What's a component in gaussian mixture model?

What is the relation between a dimension and a component in a Gaussian Mixture Model? And what are the meanings of dimension and component? Thank you.

Please correct me if Im wrong: my understanding is the observed data have many dimensions. Each dimension represents a feature/aspect of the collected data and has its own Gaussian distribution. I don't know where "component" fits into this picture and what it means.

• I personally like this very concise description, by J.K. Vermunt: Latent Profile Model.
– chl
Commented Mar 28, 2011 at 7:43
• The link above on latent profile model has been removed :( Commented Oct 2, 2013 at 16:09
• Here's a newer link to the paper, but just googling for a paper written by J.K. Vermunt called Latent Profile model turns up pretty easily. researchgate.net/publication/239844183_Latent_profile_model Commented Dec 27, 2020 at 14:34

A mixture of Gaussians algorithm is a probabilistic generalization of the $k$-means algorithm. Each mean vector in $k$-means is component. The number of elements in each of the $k$ vectors is the dimension of the model. Thus, if you have $n$ dimensions, you have a $k\times n$ matrix of mean vectors.