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Abstract Energy landscape analysis is a data‐driven method to analyse multidimensional time series, including functional magnetic resonance imaging (fMRI) data. It has been shown to be a useful characterization of fMRI data in health and disease. It fits an Ising model to the data and captures the dynamics of the data as movement of a noisy ball constrained on the energy landscape derived from the estimated Ising model. In the present study, we examine test–retest reliability of the energy landscape analysis. To this end, we construct a permutation test that assesses whether or not indices characterizing the energy landscape are more consistent across different sets of scanning sessions from the same participant (i.e. within‐participant reliability) than across different sets of sessions from different participants (i.e. between‐participant reliability). We show that the energy landscape analysis has significantly higher within‐participant than between‐participant test–retest reliability with respect to four commonly used indices. We also show that a variational Bayesian method, which enables us to estimate energy landscapes tailored to each participant, displays comparable test–retest reliability to that using the conventional likelihood maximization method. The proposed methodology paves the way to perform individual‐level energy landscape analysis for given data sets with a statistically controlled reliability.
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This content will become publicly available on May 9, 2026
Energy landscape analysis based on the Ising model: Tutorial review
We review a class of energy landscape analysis method that uses the Ising model and takes multivariate time series data as input. The method allows one to capture dynamics of the data as trajectories of a ball from one basin to a different basin to yet another, constrained on the energy landscape specified by the estimated Ising model. While this energy landscape analysis has mostly been applied to functional magnetic resonance imaging (fMRI) data from the brain for historical reasons, there are emerging applications outside fMRI data and neuroscience. To inform such applications in various research fields, this review paper provides a detailed tutorial on each step of the analysis, terminologies, concepts underlying the method, and validation, as well as recent developments of extended and related methods.
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- Award ID(s):
- 2204936
- PAR ID:
- 10610785
- Editor(s):
- Cherifi, Hocine
- Publisher / Repository:
- PLoS
- Date Published:
- Journal Name:
- PLOS Complex Systems
- Volume:
- 2
- Issue:
- 5
- ISSN:
- 2837-8830
- Page Range / eLocation ID:
- e0000039
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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