def _tda_vectorisations_pipeline(self):
persistence_image = Pipeline([
("Rotator",
tda.DiagramPreprocessor(scaler=tda.BirthPersistenceTransform())),
("PersistenceImage", tda.PersistenceImage()),
("Scaler", RobustScaler())
])
return Pipeline([
("Translate", TranslateChunks()),
("Extract", ExtractKeypoints(self.selected_keypoints)),
("Smoothing", SmoothChunks()), ("Flattening", FlattenTo3D()),
("Persistence", Persistence(max_alpha_square=1, complex_='alpha')),
("Separator", tda.DiagramSelector(limit=np.inf,
point_type="finite")),
("Prominent", tda.ProminentPoints()),
("Union",
FeatureUnion([("PersistenceImage", persistence_image),
("Landscape",
Pipeline([("TDA", tda.Landscape(resolution=10)),
("Scaler", RobustScaler())])),
("TopologicalVector",
Pipeline([("TDA", tda.TopologicalVector()),
("Scaler", RobustScaler())])),
("Silhouette",
Pipeline([("TDA", tda.Silhouette()),
("Scaler", RobustScaler())])),
("BettiCurve",
Pipeline([("TDA", tda.BettiCurve()),
("Scaler", RobustScaler())]))])),
("Scaler", RobustScaler())
])
import matplotlib.pyplot as plt
import numpy as np
def arctan(C, p):
return lambda x: C * np.arctan(np.power(x[1], p))
D = np.array([[0.0, 4.0], [1.0, 2.0], [3.0, 8.0], [6.0, 8.0]])
plt.scatter(D[:, 0], D[:, 1])
plt.plot([0.0, 10.0], [0.0, 10.0])
plt.show()
diags = [D]
LS = tda.Landscape(resolution=1000)
L = LS.fit_transform(diags)
plt.plot(L[0][:1000])
plt.plot(L[0][1000:2000])
plt.plot(L[0][2000:3000])
plt.show()
def pow(n):
return lambda x: np.power(x[1] - x[0], n)
SH = tda.Silhouette(resolution=1000, weight=pow(5))
S = SH.fit_transform(diags)
plt.plot(S[0])
plt.show()
def dgms_vecs(self, **kwargs):
"""
:param kwargs: pass all kwargs here. PI('bandwidth', 'weight', 'im_range', 'resolution'), PL('num_landscapes', 'resolution')
:return: np.array of shape (n_dgms, n_dim) where all zero columns are removed
"""
self.param = kwargs
t1 = time.time()
def arctan(C, p):
return lambda x: C * np.arctan(np.power(x[1], p))
if self.vec_type == 'pi':
if True:
diagsT = DiagramPreprocessor(use=True,
scalers=[
([0, 1],
BirthPersistenceTransform())
]).fit_transform(self.diags)
PI = PersistenceImage(bandwidth=1.,
weight=lambda x: x[1],
im_range=[0, 10, 0, 10],
resolution=[100, 100])
res = PI.fit_transform(diagsT)
if False:
diagsT = tda.DiagramPreprocessor(
use=True,
scalers=[([0, 1], tda.BirthPersistenceTransform())
]).fit_transform(self.diags)
PI = tda.PersistenceImage(bandwidth=1.,
weight=lambda x: x[1],
im_range=[0, 10, 0, 10],
resolution=[100, 100])
res = PI.fit_transform(diagsT)
if False:
diagsT = tda.DiagramPreprocessor(
use=True,
scalers=[([0, 1], tda.BirthPersistenceTransform())
]).fit_transform(self.diags)
kwargs = filterdict(
kwargs, ['bandwidth', 'weight', 'im_range', 'resolution'])
kwargs['weight'] = arctan(kwargs['weight'][0],
kwargs['weight'][1])
# PI = tda.PersistenceImage(**kwargs)
PI = tda.PersistenceImage(bandwidth=1.,
weight=lambda x: x[1],
im_range=[0, 10, 0, 10],
resolution=[100, 100])
# PI = tda.PersistenceImage(bandwidth=1.0, weight=arctan(1.0, 1.0), im_range=[0, 1, 0, 1], resolution=[25, 25])
res = PI.fit_transform(diagsT)
elif self.vec_type == 'pi_':
kwargs_ = filterdict(
kwargs, ['bandwidth', 'weight', 'im_range', 'resolution'])
diagsT = DiagramPreprocessor(use=True,
scalers=[
([0,
1], BirthPersistenceTransform())
]).fit_transform(self.diags)
PI = PersistenceImage(
**kwargs_
) #(bandwidth=1., weight=lambda x: x[1], im_range=[0, 2, 0, 2], resolution=[20, 20])
res = PI.fit_transform(diagsT)
elif self.vec_type == 'pl':
kwargs_ = filterdict(kwargs, ['num_landscapes', 'resolution'])
LS = tda.Landscape(**kwargs_)
# LS = tda.Landscape(num_landscapes=5, resolution=100)
# print('self.diags', self.diags[1], self.diags[2])
# diags = [np.array(diag) for diag in self.diags]
# D = np.array([[0., 4.], [1., 2.], [3., 8.], [6., 8.]])
# res = LS.fit_transform([D, D])
# matheiu's implementation
# LS = Landscape(resolution=1000)
# D = np.array([[0., 4.], [1., 2.], [3., 8.], [6., 8.]])
# diags = [D]
res = LS.fit_transform(self.diags)
elif self.vec_type == 'pervec': # permutation vector, i.e. the historgram of coordinates of dgm
dgms = self.dgms
kwargs = filterdict(kwargs, ['dim'])
res = coordinate(dgms[0], **kwargs)
for i in range(1, len(dgms)):
tmp = coordinate(dgms[i], **kwargs)
res = np.concatenate((res, tmp), axis=0)
assert res.shape[0] == len(dgms)
else:
raise Exception('Unknown vec_type. You can only chose pi or pl')
t2 = time.time()
t = precision_format((t2 - t1), 1)
self.t = t
if kwargs.get('keep_zero', None) == True:
return normalize_(res, axis=self.axis)
return rm_zerocol(normalize_(res, axis=self.axis), cor_flag=False)
def sklearn_tda():
def arctan(C, p):
return lambda x: C * np.arctan(np.power(x[1], p))
D = np.array([[0.0, 4.0], [1.0, 2.0], [3.0, 8.0], [6.0, 8.0]])
plt.scatter(D[:, 0], D[:, 1])
plt.plot([0.0, 10.0], [0.0, 10.0])
plt.show()
diags = [D]
LS = tda.Landscape(resolution=1000)
L = LS.fit_transform(diags)
plt.plot(L[0][:1000])
plt.plot(L[0][1000:2000])
plt.plot(L[0][2000:3000])
plt.show()
SH = tda.Silhouette(resolution=1000, weight=lambda x: np.power(x[1] - x[0], 5))
S = SH.fit_transform(diags)
plt.plot(S[0])
plt.show()
BC = tda.BettiCurve(resolution=1000)
B = BC.fit_transform(diags)
plt.plot(B[0])
plt.show()
diagsT = tda.DiagramPreprocessor(use=True, scaler=tda.BirthPersistenceTransform()).fit_transform(diags)
PI = tda.PersistenceImage(bandwidth=1.0, weight=arctan(1.0, 1.0), im_range=[0, 10, 0, 10], resolution=[100, 100])
I = PI.fit_transform(diagsT)
plt.imshow(np.flip(np.reshape(I[0], [100, 100]), 0))
plt.show()
plt.scatter(D[:, 0], D[:, 1])
D = np.array([[1.0, 5.0], [3.0, 6.0], [2.0, 7.0]])
plt.scatter(D[:, 0], D[:, 1])
plt.plot([0.0, 10.0], [0.0, 10.0])
plt.show()
diags2 = [D]
SW = tda.SlicedWassersteinKernel(num_directions=10, bandwidth=1.0)
X = SW.fit(diags)
Y = SW.transform(diags2)
print(("SW kernel is " + str(Y[0][0])))
PWG = tda.PersistenceWeightedGaussianKernel(bandwidth=1.0, weight=arctan(1.0, 1.0))
X = PWG.fit(diags)
Y = PWG.transform(diags2)
print(("PWG kernel is " + str(Y[0][0])))
PSS = tda.PersistenceScaleSpaceKernel(bandwidth=1.0)
X = PSS.fit(diags)
Y = PSS.transform(diags2)
print(("PSS kernel is " + str(Y[0][0])))
W = tda.WassersteinDistance(wasserstein=1, delta=0.001)
X = W.fit(diags)
Y = W.transform(diags2)
print(("Wasserstein-1 distance is " + str(Y[0][0])))
sW = tda.SlicedWassersteinDistance(num_directions=10)
X = sW.fit(diags)
Y = sW.transform(diags2)
print(("sliced Wasserstein distance is " + str(Y[0][0])))