Gaussian Mixture Model (GMM)

A Gaussian mixture model is a probabilistic clustering method that represents data as a weighted mixture of multivariate normal distributions, fitted by expectation-maximization, giving each observation a probability of membership in each cluster.

가우시안 혼합모형은 데이터를 다변량 정규분포들의 가중 혼합으로 표현하고 기댓값-최대화 알고리즘으로 추정하여, 각 관측치가 각 군집에 속할 확률을 제공하는 확률적 군집분석 방법입니다.

How do I find clusters that can have different shapes and give each case a probability of membership?

모양이 서로 다를 수 있는 군집을 찾고 각 사례의 소속 확률을 구하려면 어떻게 하나요?

A Gaussian mixture model clusters continuous data by assuming each cluster is a multivariate normal distribution with its own mean and covariance, so clusters may differ in size, shape, and orientation. It fits when soft, probabilistic cluster membership is useful and the number of components can be chosen with BIC.

When to use Gaussian Mixture Model (GMM)

• Continuous features where clusters may be elliptical or differ in spread
• Need for posterior membership probabilities rather than hard assignments
• Model-based selection of the number of clusters using information criteria

When to use something else

• Categorical indicators: use latent class analysis
• Clusters with arbitrary non-elliptical shapes: use DBSCAN

Assumptions and requirements

• Continuous features approximately normal within each component
• Sufficient sample size for the chosen covariance structure
• Number of components and covariance type selected by BIC or similar criteria
• Multiple starts, because expectation-maximization can reach local optima

What the analysis reports

• BIC across numbers of components and covariance types
• Mixing proportions, component means, and covariances
• Posterior membership probabilities for each observation
• Classification uncertainty or entropy

How to report it

A [k]-component Gaussian mixture model with [covariance type] covariance was selected on the basis of the lowest BIC ([value]).

Related methods

• K-Means Clustering
• Latent Class Analysis
• Latent Profile Analysis

Run Gaussian Mixture Model (GMM) on Quorant