De-Individualizing fMRI Signals via Mahalanobis Whitening and Bures Geometry

TL;DR

The paper tackles separating subject-specific from task-specific information in fMRI by applying Mahalanobis whitening to BOLD time series and evaluating the resulting data with distance-based, manifold-embedding approaches. It introduces a two-stage de-individualization workflow (mean removal followed by whitening with $W = \operatorname{cov}(\bar{S},\bar{S})$) and compares distances such as the Bures distance $d_B$ and the Frobenius distance $d_F$, with a preprocessing-informed distance $d_M$ guiding task clustering. Empirically, Bures-based embeddings recover subject identity, while the $d_M$-driven Isomap embedding reveals task-based patterns, with validation data confirming robustness to task ordering. The work offers interpretable preprocessing-driven tools for disentangling brain-behavior relationships and holds potential for biomarker discovery and improved diagnostic consistency in neurodegenerative contexts.

Abstract

Functional connectivity has been widely investigated to understand brain disease in clinical studies and imaging-based neuroscience, and analyzing changes in functional connectivity has proven to be valuable for understanding and computationally evaluating the effects on brain function caused by diseases or experimental stimuli. By using Mahalanobis data whitening prior to the use of dimensionality reduction algorithms, we are able to distill meaningful information from fMRI signals about subjects and the experimental stimuli used to prompt them. Furthermore, we offer an interpretation of Mahalanobis whitening as a two-stage de-individualization of data which is motivated by similarity as captured by the Bures distance, which is connected to quantum mechanics. These methods have potential to aid discoveries about the mechanisms that link brain function with cognition and behavior and may improve the accuracy and consistency of Alzheimer's diagnosis, especially in the preclinical stage of disease progression.

Figures (7)

• Figure 1: A comparison of embedding quality and clustering performance for various levels of preprocessing. The top row contains embeddings of task scans, and the bottom row displays clustering-based evaluation scores. (a) An embedding based on un-processed task scans. (b) An embedding based on task scans which have been de-meaned and scaled to have a variance of 1. (c) An embedding based on whitened task scans, which gives the best task-based clustering result.
• Figure 2: One subject's BOLD timeseries after mapping from voxel representation to region-averaged values. (a) A parent scan. Vertical lines delineate tasks, cues, and rests. Extracted tasks are indicated by colored boxes around their labels. (b) 8 task scans extracted from the parent scan. Border color corresponds to the colored boxes around task names in the parent scan.
• Figure 3: An example of a functional connectome, which is a region-against-region correlation matrix of BOLD signals.
• Figure 4: A UMAP embedding of task scans based on pairwise Bures distances between functional connectomes. The smaller figures show the same, zoomed-in view of the data. On the left, task scans are colored by task, and on the right, they are colored by individual. Note that a subset of 100 subjects are shown here, rather than the full dataset.
• Figure 5: A Isomap embedding of task scans based on pairwise Frobenius distances between un-processed task scans. Colors in the rightmost subplot appear duplicated due to the number of classes present; each cluster of a single color contains all 8 task scans from a single individual.