ABSTRACT
Clustering based on Gaussian mixture models is a classical and powerful approach. Celeux and Govaert (1995) summarized sixteen Gaussian mixture models which result in sixteen clustering algorithms. These sixteen Gaussian mixture models are based on different assumptions on the component variance matrices. Four commonly used Gaussian mixture models are (Celeux and Govaert, 1995):
(a) No restriction is imposed on the component variance matrices Σ0,Σ1,· · · , and Σk−1;
(b) Σ0 = Σ1 = · · · = Σk−1 = Σ; (c) Σ0 = Σ1 = · · · = Σk−1 = Diag(σ20 , σ21 , · · · , σ2d−1), where
σ0, σ1, · · · , σd−1 are unknown; (d) Σ0 = Σ1 = · · · = Σk−1 = Diag(σ2, σ2, · · · , σ2), where σ is unknown. In this chapter, we implement the clustering algorithm based on the first
Gaussian mixture model, i.e., the most general one.
