# GMM Initialization Methods#

Examples of the different methods of initialization in Gaussian Mixture Models

See Gaussian mixture models for more information on the estimator.

Here we generate some sample data with four easy to identify clusters. The
purpose of this example is to show the four different methods for the
initialization parameter *init_param*.

The four initializations are *kmeans* (default), *random*, *random_from_data* and
*k-means++*.

Orange diamonds represent the initialization centers for the gmm generated by
the *init_param*. The rest of the data is represented as crosses and the
colouring represents the eventual associated classification after the GMM has
finished.

The numbers in the top right of each subplot represent the number of iterations taken for the GaussianMixture to converge and the relative time taken for the initialization part of the algorithm to run. The shorter initialization times tend to have a greater number of iterations to converge.

The initialization time is the ratio of the time taken for that method versus
the time taken for the default *kmeans* method. As you can see all three
alternative methods take less time to initialize when compared to *kmeans*.

In this example, when initialized with *random_from_data* or *random* the model takes
more iterations to converge. Here *k-means++* does a good job of both low
time to initialize and low number of GaussianMixture iterations to converge.

```
# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
from timeit import default_timer as timer
import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets._samples_generator import make_blobs
from sklearn.mixture import GaussianMixture
from sklearn.utils.extmath import row_norms
print(__doc__)
# Generate some data
X, y_true = make_blobs(n_samples=4000, centers=4, cluster_std=0.60, random_state=0)
X = X[:, ::-1]
n_samples = 4000
n_components = 4
x_squared_norms = row_norms(X, squared=True)
def get_initial_means(X, init_params, r):
# Run a GaussianMixture with max_iter=0 to output the initialization means
gmm = GaussianMixture(
n_components=4, init_params=init_params, tol=1e-9, max_iter=0, random_state=r
).fit(X)
return gmm.means_
methods = ["kmeans", "random_from_data", "k-means++", "random"]
colors = ["navy", "turquoise", "cornflowerblue", "darkorange"]
times_init = {}
relative_times = {}
plt.figure(figsize=(4 * len(methods) // 2, 6))
plt.subplots_adjust(
bottom=0.1, top=0.9, hspace=0.15, wspace=0.05, left=0.05, right=0.95
)
for n, method in enumerate(methods):
r = np.random.RandomState(seed=1234)
plt.subplot(2, len(methods) // 2, n + 1)
start = timer()
ini = get_initial_means(X, method, r)
end = timer()
init_time = end - start
gmm = GaussianMixture(
n_components=4, means_init=ini, tol=1e-9, max_iter=2000, random_state=r
).fit(X)
times_init[method] = init_time
for i, color in enumerate(colors):
data = X[gmm.predict(X) == i]
plt.scatter(data[:, 0], data[:, 1], color=color, marker="x")
plt.scatter(
ini[:, 0], ini[:, 1], s=75, marker="D", c="orange", lw=1.5, edgecolors="black"
)
relative_times[method] = times_init[method] / times_init[methods[0]]
plt.xticks(())
plt.yticks(())
plt.title(method, loc="left", fontsize=12)
plt.title(
"Iter %i | Init Time %.2fx" % (gmm.n_iter_, relative_times[method]),
loc="right",
fontsize=10,
)
plt.suptitle("GMM iterations and relative time taken to initialize")
plt.show()
```

**Total running time of the script:** (0 minutes 0.584 seconds)

Related examples

An example of K-Means++ initialization

A demo of K-Means clustering on the handwritten digits data

Gaussian Mixture Model Ellipsoids