# Functional Connectome Fingerprinting Through Tucker Tensor Decomposition
## 4 Discussion
This indicates that the participants factor matrix derived from ST-HOSVD better captures the individual-specific features of FC patterns compared to vectorized FCs. Panels C, D, and E, respectively, display qualitative examples in which the proposed framework fails to correctly match the Emotion FCs of one participant, but succeeds in matching the FCs of participants that cannot be matched using FCs directly. Visually speaking, it is easy to see similarities between the FCs from participants 2 and 3, however the same cannot be said about the FCs from participant 6. While these results demonstrate the improved fingerprinting capability of the ST-HOSVD-based framework, potential limitations exist. Factors such as variations in FC stability across tasks or inter-individual differences in connectivity patterns could influence the framework's performance. Additionally, differences in cohort size, scanner parameters, or preprocessing pipelines may affect the generalizability of the results, and should be further analyzed in future studies. Both CP and Tucker decomposition are commonly used tensor decomposition techniques for dimensionality reduction and feature extraction purposes. In the context of fingerprinting, CP falls short due to two key reasons. First, the assumption that the original high-dimensional data can be reconstructed using non-interacting components is too restrictive, as we know that there are innate interactions between brain regions under a functional connectivity standpoint [47]. Second, due to CP decomposition being a single-rank decomposition, we cannot freely explore the dynamics of compressing the different dimensions of the data. Conversely, the Tucker's core plays a pivotal role in capturing the interactions between components while giving us the flexibility to explore how different levels of compression of the brain parcellation and participants' information affect fingerprinting, thus overcoming both drawbacks of CP decomposition. However, drawing neuroscientific insights directly from the factor matrices derived from Tucker decomposition of FCs is non-trivial due to the existence of the core tensor [21], which captures several interactions between the components from each factor matrix. FC fingerprinting, while having the potential to provide valuable insights in clinical and forensic settings, raises significant ethical concerns regarding privacy, bias, and potential misuse. The sensitive nature of neuroimaging data, which can reveal information about an individual's cognitive state, mental health, or even predispositions to certain conditions, makes it highly vulnerable to privacy breaches. Without proper anonymization, such data could be exploited for unauthorized profiling or discrimination. To safeguard privacy,robust anonymization techniques, such as de-identification and differential privacy, should be implemented. Additionally, data security measures, including encryption during storage and transmission, as well as strict access controls, are essential to prevent unauthorized usage. Bias is another concern, as models trained on non-representative datasets may lead to inaccurate or unfair identifications, particularly in forensic applications. Ensuring diverse, unbiased datasets and regularly auditing algorithms for fairness can help mitigate this risk. Addressing these ethical implications is crucial to prevent the misuse of neuroimaging fingerprinting and protect individual rights. Our study has limitations. As discussed above in detail, interpreting the factor matrices derived from Tucker decomposition is not straightforward due to the presence of a core tensor that captures complex interactions between all factor matrices [21]. Additionally, the proposed fingerprinting framework does not allow for incremental updates to the core and factor matrices when FCs from new participants are introduced. Rather, the entire Tucker decomposition and fingerprinting framework would need to be recomputed. Our study leads to several avenues for further research.