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

The paper titled "Clustering without clusters: the meta-criterion and centroid reliability mistake continuous dynamics for discrete states" explores the concept of clustering in dynamical systems, specifically with regards to EEG data. The analysis begins with the application of the meta-criterion, a heuristic method used to determine the optimal number of clusters.

The study addresses three key questions: first, what number does the meta-criterion suggest for non-cluster-forming dynamical systems? Second, do the centroids, or central points, of these clusters fall within random attractor regions? And third, do the topographies, or spatial patterns, of EEG data form clusters or a single connected structure in sensor space?

The findings reveal that the meta-criterion often suggests spurious optimal cluster numbers, ranging from 4 to 8, with high confidence across different attractor geometries. This suggests that the method may incorrectly identify clusters in systems that do not naturally form them. Additionally, the centroids of these clusters reliably fall within the same attractor regions, indicating a lack of true clustering in the data.

Furthermore, topological analysis of both dynamical systems and resting-state EEG data shows that all these systems form a single connected structure in their respective phase space, rather than forming clusters.

The paper concludes that the meta-criterion should be used with caution, and its results should not be considered as definitive proof of cluster existence. Cluster numbers that deviate from the meta-criterion should not be dismissed outright. The authors also suggest that evidence for the existence of clusters in resting-state EEG data is still lacking, and that microstate clustering may merely correspond to the partitioning of a single connected structure.