# Functional Connectome Fingerprinting Through Tucker Tensor Decomposition
## 4 Discussion
The results from this analysis imply that the dimension of the participants information, represented by the participants rank, can be considerably compressed while preserving fingerprints. This indicates that there is some redundancy in inter-participant variability, with not every participant adding new information to the data. However, it is important to emphasize that the compressibility of the participants dimension is likely cohort-size dependent, and must, therefore, be reexamined when dealing with different cohort sizes. The within-condition results shown in Figure 4A confirm the presence of functional connectome fingerprints and demonstrate that the proposed framework is particularly effective in uncovering them, compared to non-decomposed functional connectomes. Notably, the obtained fingerprinting results were substantially higher than those obtained with FCs, especially for parcellation granularity 214, where fingerprinting performance was notably low (ranging from 37% to 83%). Noting that resting-state achieves matching rates of 100% in Figure 4A, in Figure 4B, a comparison between tasks and resting-state is carried out when the FCs of both are computed with an equal number of time-points. The higher matching rates obtained from Emotion, Relational, and Gambling in comparison to resting-state suggest that, to some degree, the fingerprints derived from resting-state stem from the considerably longer duration of resting-state relative to fMRI tasks. Unlike during fMRI tasks, participants in the resting-state condition are not engaged with any specific stimulus and, therefore, resting-state FCs encode \"baseline\" functional couplings among brain regions. Therefore, between-condition analyses allow us to assess the extent to which these couplings--captured by the resting-state brain parcellation factor matrix--can be recovered when participants engage in tasks. Even though extracting fingerprints in this setting is inherently more challenging compared to the within-condition setting, we were able to substantially increase matching rates relative to using original FCs. In Figure 5, it is shown that results are more sensitive to the parcellation and participant ranks, with a clear benefit in setting both to be the maximum value possible in many of the tasks. Furthermore, in Figure 6 it is shown that ST-HOSVD provided an even greater improvement over matching rates relative to FCs compared to the within-conditionfingerprints. This supports the rationale that baseline functional couplings exist and can also be effectively uncovered while participants are engaged in a task. We also explored the effect of reducing the resting-state BOLD time series duration to match the duration of each task. Doing so enables determining whether the entire scanning length is necessary to extract \"key features\" that facilitate obtaining between-condition fingerprints. From both sampling procedures carried out in this study, it is clear that randomly sampling time points is the superior strategy for fingerprinting. Comparing the results of Figure 7A,B, we see that randomly sampling time points of resting-state scans is not only more effective than sampling them consecutively, but also as effective as constructing resting-state FCs using the full scan length (as shown in Figure 5). This result aligns with the fingerprinting improvements seen when sub-sampling frames of edge-based time-series [46]. The results presented in Figure 8 highlight the effectiveness of the proposed ST-HOSVD-based framework in enhancing FC fingerprinting relative to using FCs directly. Panels A and B illustrate the identifiability matrices and participant similarity distributions for Emotion and resting-state, respectively. The ST-HOSVD framework considerably improves the separation between within-participant and between-participant similarity, as evident by the clearer diagonal structure in the identifiability matrices and the sharper peak of the within-participant similarity distribution.