Multivariate visibility graphs for fMRI data
- 1. Multivariate visibility graphs: from time series to temporal networks An application to BOLD fMRI data Lucas Lacasa School of Mathematical Sciences Queen Mary University of London @wetuad Sebastiano Stramaglia Physics Department and INFN University of Bari @SebinoStram Speranza Sannino Dept of Electrical Engineering University of Cagliari Daniele Marinazzo Department of Data Analysis Ghent University @dan_marinazzo
- 2. Visibility graphs were defined in computational geometry/computer science as the backbone graph capturing visibility paths (intervisible locations) in landscapes • Each node represents a location • Two locations are connected by a link if they are visible
- 3. Visibility graphs were defined in computational geometry/computer science as the backbone graph capturing visibility paths (intervisible locations) in landscapes • Each node represents a location • Two locations are connected by a link if they are visible
- 4. 1D LANDSCAPES CAN BE CONSIDERED AS TIME SERIES
- 5. 1D LANDSCAPES CAN BE CONSIDERED AS TIME SERIES
- 6. 1D LANDSCAPES CAN BE CONSIDERED AS TIME SERIES
- 7. 1D LANDSCAPES CAN BE CONSIDERED AS TIME SERIES
- 8. Natural Visibility Algorithm Lacasa, Luque, Ballesteros, Luque, Nuño, PNAS 105 (2008)
- 9. Example of a time series (20 data values) and the associated graph derived from the visibility algorithm. Lacasa, Luque, Ballesteros, Luque, Nuño, PNAS 105 (2008)
- 10. Natural Visibility Horizontal Visibility Natural version * naïve runtime O(n^2) * optimized runtime O(nlogn) * Analytically cumbersome * Fitted for long-range correlations and non- stationary series Horizontal version * generates outerplanar graphs * naïve runtime O(nlogn) * analytically tractable * Fitted for short-range correlations
- 11. The visibility graph of a time series remains invariant under several transformations Lacasa, Luque, Ballesteros, Luque, Nuño, PNAS 105 (2008)
- 12. EXTENSION TO MULTIVARIATE TIME SERIES: MULTIPLEX NETWORKS Lacasa, Nicosia, Latora, Scientific Reports 5, 15508 (2015)
- 13. Scalable: runtime complexity O(d) in the number of layers d
- 14. Relationship between layers • Edge overlap • Mutual information • …
- 15. Spatio-temporal dynamics: diffusively coupled chaotic maps
- 16. Captures different dynamical regimes and main features
- 17. Empirical study -- Visibility multiplex of multivariate financial series .com bubble Great recession Financially stable period
- 18. Comparison with a standard mutual information multivariate analysis Multiplex visibility graph Multivariate series
- 19. Network structure for correlated data
- 20. Why visibility, and why applied to fMRI? • Useful: both informative and descriptive • Robust to processing • Computationally easy and efficient • Amenable to analytical insight • Versatile, in both multivariate and univariate settings • Novel, building a bridge between time series and networks
- 21. More motivations specific to fMRI Peaks of BOLD signal encode relevant information on coactivation and correlated activity Tagliazucchi et al. 2012, Wu et al. 2013, Liu and Duyn 2013 Plus, visibility allows looking both at local and global activity
- 22. Examples of visibility in BOLD time series
- 23. Visibility graphs for BOLD signals
- 24. Modular temporal networks Different modules: different temporal regimes, mainly adjacent points TR Dynamic functional connectivity (Hutchison et al. 2013, Leonardi et al. 2013, Hansen et al. 2015, Hindriks et al. 2016, Kudela et al. 2017)
- 25. Dynamical functional connectivity in the visibility framework: partition distance and Sorensen index
- 26. Application to a large open fMRI dataset • Parcellation into 278 ROIs (Shen’s 2013 template) • Natural visibility graph for each ROI • Pairwise mutual information across ROIs • Average MI for each intrinsic connectivity network, defined according to Yeo
- 27. Average MI across RSNs
- 28. Differences in the limbic system • MANCOVAN with age, and framewise displacement as covariates • p-value 0.005, Bonferroni-Holm corrected • Shift function to assess differences across quantiles In the same regions: • lower Regional Homogeneity (ReHo) Zang et al. (2004) • higher coefficient of variation of the BOLD signal Wu and Marinazzo (2016) • lower value of the fractional amplitude of low-frequency fluctuations (fALFF) Zou et al. (2008) thanks to neurovault.org
- 30. Applications to EEG Univariate Multivariate
- 31. Applications to (neuro) images: segmentation
- 32. Thanks! Daniele Marinazzo Department of Data Analysis Ghent University @dan_marinazzo http://users.ugent.be/~dmarinaz/ Daniele.Marinazzo@UGent.be Code on https://github.com/danielemarinazzo/Visibility_LA5C_data http://www.maths.qmul.ac.uk/~lacasa/Software.html