Selecting the number of discrete brain states in clustering-based analyses

Develop principled methods to determine the appropriate number of clusters or states in clustering-based discretizations of neuroimaging time series used to define discrete brain states, providing criteria that are statistically sound and tailored to the properties of neural dynamics.

Background

Clustering approaches are commonly used to define discrete brain states from continuous neural recordings, but many rely on pre-specifying the number of clusters. The choice of this number critically impacts downstream discrete-state modeling (e.g., Markov chains) and estimates of non-equilibrium measures.

Current practice often resorts to generic heuristics (e.g., the Silhouette criterion). A principled approach specific to neural time series could improve robustness, interpretability, and reproducibility of state-based analyses.

References

In many cases, the appropriate number is not known and must be chosen according to other principles, e.g., the Silhouette criterion which determines the consistency of a particular clustering.

— Nonequilibrium physics of brain dynamics  (2504.12188 - Nartallo-Kaluarachchi et al., 16 Apr 2025) in Subsubsection 'Clustering approaches' under 'Discrete-state models' (Section: Analysis of neuroimaging and continuous-valued recordings)

A natural refinement is to choose the number of clusters by within-cluster cohesion at additional computational cost, which we leave to future work.

— Distribution-aware Language Neuron Identification in Multilingual Large Language Models  (2609.10993 - Kim et al., 10 Sep 2026) in Appendix, Section “Robustness of the Identifier Design,” paragraph “The $K{=}2$ bipartition is a selection decision, not a bimodality assumption.”