Clustering without clusters: the meta-criterion and centroid reliability mistake continuous dynamics for discrete states

Microstate analysis starts with clustering and the meta-criterion is a heuristic to find an optimum cluster number. We address the following questions: (i) what number is found for non-cluster-forming dynamical systems, (ii) do centroids fall in random attractor regions, (iii) do EEG topographies form clusters or a single connected structure in sensor space? We find that (i) the meta-criterion suggests spurious optimal cluster numbers (4-8) with high confidence on different attractor geometries, (ii) cluster centroids reliably fall in the same attractor regions, (iii) topological analysis of dynamical systems and resting-state EEG suggests that all form a single connected structure in their respective phase space, not clusters. We conclude that the meta-criterion should be used with caution and its results should not be taken as representing a ground truth. Cluster numbers deviating from the meta-criterion should not be discarded. A more far-reaching implication is that evidence for the existence of clusters in resting-state EEG data is still lacking. Microstate clustering may correspond to the partitioning of a single connected structure.