Gaussian Mixture Model
From the book
Chapter 13: Probability and Random Variables. In the chapter mind map this icon labels GMM. The discussion below is excerpted and lightly edited from § Definition: Gaussian Mixture Model (GMM) in Mathematics for AI and Machine Learning.
A Gaussian Mixture Model (GMM) is a mixture distribution where each component is a Gaussian distribution. For a GMM with $K$ components, the PDF is:
where $\pi_k \ge 0$, $\sum_{k=0}^{K-1} \pi_k = 1$, and $\mathcal{N}(x \mid \mu_k, \Sigma_k)$ is the PDF of a multivariate Gaussian with mean $\mu_k$ and covariance matrix $\Sigma_k$.
What this drawing shows
What you see. Shows a density made from multiple Gaussian components, representing multimodal probabilistic clustering.
In the mind map. Chapter 13 — GMM. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 13: Probability and Random Variables — see the mind-map node GMM.