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# Density Estimation for a Gaussian Mixture in Scikit-learn

Plot the density estimation of a mixture of two Gaussians. Data is generated from two Gaussians with different centers and covariance matrices.

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### Version¶

In [1]:
import sklearn
sklearn.__version__

Out[1]:
'0.18.1'

### Imports¶

In [2]:
import plotly.plotly as py
import plotly.graph_objs as go

import numpy as np
import matplotlib.pyplot as plt
from sklearn import mixture


### Calculations¶

In [3]:
n_samples = 300

# generate random sample, two components
np.random.seed(0)

# generate spherical data centered on (20, 20)
shifted_gaussian = np.random.randn(n_samples, 2) + np.array([20, 20])

# generate zero centered stretched Gaussian data
C = np.array([[0., -0.7], [3.5, .7]])
stretched_gaussian = np.dot(np.random.randn(n_samples, 2), C)

# concatenate the two datasets into the final training set
X_train = np.vstack([shifted_gaussian, stretched_gaussian])

# fit a Gaussian Mixture Model with two components
clf = mixture.GaussianMixture(n_components=2, covariance_type='full')
clf.fit(X_train)

# display predicted scores by the model as a contour plot
x = np.linspace(-20., 30.)
y = np.linspace(-20., 40.)
X, Y = np.meshgrid(x, y)
XX = np.array([X.ravel(), Y.ravel()]).T
Z = -clf.score_samples(XX)
Z = Z.reshape(X.shape)


### Plot Results¶

In [4]:
CS = go.Contour(x=x, y=y, z=Z,
colorscale='Jet',
contours=dict(coloring='lines'),
line=dict(width=1.5))

trace = go.Scatter(x=X_train[:, 0], y=X_train[:, 1],
mode='markers', marker=dict(color='black'),
showlegend=False)

layout = go.Layout(title='Negative log-likelihood predicted by a GMM',
xaxis=dict(zeroline=False, showgrid=False),
yaxis=dict(zeroline=False, showgrid=False),
hovermode='closest')
fig = go.Figure(data=[CS, trace], layout=layout)

In [5]:
py.iplot(fig)

Out[5]:
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