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import numpy as np
import holoviews as hv
hv.extension('matplotlib')
Bivariate
provides a convenient way to visualize a 2D distribution of values as a Kernel density estimate and therefore provides a 2D extension to the Distribution
element. Kernel density estimation is a non-parametric way to estimate the probability density function of a random variable.
The KDE works by placing a Gaussian kernel at each sample with the supplied bandwidth, which are then summed to produce the density estimate. By default the bandwidth is determined using the Scott's method, which usually produces good results, but it may be overridden by an explicit value.
To start with we will create a Bivariate
with 1,000 normally distributed samples:
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normal = np.random.randn(1000, 2)
hv.Bivariate(normal)
A Bivariate
might be filled or not and we can define a cmap
to control the coloring:
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hv.Bivariate(normal).opts(colorbar=True, cmap='Blues', filled=True)
We can set explicit values for the bandwidth
to see the effect. Since the densities will vary across the NdLayout
we will enable axiswise normalization ensuring they are normalized separately:
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hv.NdLayout({bw: hv.Bivariate(normal).opts(axiswise=True, bandwidth=bw)
for bw in [0.05, 0.1, 0.5, 1]}, 'Bandwidth')
Underlying the Bivariate
element is the bivariate_kde
operation, which computes the KDE for us automatically when we plot the element. We can also use this operation directly and print the output highlighting the fact that the operation simply returns an Contours
or Polygons
element. It also affords more control over the parameters letting us directly set not only the bandwidth
and cut
values but also a x_range
, y_range
, bw_method
and the number of samples (n_samples
) to approximate the KDE with:
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from holoviews.operation.stats import bivariate_kde
dist = hv.Bivariate(normal)
kde = bivariate_kde(dist, x_range=(-4, 4), y_range=(-4, 4), bw_method='silverman', n_samples=20)
kde
For full documentation and the available style and plot options, use hv.help(hv.Bivariate).