarning, lsvc.fit, X, Y)
assert lsvc.n_iter_ == 2
lsvr = svm.LinearSVR(random_state=0, max_iter=2)
assert_warns(ConvergenceWarning, lsvr.fit, iris.data, iris.target)
assert lsvr.n_iter_ == 2
def test_svr_coef_sign():
# Test that SVR(kernel="linear") has coef_ with the right sign.
# Non-regression test for #2933.
X = np.random.RandomState(21).randn(10, 3)
y = np.random.RandomState(12).randn(10)
for svr in [svm.SVR(kernel='linear'), svm.NuSVR(kernel='linear'),
svm.LinearSVR()]:
svr.fit(X, y)
assert_array_almost_equal(
svr.predict(X), np.dot(X, svr.coef_.ravel()) + svr.intercept_
)
def test_linear_svc_intercept_scaling():
# Test that the right error message is thrown when intercept_scaling <= 0
for i in [-1, 0]:
lsvc = svm.LinearSVC(intercept_scaling=i)
msg = ('Intercept scaling is %r but needs to be greater than 0.'
' To disable fitting an intercept,'
' set fit_intercept=False.' % lsvc.intercept_scaling)
assert_raise_message(ValueError, msg, lsvc.fit, X, Y)
def test_lsvc_intercept_scaling_zero():
# Test that intercept_scaling is ignored when fit_intercept is False
lsvc = svm.LinearSVC(fit_intercept=False)
lsvc.fit(X, Y)
assert lsvc.intercept_ == 0.
def test_hasattr_predict_proba():
# Method must be (un)available before or after fit, switched by
# `probability` param
G = svm.SVC(probability=True)
assert hasattr(G, 'predict_proba')
G.fit(iris.data, iris.target)
assert hasattr(G, 'predict_proba')
G = svm.SVC(probability=False)
assert not hasattr(G, 'predict_proba')
G.fit(iris.data, iris.target)
assert not hasattr(G, 'predict_proba')
# Switching to `probability=True` after fitting should make
# predict_proba available, but calling it must not work:
G.probability = True
assert hasattr(G, 'predict_proba')
msg = "predict_proba is not available when fitted with probability=False"
assert_raise_message(NotFittedError, msg, G.predict_proba, iris.data)
def test_decision_function_shape_two_class():
for n_classes in [2, 3]:
X, y = make_blobs(centers=n_classes, random_state=0)
for estimator in [svm.SVC, svm.NuSVC]:
clf = OneVsRestClassifier(
estimator(decision_function_shape="ovr")).fit(X, y)
assert len(clf.predict(X)) == len(y)
def test_ovr_decision_function():
# One point from each quadrant represents one class
X_train = np.array([[1, 1], [-1, 1], [-1, -1], [1, -1]])
y_train = [0, 1, 2, 3]
# First point is closer to the decision boundaries than the second point
base_points = np.array([[5, 5], [10, 10]])
# For all the quadrants (classes)
X_test = np.vstack((
base_points * [1, 1], # Q1
base_points * [-1, 1], # Q2
base_points * [-1, -1], # Q3
base_points * [1, -1] # Q4
))
y_test = [0] * 2 + [1] * 2 + [2] * 2 + [3] * 2
clf = svm.SVC(kernel='linear', decision_function_shape='ovr')
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
# Test if the prediction is the same as y
assert_array_equal(y_pred, y_test)
deci_val = clf.decision_function(X_test)
# Assert that the predicted class has the maximum value
assert_array_equal(np.argmax(deci_val, axis=1), y_pred)
# Get decision value at test points for the predicted class
pred_class_deci_val = deci_val[range(8), y_pred].reshape((4, 2))
# Assert pred_class_deci_val > 0 here
assert np.min(pred_class_deci_val) > 0.0
# Test if the first point has lower decision value on every quadrant
# compared to the second point
assert np.all(pred_class_deci_val[:, 0] < pred_class_deci_val[:, 1])
@pytest.mark.parametrize("SVCClass", [svm.SVC, svm.NuSVC])
def test_svc_invalid_break_ties_param(SVCClass):
X, y = make_blobs(random_state=42)
svm = SVCClass(kernel="linear", decision_function_shape='ovo',
break_ties=True, random_state=42).fit(X, y)
with pytest.raises(ValueError, match="break_ties must be False"):
svm.predict(y)
@pytest.mark.parametrize("SVCClass", [svm.SVC, svm.NuSVC])
def test_svc_ovr_tie_breaking(SVCClass):
"""Test if predict breaks ties in OVR mode.
Related issue: https://github.com/scikit-learn/scikit-learn/issues/8277
"""
X, y = make_blobs(random_state=27)
xs = np.linspace(X[:, 0].min(), X[:, 0].max(), 1000)
ys = np.linspace(X[:, 1].min(), X[:, 1].max(), 1000)
xx, yy = np.meshgrid(xs, ys)
svm = SVCClass(kernel="linear", decision_function_shape='ovr',
break_ties=False, random_state=42).fit(X, y)
pred = svm.predict(np.c_[xx.ravel(), yy.ravel()])
dv = svm.decision_function(np.c_[xx.ravel(), yy.ravel()])
assert not np.all(pred == np.argmax(dv, axis=1))
svm = SVCClass(kernel="linear", decision_function_shape='ovr',
break_ties=True, random_state=42).fit(X, y)
pred = svm.predict(np.c_[xx.ravel(), yy.ravel()])
dv = svm.decision_function(np.c_[xx.ravel(), yy.ravel()])
assert np.all(pred == np.argmax(dv, axis=1))
def test_gamma_auto():
X, y = [[0.0, 1.2], [1.0, 1.3]], [0, 1]
assert_no_warnings(svm.SVC(kernel='linear').fit, X, y)
assert_no_warnings(svm.SVC(kernel='precomputed').fit, X, y)
def test_gamma_scale():
X, y = [[0.], [1.]], [0, 1]
clf = svm.SVC()
assert_no_warnings(clf.fit, X, y)
assert_almost_equal(clf._gamma, 4)
# X_var ~= 1 shouldn't raise warning, for when
# gamma is not explicitly set.
X, y = [[1, 2], [3, 2 * np.sqrt(6) / 3 + 2]], [0, 1]
assert_no_warnings(clf.fit, X, y)
@pytest.mark.parametrize(
"SVM, params",
[(LinearSVC, {'penalty': 'l1', 'loss': 'squared_hinge', 'dual': False}),
(LinearSVC, {'penalty': 'l2', 'loss': 'squared_hinge', 'dual': True}),
(LinearSVC, {'penalty': 'l2', 'loss': 'squared_hinge', 'dual': False}),
(LinearSVC, {'penalty': 'l2', 'loss': 'hinge', 'dual': True}),
(LinearSVR, {'loss': 'epsilon_insensitive', 'dual': True}),
(LinearSVR, {'loss': 'squared_epsilon_insensitive', 'dual': True}),
(LinearSVR, {'loss': 'squared_epsilon_insensitive', 'dual': True})]
)
def test_linearsvm_liblinear_sample_weight(SVM, params):
X = np.array([[1, 3], [1, 3], [1, 3], [1, 3],
[2, 1], [2, 1], [2, 1], [2, 1],
[3, 3], [3, 3], [3, 3], [3, 3],
[4, 1], [4, 1], [4, 1], [4, 1]], dtype=np.dtype('float'))
y = np.array([1, 1, 1, 1, 2, 2, 2, 2,
1, 1, 1, 1, 2, 2, 2, 2], dtype=np.dtype('int'))
X2 = np.vstack([X, X])
y2 = np.hstack([y, 3 - y])
sample_weight = np.ones(shape=len(y) * 2)
sample_weight[len(y):] = 0
X2, y2, sample_weight = shuffle(X2, y2, sample_weight, random_state=0)
base_estimator = SVM(random_state=42)
base_estimator.set_params(**params)
base_estimator.set_params(tol=1e-12, max_iter=1000)
est_no_weight = base.clone(base_estimator).fit(X, y)
est_with_weight = base.clone(base_estimator).fit(
X2, y2, sample_weight=sample_weight
)
for method in ("predict", "decision_function"):
if hasattr(base_estimator, method):
X_est_no_weight = getattr(est_no_weight, method)(X)
X_est_with_weight = getattr(est_with_weight, method)(X)
assert_allclose(X_est_no_weight, X_est_with_weight)
def test_n_support_oneclass_svr():
# Make n_support is correct for oneclass and SVR (used to be
# non-initialized)
# this is a non regression test for issue #14774
X = np.array([[0], [0.44], [0.45], [0.46], [1]])
clf = svm.OneClassSVM()
assert not hasattr(clf, 'n_support_')
clf.fit(X)
assert clf.n_support_ == clf.support_vectors_.shape[0]
assert clf.n_support_.size == 1
assert clf.n_support_ == 3
y = np.arange(X.shape[0])
reg = svm.SVR().fit(X, y)
assert reg.n_support_ == reg.support_vectors_.shape[0]
assert reg.n_support_.size == 1
assert reg.n_support_ == 4
# TODO: Remove in 0.25 when probA_ and probB_ are deprecated
@pytest.mark.parametrize("SVMClass, data", [
(svm.OneClassSVM, (X, )),
(svm.SVR, (X, Y))
])
@pytest.mark.parametrize("deprecated_prob", ["probA_", "probB_"])
def test_svm_probA_proB_deprecated(SVMClass, data, deprecated_prob):
clf = SVMClass().fit(*data)
msg = ("The {} attribute is deprecated in version 0.23 and will be "
"removed in version 0.25.").format(deprecated_prob)
with pytest.warns(FutureWarning, match=msg):
getattr(clf, deprecated_prob)
@pytest.mark.parametrize("Estimator", [svm.SVC, svm.SVR])
def test_custom_kernel_not_array_input(Estimator):
"""Test using a custom kernel that is not fed with array-like for floats"""
data = ["A A", "A", "B", "B B", "A B"]
X = np.array([[2, 0], [1, 0], [0, 1], [0, 2], [1, 1]]) # count encoding
y = np.array([1, 1, 2, 2, 1])
def string_kernel(X1, X2):
assert isinstance(X1[0], str)
n_samples1 = _num_samples(X1)
n_samples2 = _num_samples(X2)
K = np.zeros((n_samples1, n_samples2))
for ii in range(n_samples1):
for jj in range(ii, n_samples2):
K[ii, jj] = X1[ii].count('A') * X2[jj].count('A')
K[ii, jj] += X1[ii].count('B') * X2[jj].count('B')
K[jj, ii] = K[ii, jj]
return K
K = string_kernel(data, data)
assert_array_equal(np.dot(X, X.T), K)
svc1 = Estimator(kernel=string_kernel).fit(data, y)
svc2 = Estimator(kernel='linear').fit(X, y)
svc3 = Estimator(kernel='precomputed').fit(K, y)
assert svc1.score(data, y) == svc3.score(K, y)
assert svc1.score(data, y) == svc2.score(X, y)
if hasattr(svc1, 'decision_function'): # classifier
assert_allclose(svc1.decision_function(data),
svc2.decision_function(X))
assert_allclose(svc1.decision_function(data),
svc3.decision_function(K))
assert_array_equal(svc1.predict(data), svc2.predict(X))
assert_array_equal(svc1.predict(data), svc3.predict(K))
else: # regressor
assert_allclose(svc1.predict(data), svc2.predict(X))
assert_allclose(svc1.predict(data), svc3.predict(K))