def test_correct_number_of_clusters():
# in 'auto' mode
n_clusters = 3
X = generate_clustered_data(n_clusters=n_clusters)
# Parameters chosen specifically for this task.
# Compute OPTICS
clust = OPTICS(max_eps=5.0 * 6.0, min_samples=4, xi=.1)
clust.fit(X)
# number of clusters, ignoring noise if present
n_clusters_1 = len(set(clust.labels_)) - int(-1 in clust.labels_)
assert n_clusters_1 == n_clusters
# check attribute types and sizes
assert clust.labels_.shape == (len(X),)
assert clust.labels_.dtype.kind == 'i'
assert clust.reachability_.shape == (len(X),)
assert clust.reachability_.dtype.kind == 'f'
assert clust.core_distances_.shape == (len(X),)
assert clust.core_distances_.dtype.kind == 'f'
assert clust.ordering_.shape == (len(X),)
assert clust.ordering_.dtype.kind == 'i'
assert set(clust.ordering_) == set(range(len(X)))
def test_bad_reachability():
msg = "All reachability values are inf. Set a larger max_eps."
centers = [[1, 1], [-1, -1], [1, -1]]
X, labels_true = make_blobs(n_samples=750, centers=centers,
cluster_std=0.4, random_state=0)
with pytest.warns(UserWarning, match=msg):
clust = OPTICS(max_eps=5.0 * 0.003, min_samples=10, eps=0.015)
clust.fit(X)
def test_precomputed_dists():
redX = X[::2]
dists = pairwise_distances(redX, metric='euclidean')
clust1 = OPTICS(min_samples=10, algorithm='brute',
metric='precomputed').fit(dists)
clust2 = OPTICS(min_samples=10, algorithm='brute',
metric='euclidean').fit(redX)
assert_allclose(clust1.reachability_, clust2.reachability_)
assert_array_equal(clust1.labels_, clust2.labels_)
def test_min_cluster_size(min_cluster_size):
redX = X[::2] # reduce for speed
clust = OPTICS(min_samples=9, min_cluster_size=min_cluster_size).fit(redX)
cluster_sizes = np.bincount(clust.labels_[clust.labels_ != -1])
if cluster_sizes.size:
assert min(cluster_sizes) >= min_cluster_size
# check behaviour is the same when min_cluster_size is a fraction
clust_frac = OPTICS(min_samples=9,
min_cluster_size=min_cluster_size / redX.shape[0])
clust_frac.fit(redX)
assert_array_equal(clust.labels_, clust_frac.labels_)
def test_extract_xi():
# small and easy test (no clusters around other clusters)
# but with a clear noise data.
rng = np.random.RandomState(0)
n_points_per_cluster = 5
C1 = [-5, -2] + .8 * rng.randn(n_points_per_cluster, 2)
C2 = [4, -1] + .1 * rng.randn(n_points_per_cluster, 2)
C3 = [1, -2] + .2 * rng.randn(n_points_per_cluster, 2)
C4 = [-2, 3] + .3 * rng.randn(n_points_per_cluster, 2)
C5 = [3, -2] + .6 * rng.randn(n_points_per_cluster, 2)
C6 = [5, 6] + .2 * rng.randn(n_points_per_cluster, 2)
X = np.vstack((C1, C2, C3, C4, C5, np.array([[100, 100]]), C6))
expected_labels = np.r_[[2] * 5, [0] * 5, [1] * 5, [3] * 5, [1] * 5,
-1, [4] * 5]
X, expected_labels = shuffle(X, expected_labels, random_state=rng)
clust = OPTICS(min_samples=3, min_cluster_size=2,
max_eps=20, cluster_method='xi',
xi=0.4).fit(X)
assert_array_equal(clust.labels_, expected_labels)
# check float min_samples and min_cluster_size
clust = OPTICS(min_samples=0.1, min_cluster_size=0.08,
max_eps=20, cluster_method='xi',
xi=0.4).fit(X)
assert_array_equal(clust.labels_, expected_labels)
X = np.vstack((C1, C2, C3, C4, C5, np.array([[100, 100]] * 2), C6))
expected_labels = np.r_[[1] * 5, [3] * 5, [2] * 5, [0] * 5, [2] * 5,
-1, -1, [4] * 5]
X, expected_labels = shuffle(X, expected_labels, random_state=rng)
clust = OPTICS(min_samples=3, min_cluster_size=3,
max_eps=20, cluster_method='xi',
xi=0.3).fit(X)
# this may fail if the predecessor correction is not at work!
assert_array_equal(clust.labels_, expected_labels)
C1 = [[0, 0], [0, 0.1], [0, -.1], [0.1, 0]]
C2 = [[10, 10], [10, 9], [10, 11], [9, 10]]
C3 = [[100, 100], [100, 90], [100, 110], [90, 100]]
X = np.vstack((C1, C2, C3))
expected_labels = np.r_[[0] * 4, [1] * 4, [2] * 4]
X, expected_labels = shuffle(X, expected_labels, random_state=rng)
clust = OPTICS(min_samples=2, min_cluster_size=2,
max_eps=np.inf, cluster_method='xi',
xi=0.04).fit(X)
assert_array_equal(clust.labels_, expected_labels)
def test_processing_order():
# Ensure that we consider all unprocessed points,
# not only direct neighbors. when picking the next point.
Y = [[0], [10], [-10], [25]]
clust = OPTICS(min_samples=3, max_eps=15).fit(Y)
assert_array_equal(clust.reachability_, [np.inf, 10, 10, 15])
assert_array_equal(clust.core_distances_, [10, 15, np.inf, np.inf])
assert_array_equal(clust.ordering_, [0, 1, 2, 3])
def test_minimum_number_of_sample_check():
# test that we check a minimum number of samples
msg = "min_samples must be no greater than"
# Compute OPTICS
X = [[1, 1]]
clust = OPTICS(max_eps=5.0 * 0.3, min_samples=10, min_cluster_size=1)
# Run the fit
assert_raise_message(ValueError, msg, clust.fit, X)
def test_cluster_hierarchy_():
rng = np.random.RandomState(0)
n_points_per_cluster = 100
C1 = [0, 0] + 2 * rng.randn(n_points_per_cluster, 2)
C2 = [0, 0] + 50 * rng.randn(n_points_per_cluster, 2)
X = np.vstack((C1, C2))
X = shuffle(X, random_state=0)
clusters = OPTICS(min_samples=20, xi=.1).fit(X).cluster_hierarchy_
assert clusters.shape == (2, 2)
diff = np.sum(clusters - np.array([[0, 99], [0, 199]]))
assert diff / len(X) < 0.05
def test_bad_extract():
# Test an extraction of eps too close to original eps
msg = "Specify an epsilon smaller than 0.15. Got 0.3."
centers = [[1, 1], [-1, -1], [1, -1]]
X, labels_true = make_blobs(n_samples=750, centers=centers,
cluster_std=0.4, random_state=0)
# Compute OPTICS
clust = OPTICS(max_eps=5.0 * 0.03,
cluster_method='dbscan',
eps=0.3, min_samples=10)
assert_raise_message(ValueError, msg, clust.fit, X)
def test_close_extract():
# Test extract where extraction eps is close to scaled max_eps
centers = [[1, 1], [-1, -1], [1, -1]]
X, labels_true = make_blobs(n_samples=750, centers=centers,
cluster_std=0.4, random_state=0)
# Compute OPTICS
clust = OPTICS(max_eps=1.0, cluster_method='dbscan',
eps=0.3, min_samples=10).fit(X)
# Cluster ordering starts at 0; max cluster label = 2 is 3 clusters
assert max(clust.labels_) == 2
def test_extract_dbscan():
# testing an easy dbscan case. Not including clusters with different
# densities.
rng = np.random.RandomState(0)
n_points_per_cluster = 20
C1 = [-5, -2] + .2 * rng.randn(n_points_per_cluster, 2)
C2 = [4, -1] + .2 * rng.randn(n_points_per_cluster, 2)
C3 = [1, 2] + .2 * rng.randn(n_points_per_cluster, 2)
C4 = [-2, 3] + .2 * rng.randn(n_points_per_cluster, 2)
X = np.vstack((C1, C2, C3, C4))
clust = OPTICS(cluster_method='dbscan', eps=.5).fit(X)
assert_array_equal(np.sort(np.unique(clust.labels_)), [0, 1, 2, 3])
def test_min_samples_edge_case():
C1 = [[0, 0], [0, 0.1], [0, -.1]]
C2 = [[10, 10], [10, 9], [10, 11]]
C3 = [[100, 100], [100, 96], [100, 106]]
X = np.vstack((C1, C2, C3))
expected_labels = np.r_[[0] * 3, [1] * 3, [2] * 3]
clust = OPTICS(min_samples=3,
max_eps=7, cluster_method='xi',
xi=0.04).fit(X)
assert_array_equal(clust.labels_, expected_labels)
expected_labels = np.r_[[0] * 3, [1] * 3, [-1] * 3]
clust = OPTICS(min_samples=3,
max_eps=3, cluster_method='xi',
xi=0.04).fit(X)
assert_array_equal(clust.labels_, expected_labels)
expected_labels = np.r_[[-1] * 9]
with pytest.warns(UserWarning, match="All reachability values"):
clust = OPTICS(min_samples=4,
max_eps=3, cluster_method='xi',
xi=0.04).fit(X)
assert_array_equal(clust.labels_, expected_labels)
def test_dbscan_optics_parity(eps, min_samples):
# Test that OPTICS clustering labels are <= 5% difference of DBSCAN
centers = [[1, 1], [-1, -1], [1, -1]]
X, labels_true = make_blobs(n_samples=750, centers=centers,
cluster_std=0.4, random_state=0)
# calculate optics with dbscan extract at 0.3 epsilon
op = OPTICS(min_samples=min_samples, cluster_method='dbscan',
eps=eps).fit(X)
# calculate dbscan labels
db = DBSCAN(eps=eps, min_samples=min_samples).fit(X)
contingency = contingency_matrix(db.labels_, op.labels_)
agree = min(np.sum(np.max(contingency, axis=0)),
np.sum(np.max(contingency, axis=1)))
disagree = X.shape[0] - agree
percent_mismatch = np.round((disagree - 1) / X.shape[0], 2)
# verify label mismatch is <= 5% labels
assert percent_mismatch <= 0.05
def test_wrong_cluster_method():
clust = OPTICS(cluster_method='superfancy')
with pytest.raises(ValueError, match="cluster_method should be one of "):
clust.fit(X)
def test_compare_to_ELKI():
# Expected values, computed with (future) ELKI 0.7.5 using:
# java -jar elki.jar cli -dbc.in csv -dbc.filter FixedDBIDsFilter
# -algorithm clustering.optics.OPTICSHeap -optics.minpts 5
# where the FixedDBIDsFilter gives 0-indexed ids.
r1 = [np.inf, 1.0574896366427478, 0.7587934993548423, 0.7290174038973836,
0.7290174038973836, 0.7290174038973836, 0.6861627576116127,
0.7587934993548423, 0.9280118450166668, 1.1748022534146194,
3.3355455741292257, 0.49618389254482587, 0.2552805046961355,
0.2552805046961355, 0.24944622248445714, 0.24944622248445714,
0.24944622248445714, 0.2552805046961355, 0.2552805046961355,
0.3086779122185853, 4.163024452756142, 1.623152630340929,
0.45315840475822655, 0.25468325192031926, 0.2254004358159971,
0.18765711877083036, 0.1821471333893275, 0.1821471333893275,
0.18765711877083036, 0.18765711877083036, 0.2240202988740153,
1.154337614548715, 1.342604473837069, 1.323308536402633,
0.8607514948648837, 0.27219111215810565, 0.13260875220533205,
0.13260875220533205, 0.09890587675958984, 0.09890587675958984,
0.13548790801634494, 0.1575483940837384, 0.17515137170530226,
0.17575920159442388, 0.27219111215810565, 0.6101447895405373,
1.3189208094864302, 1.323308536402633, 2.2509184159764577,
2.4517810628594527, 3.675977064404973, 3.8264795626020365,
2.9130735341510614, 2.9130735341510614, 2.9130735341510614,
2.9130735341510614, 2.8459300127258036, 2.8459300127258036,
2.8459300127258036, 3.0321982337972537]
o1 = [0, 3, 6, 4, 7, 8, 2, 9, 5, 1, 31, 30, 32, 34, 33, 38, 39, 35, 37, 36,
44, 21, 23, 24, 22, 25, 27, 29, 26, 28, 20, 40, 45, 46, 10, 15, 11,
13, 17, 19, 18, 12, 16, 14, 47, 49, 43, 48, 42, 41, 53, 57, 51, 52,
56, 59, 54, 55, 58, 50]
p1 = [-1, 0, 3, 6, 6, 6, 8, 3, 7, 5, 1, 31, 30, 30, 34, 34, 34, 32, 32, 37,
36, 44, 21, 23, 24, 22, 25, 25, 22, 22, 22, 21, 40, 45, 46, 10, 15,
15, 13, 13, 15, 11, 19, 15, 10, 47, 12, 45, 14, 43, 42, 53, 57, 57,
57, 57, 59, 59, 59, 58]
# Tests against known extraction array
# Does NOT work with metric='euclidean', because mrex euclidean has
# worse numeric precision. 'minkowski' is slower but more accurate.
clust1 = OPTICS(min_samples=5).fit(X)
assert_array_equal(clust1.ordering_, np.array(o1))
assert_array_equal(clust1.predecessor_[clust1.ordering_], np.array(p1))
assert_allclose(clust1.reachability_[clust1.ordering_], np.array(r1))
# ELKI currently does not print the core distances (which are not used much
# in literature, but we can at least ensure to have this consistency:
for i in clust1.ordering_[1:]:
assert (clust1.reachability_[i] >=
clust1.core_distances_[clust1.predecessor_[i]])
# Expected values, computed with (future) ELKI 0.7.5 using
r2 = [np.inf, np.inf, np.inf, np.inf, np.inf, np.inf, np.inf, np.inf,
np.inf, np.inf, np.inf, 0.27219111215810565, 0.13260875220533205,
0.13260875220533205, 0.09890587675958984, 0.09890587675958984,
0.13548790801634494, 0.1575483940837384, 0.17515137170530226,
0.17575920159442388, 0.27219111215810565, 0.4928068613197889,
np.inf, 0.2666183922512113, 0.18765711877083036, 0.1821471333893275,
0.1821471333893275, 0.1821471333893275, 0.18715928772277457,
0.18765711877083036, 0.18765711877083036, 0.25468325192031926,
np.inf, 0.2552805046961355, 0.2552805046961355, 0.24944622248445714,
0.24944622248445714, 0.24944622248445714, 0.2552805046961355,
0.2552805046961355, 0.3086779122185853, 0.34466409325984865,
np.inf, np.inf, np.inf, np.inf, np.inf, np.inf, np.inf, np.inf,
np.inf, np.inf, np.inf, np.inf, np.inf, np.inf, np.inf, np.inf,
np.inf, np.inf]
o2 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 11, 13, 17, 19, 18, 12, 16, 14,
47, 46, 20, 22, 25, 23, 27, 29, 24, 26, 28, 21, 30, 32, 34, 33, 38,
39, 35, 37, 36, 31, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53,
54, 55, 56, 57, 58, 59]
p2 = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 15, 15, 13, 13, 15,
11, 19, 15, 10, 47, -1, 20, 22, 25, 25, 25, 25, 22, 22, 23, -1, 30,
30, 34, 34, 34, 32, 32, 37, 38, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1]
clust2 = OPTICS(min_samples=5, max_eps=0.5).fit(X)
assert_array_equal(clust2.ordering_, np.array(o2))
assert_array_equal(clust2.predecessor_[clust2.ordering_], np.array(p2))
assert_allclose(clust2.reachability_[clust2.ordering_], np.array(r2))
index = np.where(clust1.core_distances_ <= 0.5)[0]
assert_allclose(clust1.core_distances_[index],
clust2.core_distances_[index])
def test_min_cluster_size_invalid2():
clust = OPTICS(min_cluster_size=len(X) + 1)
with pytest.raises(ValueError, match="must be no greater than the "):
clust.fit(X)
def test_min_cluster_size_invalid(min_cluster_size):
clust = OPTICS(min_cluster_size=min_cluster_size)
with pytest.raises(ValueError, match="must be a positive integer or a "):
clust.fit(X)