def test_vmf_log_detect_breakage():
'''
Find where scipy approximation breaks down.
This doesn't really test anything but demonstrates where approximation
should be applied instead.
'''
n_examples = 3
kappas = [5, 30, 100, 1000, 5000]
n_features = range(2, 500)
breakage_points = []
for kappa in kappas:
first_breakage = None
for n_f in n_features:
mu = np.random.randn(n_f)
mu /= np.linalg.norm(mu)
X = np.random.randn(n_examples, n_f)
for ee in range(n_examples):
X[ee, :] /= np.linalg.norm(X[ee, :])
try:
von_mises_fisher_mixture._vmf_log(X, kappa, mu)
except:
if first_breakage is None:
first_breakage = n_f
breakage_points.append(first_breakage)
print('Scipy vmf_log breaks for kappa={} at n_features={}'.format(
kappa, first_breakage))
print(breakage_points)
assert_array_equal(breakage_points, [141, 420, 311, 3, 3])
def test_vmf_log_dense():
'''
Test that approximation approaches whatever scipy has.
'''
n_examples = 2
n_features = 50
kappas = np.linspace(2, 600, 20)
mu = np.random.randn(n_features)
mu /= np.linalg.norm(mu)
X = np.random.randn(n_examples, n_features)
for ee in range(n_examples):
X[ee, :] /= np.linalg.norm(X[ee, :])
diffs = []
for kappa in kappas:
v = von_mises_fisher_mixture._vmf_log(X, kappa, mu)
v_approx = von_mises_fisher_mixture._vmf_log_asymptotic(X, kappa, mu)
normalized_approx_diff = (np.linalg.norm(v - v_approx) /
np.linalg.norm(v))
print(normalized_approx_diff)
diffs.append(normalized_approx_diff)
assert diffs[0] > 10 * diffs[-1]
def sim_multimodal():
to_save = []
data_cells = []
# Data pre-processing
for i in range(40):
read_sim(i,
f_in='datasets/multimodal_sim2.npy',
f_out='datasets/transformed/multimodal_sim2_cell' + str(i))
# Angles to query
Thq = np.linspace(-np.pi, np.pi, 360)[:, None]
Xq = np.hstack((np.cos(Thq), np.sin(Thq)))
# Fit one cell at a time
for i in range(40):
print('\ncell no={}'.format(i))
try:
# Read data
read_data = np.load('datasets/transformed/multimodal_sim2_cell' +
str(i) + '.npz')
data, xx, yy = read_data['data'], read_data['xx'], read_data['yy']
if data.shape[0] <= 1:
continue
# Data
Th = data[:, 4][:, None]
X = np.hstack((np.cos(Th), np.sin(Th)))
db = DBSCAN().fit(X)
core_samples_mask = np.zeros_like(db.labels_, dtype=bool)
core_samples_mask[db.core_sample_indices_] = True
labels = db.labels_
# Number of clusters in labels, ignoring noise if present.
n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)
unique_labels = set(labels)
print("n_clusters_={}, labels={}".format(n_clusters_,
unique_labels))
for k in unique_labels:
if k == -1: # noisy samples
continue
class_member_mask = (labels == k)
xy = X[class_member_mask & core_samples_mask]
if k == 0:
db_centers = np.mean(xy, axis=0)[None, :]
else:
db_centers = np.concatenate(
(db_centers, np.mean(xy, axis=0)[None, :]), axis=0)
print("db_centers=", db_centers)
# TBD: "NOTE:: play with max_iter if you get the denom=inf error"
# Mixture of von Mises Fisher clustering (soft)
vmf_soft = VonMisesFisherMixture(n_clusters=n_clusters_,
posterior_type='soft',
init=db_centers,
n_init=1,
verbose=True,
max_iter=20)
vmf_soft.fit(X)
y = 0
for cn in range(n_clusters_):
y += vmf_soft.weights_[cn] * np.exp(
von_mises_fisher_mixture._vmf_log(
Xq, vmf_soft.concentrations_[cn],
vmf_soft.cluster_centers_[cn]))
yq = np.array(y)[:, None]
to_save.append(yq)
data_cells.append(i)
# Plot
pl.figure(figsize=(15, 4))
pl.subplot(131)
mesh = np.vstack((xx.ravel(), yy.ravel())).T
pl.scatter(mesh[:, 0], mesh[:, 1], c='k', marker='.')
pl.scatter(data[:, 1],
data[:, 2],
c=data[:, 0],
marker='*',
cmap='jet')
pl.colorbar()
pl.xlim([0, 20])
pl.ylim([-5, 30])
pl.title('data')
pl.subplot(132)
pl.scatter(Xq[:, 0], Xq[:, 1], c=yq[:], cmap='jet')
pl.colorbar()
pl.scatter(X[:, 0] * 0.9, X[:, 1] * 0.9, c='k', marker='+')
pl.title('data and extimated distribution')
pl.subplot(133, projection='polar')
pl.polar(Thq, yq)
pl.title('polar plot')
pl.savefig('outputs/multimodal_sim2_cell{}'.format(i))
#pl.show()
except:
print(' skipped...')
continue
def sim_unimodal():
to_save = []
data_cells = []
# Data pre-processing
for i in range(40):
read_sim(i,
f_in='datasets/unimodal_sim1.npy',
f_out='datasets/transformed/unimodal_sim1_cell' + str(i))
# Angles to query
Thq = np.linspace(-np.pi, np.pi, 360)[:, None]
Xq = np.hstack((np.cos(Thq), np.sin(Thq)))
# Fit one cell at a time
for i in range(40):
print('cell no={}'.format(i))
try:
# Read data
read_data = np.load('datasets/transformed/unimodal_sim1_cell' +
str(i) + '.npz')
data, xx, yy = read_data['data'], read_data['xx'], read_data['yy']
if data.shape[0] <= 1:
continue
# Data
Th = data[:, 4][:, None]
X = np.hstack((np.cos(Th), np.sin(Th)))
# Von Mises clustering (soft)
vmf_soft = VonMisesFisherMixture(n_clusters=1,
posterior_type='soft',
n_init=20)
vmf_soft.fit(X)
y0 = np.exp(
von_mises_fisher_mixture._vmf_log(
Xq, vmf_soft.concentrations_[0],
vmf_soft.cluster_centers_[0]))
y = y0 * vmf_soft.weights_[0]
# Query
yq = np.array(y)[:, None]
to_save.append(yq)
data_cells.append(i)
# Plot
pl.figure(figsize=(15, 4))
pl.subplot(131)
mesh = np.vstack((xx.ravel(), yy.ravel())).T
pl.scatter(mesh[:, 0], mesh[:, 1], c='k', marker='.')
pl.scatter(data[:, 1],
data[:, 2],
c=data[:, 0],
marker='*',
cmap='jet')
pl.colorbar()
pl.xlim([0, 20])
pl.ylim([-5, 30])
pl.title('data')
pl.subplot(132)
pl.scatter(Xq[:, 0], Xq[:, 1], c=y0[:], cmap='jet')
pl.colorbar()
pl.scatter(X[:, 0] * 0.9, X[:, 1] * 0.9, c='k', marker='+')
pl.title('data and extimated distribution')
pl.subplot(133, projection='polar')
pl.polar(Thq, yq)
pl.title('polar plot')
#pl.show()
pl.savefig('outputs/unimodal_sim1_cell{}'.format(i))
except:
print(' skipped...')
continue