Efficacy of functional connectome fingerprinting using tangent-space brain networks Open Access

Functional connectivity is a mathematical estimate of the interactions between different brain regions, often derived from pairwise correlations (or other similarity measures) of neurophysiological signals such as BOLD signals obtained in fMRI scans (Bastos & Schoffelen, 2016; Martin et al., 2017; Oliver, Hlinka, Kopal, & Davidsen, 2019). In contrast to structural brain connectivity derived from physical connections of neurons or white matter tracts (Griffa, Baumann, Thiran, & Hagmann, 2013; Škoch et al., 2022), functional connectivity depends on the context (e.g., rest, task, etc.) and can change on very short time scales. Combined with tools from network neuroscience (Bassett & Sporns, 2017), functional connectomes (FCs), the matrix representation of functional connectivity, have been used to study group-averaged properties of the brain in the resting state, during tasks, and in the context of disease (Allen et al., 2022; Cabral, Kringelbach, & Deco, 2014; Du, Fu, & Calhoun, 2018; Faryadras, Burles, Iaria, & Davidsen, 2024). Increasingly, there is also interest in applying FCs in clinical settings, and as such, an accompanying interest in studying single-subject variability for both structural and functional connectivity (Allen et al., 2022; Barch et al., 2013; Gordon, Laumann, Gilmore, et al., 2017; Mueller et al., 2013; Oliver et al., 2019; Škoch et al., 2022). This is on top of the already-existing interest in how different anatomical regions of the brain can functionally vary across individuals (Kane & Engle, 2002; Vogel & Machizawa, 2004).

To this end, it has also been demonstrated that the subject-specific differences of FCs can serve as a “fingerprint” for identifying individuals (Finn et al., 2015), thus motivating FC fingerprinting. The original formulation is as follows: Given a known database of FCs belonging to unique individuals, and an unknown “target” FC, the task of fingerprinting is to identify which individual in the known database the target FC belongs to, with the identification accuracy being calculated as a measure of how many correct identifications are made. Using this approach, Finn et al. (2015) were able to demonstrate identification accuracies of 94% when using whole-brain FCs. Subsequent studies have taken different approaches to fingerprinting, such as using principle component analysis, but nevertheless found similar results (Amico & Goñi, 2018). The notion of fingerprinting has also been expanded beyond the task of subject identification, moving toward applying it in clinical settings. For example, patients with schizophrenia exhibited less longitudinally stable FCs relative to healthy controls (Kaufmann et al., 2018), while other studies have applied fingerprinting to identify predictors of treatment responses (Nemati et al., 2020). We also point the reader to a recent review of fingerprinting analysis (Ramduny & Kelly, 2024).

Ultimately, the ability and efficacy of distinguishing individuals, or the same individual longitudinally, comes down to a question of “distances”—FCs belonging to the same subject should have lower distances in some mathematical sense, which can be used as a classifier (Fawcett, 2006). Temporally diverging FCs could then also indicate the presence and evolution of disease (Supekar, Menon, Rubin, Musen, & Greicius, 2008), or perhaps converging FCs could reflect the efficacy of treatment for disorders such as depression (Wang, Hermens, Hickie, & Lagopoulos, 2012). Accurately defining distances in FC space can also be important to understand dynamical functional connectivity on short timescales and how it relates to behavior (Menon & Krishnamurthy, 2019).

However, defining a distance on the mathematical space of FCs is not trivial. FCs generated from correlation analysis are positive semidefinite (meaning all eigenvalues are greater than, or equal to, zero) (Wasserman, 2013). This imposes constraints on the possible values that the elements of the matrix can take on, which in turn curves the space of possible FCs, creating a manifold of possible values called the positive semidefinite manifold (Bhatia, 2015). For covariance matrices, this space is an infinite convex cone (Abbas et al., 2021). For correlation matrices (i.e., the time series is first standardized by z scoring), the space is a compact convex manifold (Rousseeuw & Molenberghs, 1994). Traditional measures of distance (or equivalently similarity), like the correlation distance, do not take into account the curvature of the space of FCs. Analogously to measuring the separation between cities on the surface of the Earth with a straight line in three dimensions, metrics that do not take into account the curvature of the space of positive semidefinite matrices can mischaracterize distances.

Geometry-aware methods are a set of techniques that take into account the curvature of this space (Venkatesh, Jaja, & Pessoa, 2020). One such method is the tangent space (TS) method, which involves projecting FCs onto a flat space that is tangent to a point on the surface of the convex manifold (Abbas et al., 2023; Ng, Varoquaux, Poline, Greicius, & Thirion, 2016). Once in this TS, traditional metrics of distance can be freely applied as this new space has zero curvature. Such an approach has been shown to improve the sensitivity of subject identification over traditional methods. For example, the work presented in Abbas et al. (2023) shows a nominal identification rate of monozygotic twins of 0.5 when using the non-TS method, and perfect identification when using the TS method (note however that this analysis used a modified version of the test-retest method presented in Finn et al., 2015). Importantly, they also observed that when distances in TS are calculated using the correlation similarity, the identification rates are not only high (often near or at unity and always higher than the non-TS method), but are also effectively independent of several hyperparameters (parcellation and regularization), reducing the amount of hyperparameter tuning relative to other geometry-aware approaches like the geodesic distance (Abbas et al., 2021; Venkatesh et al., 2020).

Here, we build on prior work and apply the TS method to the Midnight Scan Club (MSC) dataset (Gordon, Laumann, Gilmore, et al., 2017) (10 subjects, 5 male and 5 female between 24 and 34 years old [average 29.1 ± 3.3 years]). The MSC dataset was chosen as its unique features complement prior studies (Abbas et al., 2023; Finn et al., 2015). Specifically, the MSC dataset is part of a growing effort by researchers to precisely study the per-subject variability of the FC, motivated in part by improving individual-level applications of FCs to clinical settings (Gratton et al., 2020). To this end, the MSC dataset contains 5 hr of resting state data, and 6 hr of task-based data for each subject, compiled over 10 sessions. The uniquely long sessions offered by the MSC dataset allow for deep explorations of intersubject variability, which can expand prior studies in FC fingerprinting (Abbas et al., 2023; Finn et al., 2015). In particular, we explore how different subnetworks contribute toward subject discriminability, including to what extent subject discriminability is task dependent. If there is variation in identification efficacy between subnetworks, what is the connection between strongly performing and poorly performing subnetworks (Vanderwal et al., 2017)? For example, previous studies have suggested a dichotomy of “control” and “processing” subnetworks that play different roles in the context of tasks, and have different network theoretic properties (Power et al., 2011). Complementing this are observations of greater flexibility in certain subnetworks like the frontopariatal subnetwork relative to unimodal sensory areas (e.g., visual, auditory) (Mueller et al., 2013; Vanderwal et al., 2017). While prior work has used non-geometry-aware techniques to study the fingerprinting efficacy of subnetworks (Finn et al., 2015), here, we take advantage of the increased sensitivity of TS analysis to gain further insight into the relationship between fingerprinting efficacy and intersubject variability.

In this manuscript, we address the aforementioned questions, and while we find in particular the dichotomy of “control” and “processing” subnetworks to be true for previously used (non-TS) methods, the TS approach suggests some deviations from it. We also compare the efficacy of the TS method against the traditional (non-TS) method (here, the correlation distance) of subject discrimination to be able to contrast our findings against previous work (Finn et al., 2015), finding that the TS method universally outperforms the non-TS method. Additionally, while the large number of long scans per subject in the MSC dataset (10 for each category of recordings, spanning 10 consecutive days) are important for answering fundamental questions regarding subject variability (Gordon, Laumann, Gilmore, et al., 2017), a natural question follows—is that much data actually required? Thus, we explore the resource requirements for subject identification (e.g., number of recordings, duration of recordings), again comparing the TS and non-TS methods, and find that the TS method requires substantially fewer resources to perform as well as the non-TS method. Moreover, the TS method offers extra degrees of freedom for performing the projection (i.e., selecting the point at which the projection is made). While previous work has studied the different mathematical techniques one can use to obtain the reference point (Abbas et al., 2023), it is not clear whether certain FCs (e.g., resting or task-based) perform better as a reference. We observe that subject identification is comparable across all tasks with regard to this, which lessens the number of preexisting recordings a fingerprinting task would be required to have. Answering all these questions of practicality and implementation is particularly important for possible future applications.

Here we analyze the open source MSC dataset, as described in greater detail in Gordon, Laumann, Gilmore, et al. (2017). Briefly, the dataset consists of 10 rest fMRI recordings (over 10 subsequent days) per 10 subjects; five male and five female between 24 and 34 years old (average 29.1 ± 3.3 years). Each session started with 30 min of resting-state recording, which involved visually fixating on a white crosshair presented against a black background. Subsequently, each subject was then scanned during the performance of three separate tasks: motor (two runs per session, 7.8 min combined), mixed design (two runs per session, 14.2 min combined), and incidental memory (three runs per session, 13.1 min combined). The subjects had to exhibit directed movement in response to visual cues in the motor task, discriminated between patterns and words in mixed task, and made binary decisions about faces, scenes, and words in the memory task.

A Siemens Trio 3T MRI scanner was used to record fMRI data. Axial functional images were taken with the following specifications: TR = 2.2 s, TE = 27 ms, flip angle = 90°, voxel size = 4 × 4 × 4 mm³, matrix size = 64 × 64 × 36. A high-resolution T1-weighted structural MRI recording (TR/TE/TI (inversion time) = 2,300/3.7/1,000 ms, voxel size = 0.8 × 0.8 × 0.8 mm³) was used as anatomical reference. One subject (MSC08) reported drowsiness, and thus was excluded from this analysis (Gordon, Laumann, Gilmore, et al., 2017). This left 90 resting-state recordings (10 per subject, with nine subjects). The Gordon-333 atlas, which parcellates the fMRI data into time series for 333 common regions of interest (ROIs) (Gordon et al., 2016; Midnight Scan Club: ROI-based information, 2017) was used to ensure the size of each FC was the same across subjects (333 × 333), a requirement of this analysis. Previous work has shown that identification rates when using the correlation distance, which we use in this manuscript (discussed below), is optimal and independent of parcellation granularity beyond 100 parcels (Abbas et al., 2023), and thus, this “hyperparameter” is fixed to 333 in this manuscript.

The preprocessing pipeline involved reducing artifacts, maximizing cross-section registration, and distortion correction by mean-field mapping. For resting-state recordings, periods of motion were removed with the provided temporal masks. These were identified as volumes above a frame-by-frame displacement (FD) threshold of 0.20 mm, as per Power et al. (2014). Frames with FD > 0.2 mm were labeled as motion-contaminated and removed from the recording. The total amount of removed frames was 28% ± 18% of the total recording time (Gordon, Laumann, Gilmore, et al., 2017). For task recordings, an additional fixation temporal mask was used to remove periods of no fixation (Gordon et al., 2023). Several task-based recordings did not have accompanying temporal masks, or had masks whose length did not match the length of the recording. These recordings were thus discarded. One subject (MSC09) had five sessions discarded and so this subject was not considered for the task analysis. As we wanted to maintain the same sessions across all subjects, any session that was not common to all remaining subjects was discarded. This resulted in 48 total recordings (six sessions per subject, eight subjects).

An important consideration for the TS projection (i.e., Equation (3)) is the invertability of C_ref. This matrix is noninevitable if det(C_ref)  =  0. Because the determinant is equal to the product of all the eigenvalues, C_ref is noninvertable if there exists at least one zero eigenvalue. If this is indeed the case, regularization can be performed by adding λ1 to C_ref, where λ  >  0 and 1 is the identity of commensurate size as C_ref (Venkatesh et al., 2020). The effect of regularization raises the eigenvalues of C_ref such that C_ref + λ1 is invertable. For clarity, we focus predominately on results for λ  =  1; however, we also tested λ  =  0.1and λ  =  10.

The distance matrix D can be decomposed into block-diagonal form, where each block corresponds to a single subject, and the size of the block is the number of FCs (or recordings) belonging to said subject. The elements of D that are within such a block are called intrasubject distances, while elements of D outside one of these blocks are intersubject distances. For the MSC, the number of intersubject distances is 7,200, while the number of intrasubject distances is 810. Because approximately 90% of the data belongs to the intersubject class, the dataset is said to be imbalanced. We generate two cumulative distance distributions from the respective “within” and “between” subject values in D.

An alternative metric for quantifying the quality of a classifier is to use the precision-recall (PR) curve, which instead plots precision, TP/(TP + FP), against recall, TP/(TP + FN), across all thresholds θ. The PR curve has been found to be more robust in the context of imbalanced datasets (Saito & Rehmsmeier, 2015). The precision can be interpreted as the proportion of correctly classified pairs of matrices among all the positive predictions made by the classification procedure, while recall is proportion of correctly classified pairs among all the actual positive instances (Géron, 2022). The AUC is again a commonly used metric for summarizing the PR curve. However, unlike the AUC-ROC, which is bounded between 0.5 and 1, the lower-bound of the AUC-PR is equal to the accuracy of a random chance classifier.

To test the efficacy of fingerprinting with respect to the length of the recording, we apply a bootstrapping approach. First, a random frame of the recording is chosen, and segments of length l are chosen on each side of the random point. The resulting window is of length 2l + 1, but we emphasize here that, because frames with large motion periods are removed, these frames may not have been originally sequentially adjacent. We then calculated the FC matrix from points within this window (Equation 1), and repeated the above fingerprinting procedure. This random sampling was repeated. For large windows l, the probability to re-sample the same section of the recording is high, while for small windows, resampling becomes less probable, thus the number of trials should depend inversely on l. We chose this to be ⌊L/2l⌋, where L  =  min (T₁,  T₂,  …,  T_N) is the smallest duration of all of the N recordings being considered (which is needed as artifact removal results in unequal total recording duration). For each trial, the AUC is calculated and finally averaged across each trial, with the standard deviation for error bars.

The Gordon 333 atlas is subdivided into a set of 13 nonoverlapping resting-state networks (RSNs) (Adhikari et al., 2021). The size of these RSNs ranges from four nodes (salience network) to 41 nodes (the default mode network), with 47 nodes belonging to an “unassigned” category. We found that fingerprinting using RSNs was unreliable for particularly small RSNs. As such, we discarded all RSNs with less than 10 nodes (four RSNs), leaving a total of eight RSNs for the analysis: visual (VIS), somato-motor hand (SMH), auditory (AUD), cingulo-opercular (COP), ventral attention network (VAN), dorsal attention network (DAN), frontal parietal network (FPN), and default mode network (DMN). Once RSNs have been established, we generated FC matricies for each RSN separately. We then recalculated the distance matrix D and repeated the fingerprinting analysis using the TS and non-TS methods, and separability is calculated from the ROC for each case. This was done for both resting-state recordings as well as task-based recordings.

In order to mimic how fingerprinting might realistically be employed in a clinical setting, we divide the collection of FCs into two groups: a database of k FCs per N subject for which the corresponding subject is known, and a target FC whose corresponding subject is not known (Finn et al., 2015). The pairwise distance between the target and each of the Nk database FCs is computed using both the TS and non-TS method. In the case of the TS method, this is done by calculating a reference point using all Nk database FCs. The k database FCs are chosen randomly from the 10 sessions, without replacement. A single target is then chosen from the remaining N × (10 − k) FCs.

To identify the subject of the target FC, we use a majority rules system; we calculate the mean target distance, averaged over all k known subject FCs. We classify the target FC as belonging to the subject with the lowest average distance. A point is awarded only if the correct subject is identified. This is repeated 100 times, with a total score calculated as the percentage of the number of successes, which we compute for each k. We performed this analysis for the resting state data as well as the somato-motor subnetwork (see below) during the motor task as a worst-case scenario.

From the MSC dataset, FCs are generated from pairwise correlations of the parcellated regions, as described in the Methods section. One such FC is shown in Figure 1a. We attempt to identify individuals based only off distances between these FCs using two methods: first, by projecting FCs into a TS where the distance is subsequently calculated (the TS method; see also Figures 1b, 1c), and second, by calculating distances directly between the FCs (non-TS), as described in the Methods section. In both cases, the pairwise correlation distance (Equation 5) serves as the distance metric. The identification rates of each method are then compared. We will first analyze the resting-state recordings, and then task-based recordings. Finally we analyze subnetworks of the Gordon 333 parcellation and the robustness of the results against recording length.

We focus first on the 90 resting-state recordings (10 for each of the nine subjects). The reference point for the TS projection was chosen to be the logarithmic mean calculated across all recordings (Equation 4), using λ  =  1 for regularization. The pairwise distances (for either TS or non-TS methods) were gathered into a distance matrix D (see the Methods section), shown in Figure 2a. When sorted by subject, D is block-diagonal, with low intrasubject distances going along the main diagonal, and high intersubject distances off the the diagonal. This indicates that FCs belonging to the same individual (intra) are closer than those belonging to different individuals (inter), as expected (Finn et al., 2015; Gordon, Laumann, Gilmore, et al., 2017).

Figure 2b shows the CDF for all the intra- (solid) and interblock (dashed) distances separately, for both the non-TS (red) and TS (blue) method. For either method, a threshold distance θ defines a decision boundary, such that FC pairs i, j with distance d_{i, j}  <  θ are classified as belonging to the same subject. Intrablock distances with d_{i, j}  <  θ correctly identify i, j with the same subject (TPs), while interblock distances with d_{i, j}  <  θ incorrectly identify i, j with the same subject (FPs). In terms of the inter- and intrasubject distance CDFs, perfect subject discriminability is possible only if there exists a value θ for which the interblock CDF is zero, while the intrasubject CDF is one. Generally though this is not the case, meaning that FPs (an interblock distance with d_{i, j}  <  θ) or FNs (an intrablock distance with d_{i, j}  >  θ) will occur.

Figure 2c shows the classification accuracy (ACC) as a function of θ for both the TS and non-TS methods (Equation 6). The ACC for the non-TS method peaks at 0.95. Due to data imbalance, it is important to contrast this value against a trivial classifier that assigns FCs to subjects randomly. Because 90% of the values of D belong to intersubject class, such a trivial classifier would have an ACC = 0.9, which is denoted by the dashed blue line in Figure 2c. Conversely, the TS method peaks at 0.9998, well above the trivial classifier accuracy. The range of θ for which the accuracy is near unity is also much broader for the TS method than the non-TS method, implying that the TS method is more robust with respect to the specific choice of θ.

We also computed the receiver operator characteristic (ROC) curve shown in Figure 2d (see the Methods section). For the TS method, the ROC appears visually constant (blue). For the non-TS method, the TPs increase monotonically with the FPs due to the overlap of the inter-intra CDFs. We use the AUC-ROC to summarize the ROC curves (see the Methods section). Whenever it is not explicit from the context, we will adopt subscripts T and S to distinguish between the TS and non-TS methods, respectively. We found AUC_T = 0.99998 (perfcurve MATLAB), while AUC_S = 0.94. We repeated our analysis for different regularizations, using λ  =  0.1 and λ  =  10, and observed that higher regularization improves subject discriminability. For λ  =  0.1, we found AUC_T = 0.9997, where as for λ  =  10, we observe perfect subject discriminability (AUC_T = 1). We also calculated the PR curve (inset of Figure 2d) as a complement to the accuracy and ROC (see the Methods section). We found the PR curve gives qualitatively similar results as the ROC curve. For the TS method, we find the AUC-PR to be 0.9997, and for the non-TS method, the AUC-PR is 0.98. For clarity, we will focus on the ROC curve for the remainder of the manuscript.

For comparison, we calculated distances using the geodesic distance as well (Equation 2). As in Abbas et al. (2021), we found that classification efficacy depends heavily on the regularization, and only outperforms the non-TS method for a relatively narrow range of values (see Supporting Information). Within this range, we found an optimal value at λ  =  1.46, which is consistent with those observed by Abbas et al. (2021). For this value, the classification accuracy reaches a high of 0.96 (θ  =  9.98), though this was not included in Figure 2c as the range of θ were very different (θ ∈ [5, 20]). The ROC and PR curves are shown in Figure 2d. We find an AUC-ROC of 0.97, and AUC-PR of 0.99. This suggests that for an optimized value of the regularization, the geodesic distance can perform better than the non-TS method, but we never observe it to outperform the TS method. Given this, we exclusively focus on the TS method in the following.

We also tested if there was observable drift in functional connectivity over the 10 sessions, spanning 10 subsequent days. For each subject, the FC corresponding to the first session was chosen as the reference. For each of the nine subsequent sessions, the distance from the initial session was calculated. Figure 2e) shows the mean distance averaged across subjects for both the TS and non-TS methods. Neither the TS nor non-TS methods displayed any significant trend. To do a more fine-grained analysis of potential day-to-day differences, we also subdivided recordings into nonoverlapping blocks of equal size. FCs generated from blocks belonging to the same session were minimally, but significantly, closer to each other than FCs belonging to different sessions (see Supporting Information Figure S2). This is consistent with day-to-day variations in a subject’s head placement. Interestingly, only the TS method was able to observe these differences, suggesting the method has higher sensitivity.

Lastly, the above analysis compares FCs pairwise. This approach may not be representative of how fingerprinting would be used in practical setting where an unknown FC is compared against a database of labeled FCs (Abbas et al., 2021; Finn et al., 2015). Using the approach outlined in the Methods section, we tested the efficacy of identifying the corresponding subject of a randomly chosen unknown FC to a database of known FCs. Because of the large number of sessions in the MSC dataset, we are also able to test the effect of the size of the database. This was done by choosing k random FCs per subject to form the database (without replacement). The unknown FC is randomly chosen from the remaining FCs. For each k ≥ 1 the TS method identified the subject of the unknown FC perfectly. The non-TS method showed a dependence on the database size. For k  =  1 the identification rate was 97%, which is on par with the classifier accuracy. As the database size increased, subject identification rates improved up until k  =  4 where it saturated at 100%.

For each of the three tasks (motor, memory, mixed) we generate the distance matrix D separately. For the non-TS method these are shown in Figure 3a. As mentioned in the Methods section, several recording days and one subject had to be removed from the task-based analysis due to missing auxiliary fixation masks. We also note that the length of the recordings was not controlled for here, but is analyzed in a later section.

Figure 3b shows the ROC curves for the individual tasks when using the non-TS method. As before, we quantify the ROCs using the AUC. we find that the mixed and memory tasks performed the best (AUC_S = 0.99 and 0.97, respectively), while the motor task performs the worst (AUC_S = 0.94). Due to different number of sessions and subjects, we also reanalyzed the rest case with the same sessions removed for consistency. We found that AUC_S = 0.98, an increase from the 0.94 in the previous section. We suspect that this is due to the task of fingerprinting being easier when the number of subjects is decreased (Ramduny & Kelly, 2024; Waller et al., 2017).

The Gordon 333 atlas is subdivided into 13 nonoverlapping resting-state subnetworks. Here, we test the efficacy of subject discriminability using these subnetworks in isolation. Only subnetworks with 10 or more ROIs were considered, leaving eight in total. For each subnetwork, we calculate the ROC-AUC for the three task cases and all available rest recordings. ROC-AUC scores for the non-TS and TS methods are shown in panels a and b of Figure 4, respectively. Table 1 summarizes the mean AUC averaged across all subnetworks of each case (denoted as $AUC¯$⁠).

Focusing first on the non-TS method, we find the average ROC-AUC for the rest case to be $AUC¯Srest=0.97$ ± 0.02 (error bars denote one standard deviation across the different subnetworks). The AUD, SMH, and VIS subnetworks performed the worst (AUC$Srest$ = 0.92, 0.95, and 0.96, respectively), while FPN, DAN, and COP performed the best (AUC$Srest$ = 0.998, 1, and 0.995 respectively). The performance of these six subnetwork follows exactly the “processing” and “control” subdivision proposed by Power et al. (2011). We also find the VAN and DMN also perform well (AUC = 0.986 and 0.998, respectively), though these are not categorized as processing and control.

These trends were observable when analyzing the task-based recordings as well; AUD, SMH, and VIS perform the worst (AUC_S = 0.84, 0.75, and 0.80, respectively). Of the remaining subnetworks, VAN, COP, and DMN have a noticeably reduced AUC score. This is largely consistent with the results by Finn et al. (2015), who used non-TS analysis for fingerprinting. For the mixed and memory tasks, we found $AUC¯Smix.=0.95$ ± 0.04, and $AUC¯Smem.=0.95$ ± 0.05. Subject discriminability was worst in the motor tasks, with $AUC¯Smot.=0.90$ ± 0.08.

The fingerprinting efficacy of some subnetworks was found to be task dependent while others were task independent. Generally, the “processing” networks outlined above (AUD, SMH, VIS) were highly task dependent, while the FPN and DAN were almost entirely task independent. Interestingly, while these processing nodes are often the worst performing in terms of fingerprinting efficacy, in the rest-based recordings, they are still capable of outperforming the rest-case whole-brain analysis (AUC_S = 0.94; dashed line in Figure 4a).

As Figure 4b shows, the TS method outperforms the traditional method for all subnetworks across all cases tested, never going below AUC_T = 0.98. The resting and memory cases both performed strongly across all subnetworks with $AUC¯Trest=0.9996$ ± 0.0004 and $AUC¯Tmem.=0.9993$ ± 0.0004. For mixed tasks, we found $AUC¯Tmix.=0.998$ ± 0.01, with the AUD subnetwork standing out as performing worse than all other subnetworks (AUC_T = 0.995 ± 0.001). Discriminability was again lowest during motor tasks (⁠$AUC¯Tmot.=0.995$ ± 0.05). Most strikingly, while the AUD and SMH again performed the worst (as in the non-TS method), the VIS subnetwork performed comparable with the processing subnetworks, despite its categorization as a control subnetwork. It is conceivable that this reflects the TS method’s increased sensitivity. We also note that these results also did not qualitatively change for regularizations of λ  =  0.1 and λ  =  10.0, and all values of λ outperformed the non-TS method (see Supporting Information Figure S4Gordon, Laumann, Gilmore, et al., 2017). However, in contrast to the regularization tests performed above, here, we found smaller regularization fared better at subject discrimination.

Finally, we repeated the fingerprinting using the unknown target FC with a known database for the SMH subnetwork in the motor task. We chose this as it presents a worst-case scenario in terms of how large the database would need to be for fingerprinting. As in the resting case, we randomly choose k FCs per subject to form the database, and a random target FC is chosen from the remainder. For the TS method we observe that for k  =  1 the identification success rate was 95%, which increases to 99% at k  =  4 (we did not test above this due to the reduced number of sessions in the task data as explained in the methods). For the non-TS method, the success rate at k  =  1 was 78%, which increased to 87% at k  =  4. This suggests that for this worst-case scenario, fingerprinting requires k  >  4, at least in the non-TS method.

Here, we test the efficacy of FC classification as a function of data length. We temporally subsample the whole-brain recordings from which FCs are generated. A bootstrapping method is used to calculate an average AUC (see the Methods section for further details). Because periods of motion are removed, results are reported as the number of frames being used, though we provide what that time would have been when sampled at 2.2 Hz for reference.

First we analyzed resting state recordings which were subsampled down to between 16 and 151 frames (30 s to 5 min). Identification using the TS method was effectively independent of the recording length, saturating close to unity even for 16 frames (Figure 5a). Conversely, classification using the non-TS method performs worse at identifying subjects for the same number of frames, with AUC_S = 0.83 ± 0.02 at 16 frames. While we observe a rapid increase to AUC_S = 0.968 ± 0.001 until 46 frames (roughly 1.5 min), the AUC_S does not saturate to 0.98 until approximately 100 frames (3.5 min).

Task recordings were subsampled to between seven and 61 frames (15 s to 2.2 min) due to their shorter original duration. Figure 5b shows that the TS method is consistently near unity, though for the shortest recording lengths, we do observe a decrease in the AUC_T, especially for the motor task (AUC$Tmot.=0.90±0.01$⁠). Again, the non-TS method performs poorly with the smallest segments (⁠$AUCSmix.=0.78$⁠, $AUCSmem.=0.75$⁠, $AUCSmot.=0.71$⁠), followed by a rapid rise until 40 frames, and a slow increase thereafter, which is consistent with Figure 5a. We also observe the motor tasks perform the worst across all recording durations, with AUC$Smot.$ = 0.95 for the longest segments. Figure 5b also shows that, when controlled for length, the mixed and memory tasks outperform the resting case using the non-TS method, whereas the motor task does not.

Finally, we tested the effect of data length on the resting-state subnetworks of the Gordon 333 parcellation. We focused on the SMH subnetwork in the motor task, as this was the worst performing subnetwork across all cases. The results are shown in Figure 5c. For the shortest segments, both TS and non-TS methods perform poorly at subject discrimination, with AUC$Tmot.$ = 0.61 ± 0.04, and AUC$Smot.$ = 0.57 ±0.03, respectively, both of which are worse than the whole brain analysis and comparable with chance levels (AUC = 0.5). While discriminability using the AUC_T improves to 0.96 for 60 frames, AUC_S only reaches 0.78 for the same amount of data, though it does not appear to yet be saturating.

We performed FC fingerprinting of resting-state and task-based fMRI recordings belonging the MSC dataset. We applied two approaches to performing this task—a geometry-aware TS method that takes into account the curvature of the positive-semidefinite matrix space to which FCs belong, as well as the standard method of calculating correlation distances directly form FCs, which does not take this curvature into account. In each analysis, we compared the efficacy of subject identification of both methods.

We first performed classification of the 90 resting state recordings (10 recordings per subject) of the MSC. Consistent with the fingerprinting analysis performed in Finn et al. (2015) we observed that, for a given discrimination threshold θ, the non-TS method was capable of reaching a high accuracy of subject discrimination (ACC = 0.95). However, the range of θ for which the method outperformed a trivial classifier (e.g., one that randomly assigns FCs) was small. Conversely, the TS method outperformed the non-TS method in all measures of classifier efficacy (accuracy, ROC, and PR), achieving near perfect scores in each, and over a considerably wider range of θ. This latter aspect is particularly important for expanding fingerprinting analysis to practical settings—a wide range of possible discrimination thresholds would allow for the addition of new data without the need to recalculate an optimal identification threshold.

One important question with regard to subject identification using FCs is whether the method simply reflects anatomical differences that could artificially improve fingerprinting efficacy (Gordon, Laumann, Adeyemo, & Petersen, 2017). Our analysis showed that subject discrimination efficacy is state dependent. This was especially true for the analysis of resting state subnetworks where certain subnetworks displayed strong task dependence while others did not. Thus, while anatomical differences may contribute toward subject discriminability, we believe these observations cannot be explained by this alone. Likewise, previous studies on FC fingerprinting (using the non-TS method) address this by applying a smoothing kernel to the BOLD signals prior to registration to a common atlas, finding this led to only a small decrease in fingerprinting efficacy (Finn et al., 2015), further suggesting evidence that the method reflects more than anatomical differences.

The above point is important as the clinical usefulness of fingerprinting methods may lie in longitudinal observations of a single subject, instead of discriminating between multiple subjects, where anatomical changes would be expected to be minimal (or at least on shorter time scales). For example, FCs have been applied to study network changes in the context of neurological diseases and disorders such as major depressive disorder (MDD) (Supekar et al., 2008; Wang et al., 2012). While MDD is associated with anatomical differences relative to healthy controls (Korgaonkar, Fornito, Williams, & Grieve, 2014), FCs could be used to track the efficacy of treatment on shorter time scales, where significant anatomical changes would not be expected. Indeed, recently, the fingerprinting approach was used to study treatment response and predictors of treatment response for MDD (Nemati et al., 2020), however, without the TS method. It is possible the increased sensitivity of the TS method would potentially prove a superior biomarker (relative to the standard non-TS method) in FC studies of not only MDD, but also potentially more general brain disorders (Du et al., 2018; Kaufmann et al., 2018).

Expanding on clinical applicability, we also studied how the size of a preexisting database can effect fingerprinting efficacy when a new FC is introduced. Prior studies have focused on datasets containing test-retest data, which only contained two FCs, limiting the extent to which this question can be studied (Finn et al., 2015). For the non-TS method, we found that fingerprinting efficacy improves monotonically with the database size, eventually saturating at perfect discriminability. For the resting state data, this was found to occur at four FCs; however, the exact point depends on the task, and may also depend on the duration of the recordings. Conversely, the TS method performs fingerprinting perfectly with only a single FC per subject in the database for resting-state data. Furthermore, we observed that the TS method was capable of near-perfect classification after only a minute worth of scans, while the non-TS method could take 3 min worth and would still not match the TS method in terms of identification efficacy. This resource efficiency could be an important point in pediatric research where frequent in-scanner movement poses a great challenge to data aquisition as well as the comfort of the patient (Ellis et al., 2020). The significantly lower amount of data required by the TS method could shorten the acquisition time required, and when paired with other methods (e.g., movie-viewing; Vanderwal et al., 2017) could ease the overall procedure, while still maintaining the usefulness of existing data. We note, however, that an important limitation in this study is the number of subjects (nominally 9), which certainly leads to higher classification efficacy (Ramduny & Kelly, 2024; Waller et al., 2017). While we conjecture that the TS method would still outperform the non-TS method with more subjects, the rate of potential efficacy decrease as a function of the number of subjects, especially relative to the non-TS method, is not known and is not addressable using the MSC data alone. Tackling this remains an interesting challenge for the future.

We also tested subject discriminability in the context of task-based recordings, which included a motor task, incidental memory, and a mixed-design task. Using the non-TS method, we observed that, when differences in data length were controlled for, subject discrimination improved for mixed and memory tasks relative to rest. This is largely consistent with what was also observed by Abbas et al. (2023), except that we observed motor tasks perform worse relative to rest. Whether this is related to the differences in the tasks Rai, Graff, Tansey, and Bray (2024) performed (detailed in Barch et al., 2013) would be interesting to investigate in the future. Despite this, it is interesting to observe this state-dependent subject discriminability and how it may relate to the task. The work presented in Abbas et al. (2023) proposes a “fingerprinting gradient” in the context of decreasing subject discrimination efficacy from individuals to monozygotic twins and finally dizygotic twins. Perhaps it is possible to postulate a conceptually similar fingerprinting gradient going from “cognitively heavy” tasks (mixed and memory), down to motor tasks that involve more stereotyped neural activity, with resting state potentially being a boundary between the two. This remains an exciting challenge for the future. However, when using the TS method, all tasks allowed for near-perfect subject discrimination, so long as the scan was at least around a minute in length. Interestingly, we observed no significant dependence on the choice in reference (e.g., using a reference generated from motor-task FCs to fingerprint resting-state FCs). This is useful as it means that a database of rest recordings (as an example) can still perform well in discriminating task-derived FCs.

While subject discrimination performed well on the whole-brain level, fingerprinting using resting-state subnetworks also performed as well, and sometimes better. We find the efficacy of a subnetworks ability to perform fingerprinting aligns closely with its membership to the “control” or sensory/motor “processing” networks (Power et al., 2011). The control network, containing the FPN, DAN, and COP, is thought to be more flexible in order to be able to adapt to novel tasks (Zanto & Gazzaley, 2013). Other studies have also found that the FPN, VAN, DMN, and DAN exhibit high intersubject variability, all of which were found to have the greatest performance in our analysis (Mueller et al., 2013; Vanderwal et al., 2017). We speculate this flexibility and variability is responsible for subject discrimination, an observation that has also been reported in Finn et al. (2015). These subnetworks, especially the FPN, are also thought to have hub-like properties in relation to various tasks, which could explain why fingerprinting efficacy was unchanged by tasks (true for both TS and non-TS methods) (Cole et al., 2013). Likewise, while not necessarily a member of the control network, the DMN interacts strongly with the FPN (Elton & Gao, 2014) and is involved in cognition, motivating its high fingerprinting efficacy.

Conversely, the more static nature of processing networks (VIS, AUD, SMH) (Zanto & Gazzaley, 2013) could be related to their poor performance at fingerprinting, at least when using non-TS methods. Other studies have also found that intersubject variability was lowest in these unimodal sensory subnetworks (Mueller et al., 2013; Vanderwal et al., 2017). While these subnetworks performed poorly relative to other subnetworks when using the TS method, objectively speaking, their AUC scores were high. One striking exception was the VIS subnetwork; using the non-TS method, the VIS subnetwork performed in line with the other processing networks (i.e., poorly), but using the TS method, it performed comparable with processing networks and was task independent. Of course, visual stimuli and feedback are important aspects of motor tasks, memory, and cognition in general (Cavanagh, 2011; Hofstetter, Achaibou, & Vuilleumier, 2012), which could motivate this finding, but does not on its own explain why the AUD network does not display the same. Visual memory has been demonstrated to be stronger than auditory memory (Cohen, Horowitz, & Wolfe, 2009), which could be related, but this is speculative. If this observation is reproducible in other studies, we believe this would form an interesting point of investigation from both the neuroscience and mathematical point of view.

While control networks were state-independent, the fingerprinting efficacy of processing subnetworks was not (with the aforementioned exception). Efficacy was lowest during motor tasks, ubiquitously improving in the rest state and even in the mixed and memory tasks, and often outperformed the whole-brain FCs (at least, for the non-TS method). This brings up two points: First, the reason why process subnetworks can so drastically improve their fingerprinting efficacy during rest is not entirely clear. It could be related, for example, to the FPN and executive control (see above), or distributed coding of neural activity (Steinmetz, Zatka-Haas, Carandini, & Harris, 2019). Second, the fact that subject discriminability improves using subnetworks could suggest that the various subnetworks cause a blurring effect in whole-brain FCs—perhaps from the processing networks themselves. This effect could be useful to consider when studying the early stages of disease when differences may be less obvious, such as in the use of FCs to study Alzheimer’s disease (Supekar et al., 2008). Moreover, we believe the variation in fingerprinting efficacy with region and task (and the dichotomy between the “control” and “processing” areas) further suggest that intersubject functional differences are being measured, and not just anatomical ones.

The distances between FCs can provide information about the intrinsic differences of individual functional brain dynamics. While comparing FCs between individuals can offer interesting insights, its potential use for understanding the evolution of a single individuals brain dynamics longitudinally, such as management of disorders or disease, is perhaps even more exciting. The results above motivate that geometry aware methods (like TS analysis) can utilize both new and existing data more efficiently, and with greater accuracy.

This project was supported by Alberta Innovates (232403074). J.D. was supported by the Natural Sciences and Engineering Research Council of Canada (RGPIN/05221-2020). S.K.V.K. was supported by Mitacs through their Globalink Research Internship program.

Supporting information for this article is available at https://doi.org/10.1162/netn_a_00445.

Davor Curic: Formal analysis; Investigation; Methodology; Software; Validation; Visualization; Writing – original draft; Writing – review & editing. Sudhanva Kalasapura Venugopal Krishna: Data curation; Formal analysis; Investigation; Software; Visualization; Writing – original draft; Writing – review & editing. Jörn Davidsen: Conceptualization; Funding acquisition; Project administration; Resources; Supervision; Writing – original draft; Writing – review & editing.

Jörn Davidsen, Alberta Innovates, Award ID: 232403074. Jörn Davidsen, Natural Sciences and Engineering Research Council of Canada (https://dx.doi.org/10.13039/501100000038), Award ID: RGPIN/05221-2020. Sudhanva Kalasapura Venugopal Krishna, Mitacs (https://dx.doi.org/10.13039/501100004489).

Functional connectome/connectivity (FC):

A matrix representation of the brain connectivity derived from the pairwise correlations of brain dynamics (such as those recorded by fMRI).

Fingerprinting:

The procedure of identifying the subject(s) that produced an unknown FC(s).

Positive semidefinite:

A mathematical property that all eigenvalues of the FC are greater (or equal to) than zero.

Positive semidefinite manifold:

The mathematical space of positive semidefinite matricies, which is a subspace of all possible matricies.

Compact convex manifold:

A space that is does not extend infinitely and has no holes, and whose curvature is convex everywhere. An example of such a space would be a sphere.

Geometry-aware methods:

Approaches to calculating distances between two FCs that account for the curvature of the space.

Tangent space:

A particular geometry-aware method that approximates distances by finding a flat space that is tangent to a point of a curved space. Analogous to observing the Earth to be flat locally, despite its convex curvature.

Regularization:

A mathematical procedure of adding a positive value λ to the diagonal of the FC to ensure it is inevitable.

Reference matrix:

The point at which the tangent space is calculated, calculated here as the logarithmic average of all FCs.

Area under the curve (AUC):

A commonly used metric for summarizing the ROC or PR curves.

Precision-recall (PR):

A plot of the relevant items among the returned items (precision), against the relevant items that were actually returned (recall).

Receiver operator characteristic (ROC):

A plot of the true positive rate and false positive rate used to visualize the performance of a classifier.