It is a robust principal curve package focused on fitting data that lies in a sphere. Splines are the estimators used for the principal curves.
The package can be installed via pip using:
pip install procurveFit a spline curve to a dataset that resembles a snake wrapped in a sphere:
from procurve.principal_curve import PrincipalCurve
from procurve.utils import create_dataset
from procurve.plotting import plot_3d, segments
import numpy as np
from mpl_toolkits.mplot3d.art3d import Line3DCollection
from figure_utils import set_figure_art
set_figure_art()
#%% Create the dataset
X = create_dataset(source="snake")
#%% Set parameters for the spline
spline_params = {"degree": 4,
"low_angle_deg": -40,
"high_angle_deg": 180,
"radius": 1.0}
#%% Create the principal curve object and fit.
pc = PrincipalCurve()
X, s, f_spline = pc.fit(X, init_fn="curve", param_fun=spline_params)
#%% Use the principal curve function
s_high_res = np.linspace(0, 1, 1000)
f_s = f_spline(s_high_res)
#%% Plot data and see results
fig, ax = plot_3d(X, plot_wireframe=True)
ax.plot(f_s[:,0], f_s[:,1], f_s[:,2], color="C3", linewidth=0.5, label="Principal curve")
line_collections_fit = segments(pc.last_iteration_log["data_sorted"],
pc.last_iteration_log["p_orthogonal"])
lc_fit = Line3DCollection(line_collections_fit, colors="C1", linewidths=0.4, label="Orthogonal projection")
ax.add_collection(lc_fit)
ax.legend(fontsize="small")
ax.set_xlim(-1.1, 1.1)
ax.set_ylim(-1.1, 1.1)
ax.set_zlim(-1.1, 1.1)Other examples .. image:: https://raw.githubusercontent.com/MauricioSalazare/procurve/master/examples/plots/samples_low_res.png
scale: 10 % align: center
The pseudo-algorithm and mathematical formulation can be found here.
Any questions, suggestions or collaborations contact Mauricio Salazar at <[email protected]>