def sw(dgms1, dgms2, kernel_type='sw', parallel_flag=False, **featkwargs):
"""
:param dgms1: numpy array
:param dgms2: numpy array
:param parallel_flag:
:param kernel_type:
:param featkwargs: when kernel_type is sw, kwargs has n_d, bw
when kernel_type is pss, kwargs has bw
when kernel_type is wg, kwargs has bw, K,p
:return: a computed kernel
"""
def arctan(C, p):
return lambda x: C * np.arctan(np.power(x[1], p))
import signal
def signal_handler(signum, frame):
raise Exception("Timed out!")
signal.signal(signal.SIGALRM, signal_handler)
time_limit = max(int(len(dgms1) * len(dgms2) * 0.2), 100)
signal.alarm(time_limit)
if parallel_flag == False:
if kernel_type == 'sw':
assert_names(['n_directions', 'bw'], featkwargs)
tda_kernel = tda.SlicedWassersteinKernel(
num_directions=featkwargs['n_directions'],
bandwidth=featkwargs['bw'])
elif kernel_type == 'pss':
assert_names(['bw'], featkwargs)
tda_kernel = tda.PersistenceScaleSpaceKernel(
bandwidth=featkwargs['bw'])
elif kernel_type == 'wg':
assert_names(['bw', 'K', 'p'], featkwargs)
tda_kernel = tda.PersistenceWeightedGaussianKernel(
bandwidth=featkwargs['bw'],
weight=arctan(featkwargs['K'], featkwargs['p']))
elif kernel_type == 'pf':
assert_names(['bw', 'bwf'], featkwargs)
# try:
tda_kernel = tda.PersistenceFisherKernel(
bandwidth_fisher=featkwargs['bwf'], bandwidth=featkwargs['bw'])
# except RuntimeWarning:
# tda_kernel = 0
# print('RuntimeWarning catched')
# print(f'dgm1', dgms1)
# print(f'dgm2', dgms2)
else:
print('Unknown kernel for function sw')
diags1 = dgms1
diags2 = dgms2
X = tda_kernel.fit(diags1)
Y = tda_kernel.transform(diags2)
Y = np.nan_to_num(Y) # todo wait for mathieu's reply
return Y
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]))
diags2 = [D]
def arctan(C,p):
return lambda x: C*np.arctan(np.power(x[1], p))
PWG = tda.PersistenceWeightedGaussianKernel(bandwidth=1., kernel_approx=None, weight=arctan(1.,1.))
X = PWG.fit(diags)
Y = PWG.transform(diags2)
print("PWG kernel is " + str(Y[0][0]))
PWG = tda.PersistenceWeightedGaussianKernel(kernel_approx=RBFSampler(gamma=1./2, n_components=100000).fit(np.ones([1,2])), weight=arctan(1.,1.))
X = PWG.fit(diags)
Y = PWG.transform(diags2)
print("Approximate PWG kernel is " + str(Y[0][0]))
PSS = tda.PersistenceScaleSpaceKernel(bandwidth=1.)
X = PSS.fit(diags)
Y = PSS.transform(diags2)
print("PSS kernel is " + str(Y[0][0]))
PSS = tda.PersistenceScaleSpaceKernel(kernel_approx=RBFSampler(gamma=1./2, n_components=100000).fit(np.ones([1,2])))
X = PSS.fit(diags)
Y = PSS.transform(diags2)
print("Approximate PSS kernel is " + str(Y[0][0]))
sW = tda.SlicedWassersteinDistance(num_directions=100)
X = sW.fit(diags)
Y = sW.transform(diags2)
print("SW distance is " + str(Y[0][0]))
SW = tda.SlicedWassersteinKernel(num_directions=100, bandwidth=1.)
def persistence_scale_kernel(X, Y, PSS_kernel=None):
if PSS_kernel is None:
PSS_kernel = tda.PersistenceScaleSpaceKernel(bandwidth=1.)
X_fit = PSS_kernel.fit([np.asarray(X)])
Y_fit = PSS_kernel.transform([np.asarray(Y)])
return Y_fit[0][0], PSS_kernel
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])))