S-Curve

This example shows how to use the DiffusionMaps class to reveal the embedded structure of S-Curve data.

import numpy as np
import matplotlib.pyplot as plt
from UQpy.utilities.kernels.GaussianKernel import GaussianKernel
from UQpy.dimension_reduction.diffusion_maps.DiffusionMaps import DiffusionMaps
from sklearn.datasets import make_swiss_roll, make_s_curve

Sample points randomly following a parametric curve and plot the 3D graphic.

n = 4000  # number of samples

# generate point cloud
# X, X_color = make_s_curve(n, random_state=3, noise=0)
X, X_color = make_s_curve(n, random_state=3, noise=0)

plot the point cloud

fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111, projection="3d")
ax.scatter(X[:, 0], X[:, 1], X[:, 2], c=X_color, cmap=plt.cm.Spectral)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
ax.set_title("S-curve data")
ax.view_init(10, 70)

Case 1: Find the optimal parameter of the Gaussian kernel scale epsilon

kernel = GaussianKernel(epsilon=0.65)


dmaps_object = DiffusionMaps(data=X,
                             alpha=1.0, n_eigenvectors=9,
                             is_sparse=True, n_neighbors=100,
                             kernel=kernel)

Find the parsimonious representation of the eigenvectors. Identify the two most informative eigenvectors.

dmaps_object.parsimonious(dim=2)

print('most informative eigenvectors:', dmaps_object.parsimonious_indices)

Plot the diffusion coordinates

DiffusionMaps._plot_eigen_pairs(dmaps_object.eigenvectors, pair_indices=dmaps_object.parsimonious_indices,
                                color=X_color, figure_size=[12, 12])
plt.show()