# Functional Connectome Fingerprinting Through Tucker Tensor Decomposition
## 4 Discussion  
Table 2 shows that under all conditions, Tucker decomposition-based methods (ST-HOSVD and HOOI) consistently achieve the highest matching rates compared to FCs and other data-driven techniques. Both methods significantly outperform PCA and CP, particularly in conditions with fewer time points, such as Emotion and Relational, where FCs, whether used directly or in combination with PCA, under-perform. The results highlight the effectiveness of Tucker decomposition techniques in enhancing fingerprinting accuracy even for fMRI conditions with a short scanning length. The results presented in Figure 2 provide meaningful insights into the influence of parcellation granularity on fingerprinting accuracy. The observed matching rate plateau at higher granularities indicates that beyond a certain threshold, increasing the parcellation resolution offers diminishing matching rate returns, which could be due to an increase  
Figure 8: Comparison between tasks that possess the lowest (Emotion) and highest (Resting-state) within-condition fingerprints for parcellation granularity of 414. (**A**). From left-to-right: first \(50\times 50\) block of the \(426\times 426\) identifiability matrix derived from vectorized FCs, first \(50\times 50\) block of the \(426\times 426\) identifiability matrix derived from the proposed fingerprinting framework based on ST-HOSVD, distribution of within-participant (main diagonal entries) and between-participant (off-diagonal entries) sessions of the FCs identifiability matrix, distribution of within-participant and between-participant sessions of the ST-HOSVD identifiability matrix. (**B**). Analogous resting-state identifiability matrices and distributions. (**C**). Participant whose Emotion test and retest FCs are incorrectly matched when computing the identifiability matrix via vectorized FCs and ST-HOSVD. (**D**,**E**). Participants whose Emotion and resting-state FCs are incorrectly matched when computing the identifiability matrix using vectorized FCs but correctly matched when computing the identifiability matrix via ST-HOSVD. in noise in the overall data of each participant. This is consistent with prior findings by [PERSON] et al. (2015) [PERSON] et al. (2015), who showed that measures from FCs estimated with long scan sessions provide meaningful information about individuals even with moderate parcellation granularity. The significantly higher matching rates for resting-state compared to tasks aligns with previous research showing that resting-state data captures more stable and individualized connectivity patterns due to its longer scanning length and more consistent brain-wide activity [9]. However, it has also been shown that when accounting for scanning length, resting-state has a lower fingerprint than tasks [13]. Interestingly, the lower performance observed for Emotion reflects the challenges of identifying individuals from shorter or more transient brain states, where brief tasks led to less reliable fingerprinting. The lack of a strict linear relationship between task length and matching rates across intermediate conditions suggests that certain cognitive tasks elicit more distinct and stable connectivity patterns, regardless of their duration. This nuanced relationship highlights the complexity of functional connectome dynamics, emphasizing the need for both sufficient data length and appropriate parcellation resolution to maximize fingerprinting reliability. As shown in Figure 3, compressing the brain parcellation information is detrimental to fingerprinting, as the highest matching rates were obtained with a brain parcellation rank of 414. In contrast, compressing the participants specific dimension overall preserves matching rate, as shown by the high matching rates obtained with participant rank as low as 150 for Relational, Gambling, Social, Language, Working Memory, and Resting-State, and have a rank of 300 for Emotion and Motor.