Clustering Singular and Non-Singular Covariance Matrices for Classification

Oregon Convention Center 

In classification problems when working in high dimensions with a large number of classes and few observations per class, linear discriminant analysis (LDA) requires the strong assumptions of a shared covariance matrix between all classes and quadratic discriminant analysis leads to singular or unstable covariance matrix estimates. Both of these can lead to lower than desired classification performance. We introduce a novel, model-based clustering method which can relax the shared covariance assumptions of LDA by clustering sample covariance matrices, either singular or non-singular. This will lead to covariance matrix estimates which are pooled within each cluster. We show using simulated and real data that our method for classification tends to yield better discrimination compared to other methods.

Finite Mixture Models

EM-algorithm

Model Based Clustering

Classification

Singular Covariance Matrices

Pattern Recognition 

Section on Statistical Computing