https://github.com/williamjameshandley/spherical_kde

Kernel density estimation on a sphere
https://github.com/williamjameshandley/spherical_kde

astronomy bandwidth cartopy information-visualization kernel-density-estimation machine-learning mollweide-projection physics probability python sphere statistics von-mises-fisher

Last synced: about 3 hours ago
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Kernel density estimation on a sphere

• Host: GitHub
• URL: https://github.com/williamjameshandley/spherical_kde
• Owner: williamjameshandley
• License: mit
• Created: 2018-03-23T18:35:05.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2021-10-18T15:51:46.000Z (about 3 years ago)
• Last Synced: 2024-10-31T20:16:07.915Z (8 days ago)
• Topics: astronomy, bandwidth, cartopy, information-visualization, kernel-density-estimation, machine-learning, mollweide-projection, physics, probability, python, sphere, statistics, von-mises-fisher
• Language: Python
• Homepage: https://pypi.org/project/spherical_kde/
• Size: 896 KB
• Stars: 27
• Watchers: 5
• Forks: 9
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.txt

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README

        
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Spherical Kernel Density Estimation

===================================

These packages allow you to do rudimentary kernel density estimation on a

sphere. Suggestions for improvements/extensions welcome.

The fundamental principle is to replace the traditional Gaussian function used

in 

[kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation)

with the

[Von Mises-Fisher distribution](https://en.wikipedia.org/wiki/Von_Mises-Fisher_distribution).

Bandwidth estimation is still rough-and-ready.

![](https://raw.github.com/williamjameshandley/spherical_kde/master/plot.png)

Example Usage

-------------

```python

import numpy

from spherical_kde import SphericalKDE

import matplotlib.pyplot as plt

import cartopy.crs

from matplotlib.gridspec import GridSpec, GridSpecFromSubplotSpec

# Choose a seed for deterministic plot

numpy.random.seed(seed=0)

# Set up a grid of figures

fig = plt.figure(figsize=(10, 10))

gs_vert = GridSpec(3, 1)

gs_lower = GridSpecFromSubplotSpec(1, 2, subplot_spec=gs_vert[1])

fig.add_subplot(gs_vert[0], projection=cartopy.crs.Mollweide())

fig.add_subplot(gs_lower[0], projection=cartopy.crs.Orthographic())

fig.add_subplot(gs_lower[1], projection=cartopy.crs.Orthographic(-10, 45))

fig.add_subplot(gs_vert[2], projection=cartopy.crs.PlateCarree())

# Choose parameters for samples

nsamples = 100

pi = numpy.pi

# Generate some samples centered on (1,1) +/- 0.3 radians

theta_samples = numpy.random.normal(loc=1, scale=0.3, size=nsamples)

phi_samples = numpy.random.normal(loc=1, scale=0.3, size=nsamples)

phi_samples = numpy.mod(phi_samples, pi*2)

kde_green = SphericalKDE(phi_samples, theta_samples)

# Generate some samples centered on (-1,1) +/- 0.4 radians

theta_samples = numpy.random.normal(loc=1, scale=0.4, size=nsamples)

phi_samples = numpy.random.normal(loc=-1, scale=0.4, size=nsamples)

phi_samples = numpy.mod(phi_samples, pi*2)

kde_red = SphericalKDE(phi_samples, theta_samples)

# Generate a spread of samples along latitude 2, height 0.1

theta_samples = numpy.random.normal(loc=2, scale=0.1, size=nsamples)

phi_samples = numpy.random.uniform(low=-pi/2, high=pi/2, size=nsamples)

phi_samples = numpy.mod(phi_samples, pi*2)

kde_blue = SphericalKDE(phi_samples, theta_samples, bandwidth=0.1)

for ax in fig.axes:

    ax.set_global()

    ax.gridlines()

    ax.coastlines(linewidth=0.1)

    kde_green.plot(ax, 'g')

    kde_green.plot_samples(ax)

    kde_red.plot(ax, 'r')

    kde_blue.plot(ax, 'b')

# Save to plot

fig.tight_layout()

fig.savefig('plot.png')

```