Deconvolving Complex Neuronal Networks into Interpretable Task-Specific Connectomes

TL;DR

The paper addresses deconvolving task-specific aggregate functional connectomes into a compact set of canonical task connectomes using non-negative matrix factorization (NMF). It constructs a population-level data matrix $X$ of vectorized connectomes and factorizes it into $W$ and $H$, enabling interpretable, additive building blocks for cognitive tasks. On 1000 HCP subjects across six tasks, the authors show high task specificity, cross-cohort generalizability, and strong anatomical/physiological grounding by mapping canonical connectomes to cortical regions. This scalable framework yields task-predictive representations and offers a principled way to study shared and unique neural processes across diverse tasks, with potential applications in clinical and cognitive neuroscience.

Abstract

Task-specific functional MRI (fMRI) images provide excellent modalities for studying the neuronal basis of cognitive processes. We use fMRI data to formulate and solve the problem of deconvolving task-specific aggregate neuronal networks into a set of basic building blocks called canonical networks, to use these networks for functional characterization, and to characterize the physiological basis of these responses by mapping them to regions of the brain. Our results show excellent task-specificity of canonical networks, i.e., the expression of a small number of canonical networks can be used to accurately predict tasks; generalizability across cohorts, i.e., canonical networks are conserved across diverse populations, studies, and acquisition protocols; and that canonical networks have strong anatomical and physiological basis. From a methods perspective, the problem of identifying these canonical networks poses challenges rooted in the high dimensionality, small sample size, acquisition variability, and noise. Our deconvolution technique is based on non-negative matrix factorization (NMF) that identifies canonical networks as factors of a suitably constructed matrix. We demonstrate that our method scales to large datasets, yields stable and accurate factors, and is robust to noise.

Figures (5)

• Figure 1: Overview of proposed framework: (1) The training phase deconvolves the data matrix of vectorized connectomes in the training set into a small number of basis vectors; (2) The testing phase computes the coefficients of the functional basis and predicts the task on new subjects.
• Figure 2: Parameter study: effect of rank on test accuracy. We set rank from 1 to 100 and use NMF to deconvolve the train data matrix. We then test task predictions based on $\hat{\mathbf{H}}$ using $\hat{\mathbf{H}} = \tilde{\mathbf{W}}^{\dagger} \mathbf{X}_{test}$. There is rapid increase in accuracy from rank 1 up to 20, after which the rate of increase slows considerably. The accuracy plateaus around 98% at rank 50.
• Figure 3: Coefficients matrix $\mathbf{H}$ of NMF. We apply NMF to factor the data matrix of rank 20. We fit columns of $\mathbf{H}$ to a normal distribution and use the 90th percentile as a cutoff to discard small values. Each plot shows the encoding of 1000 subjects performing one task, visualizing $\mathbf{W}_i$ (corresponding to the canonical connectomes) that make up that particular task.
• Figure 4: Correlation network analysis. We take the mean of each task's corresponding linear coefficients and compute the Pearson coefficient across these averaged task vectors. We then construct the similarity network using the Pearson coefficient and connect each task with its most significant canonical connectomes.
• Figure 5: Canonical Task Connectomes have strong anatomical basis. From each column $\mathbf{W}_{i}$, we construct $region \times region$ canonical task connectome. The correlation values for the 360 regions are summed as an active factor, and the top 2% of highly active regions are retained. MRIcroGL is then used to visualize the most active regions for each task.