Joint embedding: A scalable alignment to compare individuals in a connectivity space

Abstract

A common coordinate space enabling comparison across individuals is vital to understanding human brain organization and individual differences. By leveraging dimensionality reduction algorithms, high-dimensional fMRI data can be represented in a low-dimensional space to characterize individual features. Such a representative space encodes the functional architecture of individuals and enables the observation of functional changes across time. However, determining comparable functional features across individuals in resting-state fMRI in a way that simultaneously preserves individual-specific connectivity structure can be challenging. In this work we propose scalable joint embedding to simultaneously embed multiple individual brain connectomes within a common space that allows individual representations across datasets to be aligned. Using Human Connectome Project data, we evaluated the joint embedding approach by comparing it to the previously established orthonormal alignment model. Alignment using joint embedding substantially increased the similarity of functional representations across individuals while simultaneously capturing their distinct profiles, allowing individuals to be more discriminable from each other. Additionally, we demonstrated that the common space established using resting-state fMRI provides a better overlap of task-activation across participants. Finally, in a more challenging scenario - alignment across a lifespan cohort aged from 6 to 85 - joint embedding provided a better prediction of age (r2 = 0.65) than the prior alignment model. It facilitated the characterization of functional trajectories across lifespan. Overall, these analyses establish that joint embedding can simultaneously capture individual neural representations in a common connectivity space aligning functional data across participants and populations and preserve individual specificity.

Keywords: Common space; Functional alignment; Functional gradient; Individual differences; Joint embedding; Lifespan.

Fig. 1

The joint embedding workflow. A) The rationale behind joint embedding. C denotes a connectivity matrix with n nodes, and f(C) the kernel to compute a similarity matrix W. B) The scalable joint embedding alignment across multiple subjects. C) Illustration of the common space established with joint embedding (JE), and alignment of individual embeddings (OA).

Fig. 2

Average similarity of individual embedding component profiles to the reference. A) Notable cortical patterns of higher similarity and reduced variation are observed in JE compared to OA (see subset 2 results in Fig. S2). B) A paired t-test for individuals reveals a significant improvement of JE over OA for both subsets (subset1: t(49)=22.88, p < 0.0001; subset2: t(49)=24.54, p < 0.0001). C) Similarity of embedding component profiles to the reference at network level shows an increased similarity and reduced variance, particularly in somatosensory and visual networks.

Fig. 3

Average within and between individual similarity of embedding component profiles in the common space (subset 1). A) JE shows increased within individual similarity and reduced variation compared to OA. B) JE shows increased between individual similarity and reduced variation compared to OA. C) A paired t-test reveals significantly higher within and between individuals similarity for JE compared to OA (within: t(49)=13.85, p < 0.0001; between: t(49) = 25.61, p < 0.0001). D) The individual variance for JE is lower than for OA across networks, particularly for somatosensory and visual networks. E) JE components show a higher discriminability than OA, revealing that the individual pattern from JE is more identifiable as compared to OA components.

Fig. 4

Higher overlap of task-activation across participants in the JE common space compared to OA for subset 1. A) For JE compared to OA, a significantly higher correlation between actual and predicted z-scores is observed in 49 of 50 task-contrasts (paired t-test for 50 individuals in subset, p < 0.05 FDR corrected). B) The averaged difference (JE-OA) of pairwise Dice coefficients between thresholded z-maps at various thresholds. C) The averaged thresholded task-activation maps (z-score > 3.1) show a higher overlap for JE in task-active regions.

Fig. 5

Embedding component profiles based on JE outperform OA for age prediction in the lifespan sample. On aggregate, age prediction from all 20 folds results in a lower MAE for JE (paired t-test, t(311) = −2.6871, p = 0.0076). Across all 20 folds, JE (mean r2 = 0.6505 ± 0.1617) showed higher r-square than OA (mean r2 = 0.6002 ± 0.1661) (paired t-test t(19) = 2.75, p = 0.0127).

Fig. 6

Trajectories of JE components across lifespan. A) Linear and quadratic trend of JE components across lifespan. B) Scatter plots of the range of the first three components across lifespan.