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()) ])
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() 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])
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])))