A parametric model assumes a specified structure for the data and estimates a finite set of parameters describing that structure. In outlier detection, the structure may be a single multivariate Gaussian or a mixture of several Gaussians. section 5.6 section 5.5
This assumption makes parametric methods restrictive when the distribution is wrong, but effective when the data matches it. Elliptic Envelope assumes one roughly Gaussian cluster; a Gaussian mixture model (GMM) represents multiple clusters. section 5.6 section 5.5
Common parameterizations include:
- A multivariate Gaussian uses a center and covariance matrix; the matrix records feature variances and pairwise covariances, capturing the distribution’s shape. section 5.5
- A GMM estimates the number of clusters, each cluster’s center and covariance matrix, and a weight expressing its likelihood. section 5.6
- GMM fitting uses expectation maximization (EM): parameters are initialized, evaluated through data likelihood, and iteratively adjusted. section 5.6
Cluster-based outlier detection
A GMM models data with three Gaussian clusters. Points near a center are probable, while points far from every center—or near a weakly weighted center—are unlikely. Overlapping regions can be more probable because several components could have generated the point. section 5.6
