In the field of machine learning, a Gaussian Mixture Model (GMM) is a probabilistic model that represents the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. It's often used for clustering probabilistic distributions.
GMMs are commonly implemented with the expectation-maximization algorithm.
In this blog, we'll implement Gaussian Mixture Models from scratch, using Scikit-learn in Python.
First, we'll import the necessary libraries.
import matplotlib.pyplot as plt from sklearn.datasets import make_blobs from sklearn.mixture import GaussianMixture
We'll use the make_blobs() function from sklearn.datasets to create a dataset containing 300 samples, each with 2 features, and grouped into 4 clusters.
X, y = make_blobs(n_samples=300, n_features=2, centers=4, cluster_std=0.60, random_state=0) plt.scatter(X[:,0], X[:,1])
Next, we create our Gaussian Mixture model. We specify the number of components to be equal to the number of clusters we know our data to have. Then, we fit the model to our data, and predict cluster assignments for each data point.
gmm = GaussianMixture(n_components=4) gmm.fit(X) labels = gmm.predict(X) plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis')
The GMM algorithm has successfully assigned each data point in our synthetic dataset to one of the four clusters we knew to exist. Note that GMM doesn't know the number of clusters in advance; this is something we had to specify. In a real-world application, determining the number of clusters may require more sophistication or domain knowledge.
This is merely a quick foray into Gaussian Mixture Models. They're a versatile tool in machine learning and have many more applications and intricacies worth exploring.
Considering the complexity involved in machine learning problems and the math behind the modeling, GMMs provide a probabilistic approach, assuming the data to be a finite mixture of Gaussian distributions.