# Functional Connectome Fingerprinting Through Tucker Tensor Decomposition
###### Abstract  
The human functional connectome (FC) is a representation of the functional couplings between brain regions derived from blood oxygen level-dependent (BOLD) signals. Over the past decade, studies related to FC fingerprinting have sought to uncover functional patterns that enable uniquely identifying individuals across repeated scanning sessions, hence demonstrating the stability and distinctiveness of functional brain organization. In this study, it is hypothesized that tensor decomposition techniques, given their ability to project high-dimensional data into lower-dimensional spaces, enable detecting the brain fingerprint with high accuracy. A mathematical framework based on Tucker decomposition is presented to uncover the FC fingerprint of 426 unrelated participants from the Young-Adult Human Connectome Project (HCP) Dataset. An analysis of how brain parcellation granularity, decomposition rank, and scan length relate to within- and between-condition (resting state-task) fingerprinting was conducted. Relative to FC matrices as well as to Principal Components Analysis (PCA), tensor decomposition significantly increases the functional connectome's fingerprint. For parcellation granularity of 214 in the within-condition setting, an improvement of 11-36% was seen across all fMRI conditions. Similarly, a substantial improvement, ranging from 43 to 72%, was observed in the between-condition setting relative to FC matrices. Compared to matching rates obtained directly on FCs and when applying other data-driven decomposition methods, Tucker decomposition led to higher or the same level of matching rates for all analyses. Furthermore, in the context of between-condition fingerprinting, results from the proposed framework suggest that partially sampling time points from resting-state time series is sufficient to uncover FC fingerprints with high accuracy. functional connectome; tensor decomposition; fingerprinting; dimensionality reduction 20251  
reliability of such findings and to capture individual-specific characteristics that may be overlooked in group-level studies, the concept of a \"brain connectivity fingerprint\" has gained growing interest [4; 5; 6]. Functional connectivity fingerprinting of the brain refers to the ability to identify an individual's functional connectome (FC) from a set of FCs in repeated fMRI imaging sessions. The existence of a brain fingerprint has been established in the last decade with work done with data from functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) [7; 8]. Such studies have shown that the functional connectome of the brain varies between individuals, therefore, serving, to some extent, as a _fingerprint_. In the literature, different studies of FC fingerprinting have been conducted with varying approaches, such as principal component analysis (PCA) [9; 10], sparse dictionary learning (SDL) [11], geodesic distance in regularized FC [12] and correlation distance in FC tangent space projections [13]. In [9], the authors show that individual connectivity profiles can be reconstructed through an optimal linear combination of PCA-derived orthogonal components. In [10], the authors perform PCA in a subset of \"learning\" FCs to obtain an eigenspace in which the \"validation\" FCs are projected, thus enabling the identification of the fMRI condition or the participant to which the \"validation\" FC belongs. In [11], SDL is used to refine FC profiles, leading to a higher distinctiveness in FCs relative to raw connectivity. PCA and SDL work on 2-dimensional data, while Tucker decomposition is designed for higher-dimensional data structures called tensors, essentially allowing it to analyze complex relationships across multiple variables in a dataset by decomposing it into a core tensor and factor matrices along each dimension. In essence, Tucker decomposition may be thought of as a \"higher-order PCA\".