What are Gaussian Mixture Models?
Gaussian Mixture Models (GMMs) are a probabilistic model used in unsupervised learning to represent a blend of multiple Gaussian distributions. They are particularly useful for clustering and density estimation. In GMMs, each component of the mixture is defined by its own mean and variance, allowing the model to capture complex data distributions.
The central idea behind GMMs is to identify subpopulations within an overall population, where each subpopulation is assumed to follow a Gaussian distribution. GMMs use the Expectation-Maximization (EM) algorithm to iteratively estimate the parameters of the Gaussians—means, covariances, and mixture weights—until convergence.
One of the primary advantages of GMMs is their flexibility; they can model data that is not necessarily spherical, unlike k-means clustering. This flexibility makes GMMs suitable for a wide range of applications, including image segmentation, speech recognition, and anomaly detection.
However, selecting the number of components (clusters) can be challenging and often involves techniques like the Bayesian Information Criterion (BIC) or Akaike Information Criterion (AIC) for model selection. In summary, Gaussian Mixture Models are a powerful tool in the arsenal of machine learning for discovering hidden patterns in data without labeled responses.