GMM.py

import numpy as np
import scipy.stats

# %matplotlib inline
import matplotlib.pyplot as plt
from matplotlib import mlab
plt.style.use("ggplot")
plt.rcParams["font.size"] = 16
plt.rcParams["figure.figsize"] = 10, 8

from sklearn.mixture import GaussianMixture

np.random.seed(111)
_c = 4      # True number of clusters
n = 1000    # number of samples per cluster

p_t = np.random.uniform(-10, 10, size=(_c, 2))
clusters = []
for x, y in p_t:
    c_samples = np.random.normal(0, 2, size=(1000, 2))
    c_samples[:, 0] += x
    c_samples[:, 1] += y
    clusters.append(c_samples)

samples = np.concatenate(clusters)

# Normalization
m = samples.mean(axis=0, keepdims=True)
s = samples.std(axis=0, keepdims=True)
samples = (samples -  m) / s

X = samples[:, 0]
Y = samples[:, 1]

n_components = 4
model = GaussianMixture(n_components, covariance_type="full")
model.fit(samples)

plt.scatter(X, Y, marker='+', c='gray')
plt.xlabel('x')
plt.ylabel('y')

x = np.linspace(-3.5, 3.5, 1000)
y = np.linspace(-3.0, 3.0, 1000)
grid0, grid1 = np.meshgrid(x, y)

for k in range(n_components):
    plt.plot(model.means_[k][0], model.means_[k][1], 'ro')
    means_k = model.means_[k]
    covars_k = model.covariances_[k]
    grid2 = mlab.bivariate_normal(grid0, grid1,
                                  np.sqrt(covars_k[0][0]), np.sqrt(covars_k[1][1]),
                                  means_k[0], means_k[1],
                                  covars_k[0][1])
    plt.contour(grid0, grid1, grid2)
    
plt.show()