# Functional Connectome Fingerprinting Through Tucker Tensor Decomposition
## 5 Conclusions  
In this work, a mathematical framework based on Tucker decomposition is presented for functional connectome fingerprinting. The ability to project high-dimensional functional connectivity data to lower dimensional spaces enables separately extracting cohort-level functional patterns, encoded by the brain parcellation factor matrix, and participant-specific patterns, contained in the participants factor matrix. Through within- and between-condition analyses, it is shown that the participant factor matrix serves, to a great extent, as a fingerprint of the participants. This is supported by the obtained matching rates ranging from 90 to 100% in the within-condition setting, which are consistently higher than those obtained from FCs directly or PCA, and 76 to 92% in the between-condition setting for the intermediate parcellation granularity of 414. Furthermore, the results from this study suggest that fingerprinting of rest vs task is highly dependent on scanning length (see Figure 4B). For up to 275 TPs (3 min 18 s), resting-state FCs had a smaller matching rate than their corresponding tasks FCs (Emotion, Relational, Gambling, Social). Beyond 275 TPs, resting-state FCs showed a higher matching rate than their corresponding task FCs(Motor, Language, Working Memory). Overall, tensor-based methods demonstrate a high potential to uncover functional connectivity fingerprints. Our work has implications in understanding how data-driven decomposition methods enable us to assess fingerprinting with respect to: (i) brain parcellation granularity from coarse grain (114) to fine grain parcellations (914); (ii) dimensionality reduction for brain parcellation rank and for participants rank; (iii) scanning length of the fMRI condition; (iv) between and within fMRI condition.  
Conceptualization, V.C., A.M.E.G. and J.G.; methodology, V.C., M.L., J.H., A.M.E.G. and J.G.; formal analysis, V.C., A.M.E.G. and J.G.; investigation, V.C., M.L., J.H., A.M.E.G. and J.G.; data curation, V.C. and M.L.; writing--original draft preparation, V.C., A.M.E.G. and J.G.; writing--review and editing, V.C., M.L., J.H., A.M.E.G. and J.G.; supervision, A.M.E.G. and J.G.; funding acquisition J.H. and J.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Institutes of Health (US), Award ID: CTSI CTR EPAR2169 (J.G). National Institutes of Health (US) R01 AA029607 (J.G), National Institutes of Health (US), Award ID: R01 NS112303 (J.H and J.G).  
Not applicable.  
Upon acceptance of this manuscript, Matlab code to perform Tucker Decomposition and subsequent fingerprinting analyses will be available at the CONNplexity Lab website at the Publications section: [[https://engineering.purdue.edu/ComplexityLab/publications](https://engineering.purdue.edu/ComplexityLab/publications)]([https://engineering.purdue.edu/ComplexityLab/publications](https://engineering.purdue.edu/ComplexityLab/publications)) (accessed on 12 February 2025).  
Data were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: [PERSON] and [PERSON]; 1U54 MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} fMRI & Functional Magnetic Resonance Imaging \\ BOLD & Blood-Oxygen-Level-Dependent \\ FC & Functional Connectome \\ PCA & Principal Component Analysis \\ CP decomposition & CANDECOMP/PARAFAC decomposition \\ ST-HOSVD & Sequentially Truncated Higher-Order Singular Value Decomposition \\ HOSVD & Higher-Order Singular Value Decomposition \\ HOOI & Higher-Order Orthogonal Iteration \\ TPs & Time points \\ PG & Parcellation granularity \\ \end{tabular}