IMM Analysis of Simulated Data using 2 extra Groups

We first simulated multivariate (5 hypothetical elements) data for 20 individuals from each of 5 groups (n = 100) by randomly selecting elemental values from normal distributions (both mean and SD varied by element and by group). Below are the4 first 2 principle components for the 5 groups. Group dispersion and overlap varied greatly.

I ran an Infinite Mixture Model with different co-variance priors, and using a leave-one-out method to assign individuals to groups. I also did not train the IMM on groups 4 and 5, and allowed the model to assign individuals to extra groups.

The posterior assignment probabilities for each individual (each colored line) are displayed below. While many co-variance matrices did a decent job classifying individuals to trained groups, the Identity (ID) co-variance matrix most consistently assigned untrained group individuals to an extra group. Since only 3 groups were trained, and the leave-one-out approach only assigned 1 individual per run, individuals from both extra groups (4 and 5) were assigned to group 4.

This is further reflected in the data summarized by group. Where individuals were mis-assigned using other co-variance matrices, reflected where groups overlapped in multivariate space (see the PCA).

For all groups, the Identity co-variance matrix assigned individuals to the correct group most often.