"""
Todo: cross-check the F-value with stats model
"""
import itertools
import warnings
import numpy as np
from scipy import stats, sparse
import pytest
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._testing import assert_warns_message
from sklearn.utils import safe_mask
from sklearn.datasets import make_classification, make_regression
from sklearn.feature_selection import (
chi2, f_classif, f_oneway, f_regression, mutual_info_classif,
mutual_info_regression, SelectPercentile, SelectKBest, SelectFpr,
SelectFdr, SelectFwe, GenericUnivariateSelect)
##############################################################################
# Test the score functions
def test_f_oneway_vs_scipy_stats():
# Test that our f_oneway gives the same result as scipy.stats
rng = np.random.RandomState(0)
X1 = rng.randn(10, 3)
X2 = 1 + rng.randn(10, 3)
f, pv = stats.f_oneway(X1, X2)
f2, pv2 = f_oneway(X1, X2)
assert np.allclose(f, f2)
assert np.allclose(pv, pv2)
def test_f_oneway_ints():
# Smoke test f_oneway on integers: that it does raise casting errors
# with recent numpys
rng = np.random.RandomState(0)
X = rng.randint(10, size=(10, 10))
y = np.arange(10)
fint, pint = f_oneway(X, y)
# test that is gives the same result as with float
f, p = f_oneway(X.astype(np.float), y)
assert_array_almost_equal(f, fint, decimal=4)
assert_array_almost_equal(p, pint, decimal=4)
def test_f_classif():
# Test whether the F test yields meaningful results
# on a simple simulated classification problem
X, y = make_classification(n_samples=200, n_features=20,
n_informative=3, n_redundant=2,
n_repeated=0, n_classes=8,
n_clusters_per_class=1, flip_y=0.0,
class_sep=10, shuffle=False, random_state=0)
F, pv = f_classif(X, y)
F_sparse, pv_sparse = f_classif(sparse.csr_matrix(X), y)
assert (F > 0).all()
assert (pv > 0).all()
assert (pv < 1).all()
assert (pv[:5] < 0.05).all()
assert (pv[5:] > 1.e-4).all()
assert_array_almost_equal(F_sparse, F)
assert_array_almost_equal(pv_sparse, pv)
def test_f_regression():
# Test whether the F test yields meaningful results
# on a simple simulated regression problem
X, y = make_regression(n_samples=200, n_features=20, n_informative=5,
shuffle=False, random_state=0)
F, pv = f_regression(X, y)
assert (F > 0).all()
assert (pv > 0).all()
assert (pv < 1).all()
assert (pv[:5] < 0.05).all()
assert (pv[5:] > 1.e-4).all()
# with centering, compare with sparse
F, pv = f_regression(X, y, center=True)
F_sparse, pv_sparse = f_regression(sparse.csr_matrix(X), y, center=True)
assert_array_almost_equal(F_sparse, F)
assert_array_almost_equal(pv_sparse, pv)
# again without centering, compare with sparse
F, pv = f_regression(X, y, center=False)
F_sparse, pv_sparse = f_regression(sparse.csr_matrix(X), y, center=False)
assert_array_almost_equal(F_sparse, F)
assert_array_almost_equal(pv_sparse, pv)
def test_f_regression_input_dtype():
# Test whether f_regression returns the same value
# for any numeric data_type
rng = np.random.RandomState(0)
X = rng.rand(10, 20)
y = np.arange(10).astype(np.int)
F1, pv1 = f_regression(X, y)
F2, pv2 = f_regression(X, y.astype(np.float))
assert_array_almost_equal(F1, F2, 5)
assert_array_almost_equal(pv1, pv2, 5)
def test_f_regression_center():
# Test whether f_regression preserves dof according to 'center' argument
# We use two centered variates so we have a simple relationship between
# F-score with variates centering and F-score without variates centering.
# Create toy example
X = np.arange(-5, 6).reshape(-1, 1) # X has zero mean
n_samples = X.size
Y = np.ones(n_samples)
Y[::2] *= -1.
Y[0] = 0. # have Y mean being null
F1, _ = f_regression(X, Y, center=True)
F2, _ = f_regression(X, Y, center=False)
assert_array_almost_equal(F1 * (n_samples - 1.) / (n_samples - 2.), F2)
assert_almost_equal(F2[0], 0.232558139) # value from statsmodels OLS
def test_f_classif_multi_class():
# Test whether the F test yields meaningful results
# on a simple simulated classification problem
X, y = make_classification(n_samples=200, n_features=20,
n_informative=3, n_redundant=2,
n_repeated=0, n_classes=8,
n_clusters_per_class=1, flip_y=0.0,
class_sep=10, shuffle=False, random_state=0)
F, pv = f_classif(X, y)
assert (F > 0).all()
assert (pv > 0).all()
assert (pv < 1).all()
assert (pv[:5] < 0.05).all()
assert (pv[5:] > 1.e-4).all()
def test_select_percentile_classif():
# Test whether the relative univariate feature selection
# gets the correct items in a simple classification problem
# with the percentile heuristic
X, y = make_classification(n_samples=200, n_features=20,
n_informative=3, n_redundant=2,
n_repeated=0, n_classes=8,
n_clusters_per_class=1, flip_y=0.0,
class_sep=10, shuffle=False, random_state=0)
univariate_filter = SelectPercentile(f_classif, percentile=25)
X_r = univariate_filter.fit(X, y).transform(X)
X_r2 = GenericUnivariateSelect(f_classif, mode='percentile',
param=25).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.zeros(20)
gtruth[:5] = 1
assert_array_equal(support, gtruth)
def test_select_percentile_classif_sparse():
# Test whether the relative univariate feature selection
# gets the correct items in a simple classification problem
# with the percentile heuristic
X, y = make_classification(n_samples=200, n_features=20,
n_informative=3, n_redundant=2,
n_repeated=0, n_classes=8,
n_clusters_per_class=1, flip_y=0.0,
class_sep=10, shuffle=False, random_state=0)
X = sparse.csr_matrix(X)
univariate_filter = SelectPercentile(f_classif, percentile=25)
X_r = univariate_filter.fit(X, y).transform(X)
X_r2 = GenericUnivariateSelect(f_classif, mode='percentile',
param=25).fit(X, y).transform(X)
assert_array_equal(X_r.toarray(), X_r2.toarray())
support = univariate_filter.get_support()
gtruth = np.zeros(20)
gtruth[:5] = 1
assert_array_equal(support, gtruth)
X_r2inv = univariate_filter.inverse_transform(X_r2)
assert sparse.issparse(X_r2inv)
support_mask = safe_mask(X_r2inv, support)
assert X_r2inv.shape == X.shape
assert_array_equal(X_r2inv[:, support_mask].toarray(), X_r.toarray())
# Check other columns are empty
assert X_r2inv.getnnz() == X_r.getnnz()
##############################################################################
# Test univariate selection in classification settings
def test_select_kbest_classif():
# Test whether the relative univariate feature selection
# gets the correct items in a simple classification problem
# with the k best heuristic
X, y = make_classification(n_samples=200, n_features=20,
n_informative=3, n_redundant=2,
n_repeated=0, n_classes=8,
n_clusters_per_class=1, flip_y=0.0,
class_sep=10, shuffle=False, random_state=0)
univariate_filter = SelectKBest(f_classif, k=5)
X_r = univariate_filter.fit(X, y).transform(X)
X_r2 = GenericUnivariateSelect(
f_classif, mode='k_best', param=5).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.zeros(20)
gtruth[:5] = 1
assert_array_equal(support, gtruth)
def test_select_kbest_all():
# Test whether k="all" correctly returns all features.
X, y = make_classification(n_samples=20, n_features=10,
shuffle=False, random_state=0)
univariate_filter = SelectKBest(f_classif, k='all')
X_r = univariate_filter.fit(X, y).transform(X)
assert_array_equal(X, X_r)
def test_select_kbest_zero():
# Test whether k=0 correctly returns no features.
X, y = make_classification(n_samples=20, n_features=10,
shuffle=False, random_state=0)
univariate_filter = SelectKBest(f_classif, k=0)
univariate_filter.fit(X, y)
support = univariate_filter.get_support()
gtruth = np.zeros(10, dtype=bool)
assert_array_equal(support, gtruth)
X_selected = assert_warns_message(UserWarning, 'No features were selected',
univariate_filter.transform, X)
assert X_selected.shape == (20, 0)
def test_select_heuristics_classif():
# Test whether the relative univariate feature selection
# gets the correct items in a simple classification problem
# with the fdr, fwe and fpr heuristics
X, y = make_classification(n_samples=200, n_features=20,
n_informative=3, n_redundant=2,
n_repeated=0, n_classes=8,
n_clusters_per_class=1, flip_y=0.0,
class_sep=10, shuffle=False, random_state=0)
univariate_filter = SelectFwe(f_classif, alpha=0.01)
X_r = univariate_filter.fit(X, y).transform(X)
gtruth = np.zeros(20)
gtruth[:5] = 1
for mode in ['fdr', 'fpr', 'fwe']:
X_r2 = GenericUnivariateSelect(
f_classif, mode=mode, param=0.01).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
assert_array_almost_equal(support, gtruth)
##############################################################################
# Test univariate selection in regression settings
def assert_best_scores_kept(score_filter):
scores = score_filter.scores_
support = score_filter.get_support()
assert_array_almost_equal(np.sort(scores[support]),
np.sort(scores)[-support.sum():])
def test_select_percentile_regression():
# Test whether the relative univariate feature selection
# gets the correct items in a simple regression problem
# with the percentile heuristic
X, y = make_regression(n_samples=200, n_features=20,
n_informative=5, shuffle=False, random_state=0)
univariate_filter = SelectPercentile(f_regression, percentile=25)
X_r = univariate_filter.fit(X, y).transform(X)
assert_best_scores_kept(univariate_filter)
X_r2 = GenericUnivariateSelect(
f_regression, mode='percentile', param=25).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.zeros(20)
gtruth[:5] = 1
assert_array_equal(support, gtruth)
X_2 = X.copy()
X_2[:, np.logical_not(support)] = 0
assert_array_equal(X_2, univariate_filter.inverse_transform(X_r))
# Check inverse_transform respects dtype
assert_array_equal(X_2.astype(bool),
univariate_filter.inverse_transform(X_r.astype(bool)))
def test_select_percentile_regression_full():
# Test whether the relative univariate feature selection
# selects all features when '100%' is asked.
X, y = make_regression(n_samples=200, n_features=20,
n_informative=5, shuffle=False, random_state=0)
univariate_filter = SelectPercentile(f_regression, percentile=100)
X_r = univariate_filter.fit(X, y).transform(X)
assert_best_scores_kept(univariate_filter)
X_r2 = GenericUnivariateSelect(
f_regression, mode='percentile', param=100).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.ones(20)
assert_array_equal(support, gtruth)
def test_invalid_percentile():
X, y = make_regression(n_samples=10, n_features=20,
n_informative=2, shuffle=False, random_state=0)
with pytest.raises(ValueError):
SelectPercentile(percentile=-1).fit(X, y)
with pytest.raises(ValueError):
SelectPercentile(percentile=101).fit(X, y)
with pytest.raises(ValueError):
GenericUnivariateSelect(mode='percentile', param=-1).fit(X, y)
with pytest.raises(ValueError):
GenericUnivariateSelect(mode='percentile', param=101).fit(X, y)
def test_select_kbest_regression():
# Test whether the relative univariate feature selection
# gets the correct items in a simple regression problem
# with the k best heuristic
X, y = make_regression(n_samples=200, n_features=20, n_informative=5,
shuffle=False, random_state=0, noise=10)
univariate_filter = SelectKBest(f_regression, k=5)
X_r = univariate_filter.fit(X, y).transform(X)
assert_best_scores_kept(univariate_filter)
X_r2 = GenericUnivariateSelect(
f_regression, mode='k_best', param=5).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.zeros(20)
gtruth[:5] = 1
assert_array_equal(support, gtruth)
def test_select_heuristics_regression():
# Test whether the relative univariate feature selection
# gets the correct items in a simple regression problem
# with the fpr, fdr or fwe heuristics
X, y = make_regression(n_samples=200, n_features=20, n_informative=5,
shuffle=False, random_state=0, noise=10)
univariate_filter = SelectFpr(f_regression, alpha=0.01)
X_r = univariate_filter.fit(X, y).transform(X)
gtruth = np.zeros(20)
gtruth[:5] = 1
for mode in ['fdr', 'fpr', 'fwe']:
X_r2 = GenericUnivariateSelect(
f_regression, mode=mode, param=0.01).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
assert_array_equal(support[:5], np.ones((5, ), dtype=np.bool))
assert np.sum(support[5:] == 1) < 3
def test_boundary_case_ch2():
# Test boundary case, and always aim to select 1 feature.
X = np.array([[10, 20], [20, 20], [20, 30]])
y = np.array([[1], [0], [0]])
scores, pvalues = chi2(X, y)
assert_array_almost_equal(scores, np.array([4., 0.71428571]))
assert_array_almost_equal(pvalues, np.array([0.04550026, 0.39802472]))
filter_fdr = SelectFdr(chi2, alpha=0.1)
filter_fdr.fit(X, y)
support_fdr = filter_fdr.get_support()
assert_array_equal(support_fdr, np.array([True, False]))
filter_kbest = SelectKBest(chi2, k=1)
filter_kbest.fit(X, y)
support_kbest = filter_kbest.get_support()
assert_array_equal(support_kbest, np.array([True, False]))
filter_percentile = SelectPercentile(chi2, percentile=50)
filter_percentile.fit(X, y)
support_percentile = filter_percentile.get_support()
assert_array_equal(support_percentile, np.array([True, False]))
filter_fpr = SelectFpr(chi2, alpha=0.1)
filter_fpr.fit(X, y)
support_fpr = filter_fpr.get_support()
assert_array_equal(support_fpr, np.array([True, False]))
filter_fwe = SelectFwe(chi2, alpha=0.1)
filter_fwe.fit(X, y)
support_fwe = filter_fwe.get_support()
assert_array_equal(support_fwe, np.array([True, False]))
@pytest.mark.parametrize("alpha", [0.001, 0.01, 0.1])
@pytest.mark.parametrize("n_informative", [1, 5, 10])
def test_select_fdr_regression(alpha, n_informative):
# Test that fdr heuristic actually has low FDR.
def single_fdr(alpha, n_informative, random_state):
X, y = make_regression(n_samples=150, n_features=20,
n_informative=n_informative, shuffle=False,
random_state=random_state, noise=10)
with warnings.catch_warnings(record=True):
# Warnings can be raised when no features are selected
# (low alpha or very noisy data)
univariate_filter = SelectFdr(f_regression, alpha=alpha)
X_r = univariate_filter.fit(X, y).transform(X)
X_r2 = GenericUnivariateSelect(
f_regression, mode='fdr', param=alpha).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
num_false_positives = np.sum(support[n_informative:] == 1)
num_true_positives = np.sum(support[:n_informative] == 1)
if num_false_positives == 0:
return 0.
false_discovery_rate = (num_false_positives /
(num_true_positives + num_false_positives))
return false_discovery_rate
# As per Benjamini-Hochberg, the expected false discovery rate
# should be lower than alpha:
# FDR = E(FP / (TP + FP)) <= alpha
false_discovery_rate = np.mean([single_fdr(alpha, n_informative,
random_state) for
random_state in range(100)])
assert alpha >= false_discovery_rate
# Make sure that the empirical false discovery rate increases
# with alpha:
if false_discovery_rate != 0:
assert false_discovery_rate > alpha / 10
def test_select_fwe_regression():
# Test whether the relative univariate feature selection
# gets the correct items in a simple regression problem
# with the fwe heuristic
X, y = make_regression(n_samples=200, n_features=20,
n_informative=5, shuffle=False, random_state=0)
univariate_filter = SelectFwe(f_regression, alpha=0.01)
X_r = univariate_filter.fit(X, y).transform(X)
X_r2 = GenericUnivariateSelect(
f_regression, mode='fwe', param=0.01).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.zeros(20)
gtruth[:5] = 1
assert_array_equal(support[:5], np.ones((5, ), dtype=np.bool))
assert np.sum(support[5:] == 1) < 2
def test_selectkbest_tiebreaking():
# Test whether SelectKBest actually selects k features in case of ties.
# Prior to 0.11, SelectKBest would return more features than requested.
Xs = [[0, 1, 1], [0, 0, 1], [1, 0, 0], [1, 1, 0]]
y = [1]
dummy_score = lambda X, y: (X[0], X[0])
for X in Xs:
sel = SelectKBest(dummy_score, k=1)
X1 = ignore_warnings(sel.fit_transform)([X], y)
assert X1.shape[1] == 1
assert_best_scores_kept(sel)
sel = SelectKBest(dummy_score, k=2)
X2 = ignore_warnings(sel.fit_transform)([X], y)
assert X2.shape[1] == 2
assert_best_scores_kept(sel)
def test_selectpercentile_tiebreaking():
# Test if SelectPercentile selects the right n_features in case of ties.
Xs = [[0, 1, 1], [0, 0, 1], [1, 0, 0], [1, 1, 0]]
y = [1]
dummy_score = lambda X, y: (X[0], X[0])
for X in Xs:
sel = SelectPercentile(dummy_score, percentile=34)
X1 = ignore_warnings(sel.fit_transform)([X], y)
assert X1.shape[1] == 1
assert_best_scores_kept(sel)
sel = SelectPercentile(dummy_score, percentile=67)
X2 = ignore_warnings(sel.fit_transform)([X], y)
assert X2.shape[1] == 2
assert_best_scores_kept(sel)
def test_tied_pvalues():
# Test whether k-best and percentiles work with tied pvalues from chi2.
# chi2 will return the same p-values for the following features, but it
# will return different scores.
X0 = np.array([[10000, 9999, 9998], [1, 1, 1]])
y = [0, 1]
for perm in itertools.permutations((0, 1, 2)):
X = X0[:, perm]
Xt = SelectKBest(chi2, k=2).fit_transform(X, y)
assert Xt.shape == (2, 2)
assert 9998 not in Xt
Xt = SelectPercentile(chi2, percentile=67).fit_transform(X, y)
assert Xt.shape == (2, 2)
assert 9998 not in Xt
def test_scorefunc_multilabel():
# Test whether k-best and percentiles works with multilabels with chi2.
X = np.array([[10000, 9999, 0], [100, 9999, 0], [1000, 99, 0]])
y = [[1, 1], [0, 1], [1, 0]]
Xt = SelectKBest(chi2, k=2).fit_transform(X, y)
assert Xt.shape == (3, 2)
assert 0 not in Xt
Xt = SelectPercentile(chi2, percentile=67).fit_transform(X, y)
assert Xt.shape == (3, 2)
assert 0 not in Xt
def test_tied_scores():
# Test for stable sorting in k-best with tied scores.
X_train = np.array([[0, 0, 0], [1, 1, 1]])
y_train = [0, 1]
for n_features in [1, 2, 3]:
sel = SelectKBest(chi2, k=n_features).fit(X_train, y_train)
X_test = sel.transform([[0, 1, 2]])
assert_array_equal(X_test[0], np.arange(3)[-n_features:])
def test_nans():
# Assert that SelectKBest and SelectPercentile can handle NaNs.
# First feature has zero variance to confuse f_classif (ANOVA) and
# make it return a NaN.
X = [[0, 1, 0], [0, -1, -1], [0, .5, .5]]
y = [1, 0, 1]
for select in (SelectKBest(f_classif, 2),
SelectPercentile(f_classif, percentile=67)):
ignore_warnings(select.fit)(X, y)
assert_array_equal(select.get_support(indices=True), np.array([1, 2]))
def test_score_func_error():
X = [[0, 1, 0], [0, -1, -1], [0, .5, .5]]
y = [1, 0, 1]
for SelectFeatures in [SelectKBest, SelectPercentile, SelectFwe,
SelectFdr, SelectFpr, GenericUnivariateSelect]:
with pytest.raises(TypeError):
SelectFeatures(score_func=10).fit(X, y)
def test_invalid_k():
X = [[0, 1, 0], [0, -1, -1], [0, .5, .5]]
y = [1, 0, 1]
with pytest.raises(ValueError):
SelectKBest(k=-1).fit(X, y)
with pytest.raises(ValueError):
SelectKBest(k=4).fit(X, y)
with pytest.raises(ValueError):
GenericUnivariateSelect(mode='k_best', param=-1).fit(X, y)
with pytest.raises(ValueError):
GenericUnivariateSelect(mode='k_best', param=4).fit(X, y)
def test_f_classif_constant_feature():
# Test that f_classif warns if a feature is constant throughout.
X, y = make_classification(n_samples=10, n_features=5)
X[:, 0] = 2.0
assert_warns(UserWarning, f_classif, X, y)
def test_no_feature_selected():
rng = np.random.RandomState(0)
# Generate random uncorrelated data: a strict univariate test should
# rejects all the features
X = rng.rand(40, 10)
y = rng.randint(0, 4, size=40)
strict_selectors = [
SelectFwe(alpha=0.01).fit(X, y),
SelectFdr(alpha=0.01).fit(X, y),
SelectFpr(alpha=0.01).fit(X, y),
SelectPercentile(percentile=0).fit(X, y),
SelectKBest(k=0).fit(X, y),
]
for selector in strict_selectors:
assert_array_equal(selector.get_support(), np.zeros(10))
X_selected = assert_warns_message(
UserWarning, 'No features were selected', selector.transform, X)
assert X_selected.shape == (40, 0)
def test_mutual_info_classif():
X, y = make_classification(n_samples=100, n_features=5,
n_informative=1, n_redundant=1,
n_repeated=0, n_classes=2,
n_clusters_per_class=1, flip_y=0.0,
class_sep=10, shuffle=False, random_state=0)
# Test in KBest mode.
univariate_filter = SelectKBest(mutual_info_classif, k=2)
X_r = univariate_filter.fit(X, y).transform(X)
X_r2 = GenericUnivariateSelect(
mutual_info_classif, mode='k_best', param=2).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.zeros(5)
gtruth[:2] = 1
assert_array_equal(support, gtruth)
# Test in Percentile mode.
univariate_filter = SelectPercentile(mutual_info_classif, percentile=40)
X_r = univariate_filter.fit(X, y).transform(X)
X_r2 = GenericUnivariateSelect(
mutual_info_classif, mode='percentile', param=40).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.zeros(5)
gtruth[:2] = 1
assert_array_equal(support, gtruth)
def test_mutual_info_regression():
X, y = make_regression(n_samples=100, n_features=10, n_informative=2,
shuffle=False, random_state=0, noise=10)
# Test in KBest mode.
univariate_filter = SelectKBest(mutual_info_regression, k=2)
X_r = univariate_filter.fit(X, y).transform(X)
assert_best_scores_kept(univariate_filter)
X_r2 = GenericUnivariateSelect(
mutual_info_regression, mode='k_best', param=2).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.zeros(10)
gtruth[:2] = 1
assert_array_equal(support, gtruth)
# Test in Percentile mode.
univariate_filter = SelectPercentile(mutual_info_regression, percentile=20)
X_r = univariate_filter.fit(X, y).transform(X)
X_r2 = GenericUnivariateSelect(mutual_info_regression, mode='percentile',
param=20).fit(X, y).transform(X)
assert_array_equal(X_r, X_r2)
support = univariate_filter.get_support()
gtruth = np.zeros(10)
gtruth[:2] = 1
assert_array_equal(support, gtruth)