Connectivity Gradient Estimation Through Joint Global-Linear and Local Embedding
Poster No:
1232
Submission Type:
Abstract Submission
Authors:
Aref Miri Rekavandi1, Saad Jbabdi1, Stephen Smith1
Institutions:
1University of Oxford, Oxford, United Kingdom
First Author:
Co-Author(s):
Introduction:
Gradients of brain connectivity have been proposed to represent continuous variations in connectivity patterns across spatial dimensions. However, principal gradients derived from resting-state fMRI data (Margulies, 2016) show significant similarity to spatial Independent Component Analysis (ICA) maps. This raises the question of whether gradient estimation provides novel insights into brain organization beyond what is already revealed by global linear low-rank analyses. Interestingly, when gradients are examined within specific ROIs (Haak, 2018), the results align well with stimulus-based maps and appear meaningful. This observation suggests that gradient analysis may be influenced by some features of the data that need careful consideration before conducting analyses and interpreting results.
Methods:
A dense connectome D is often composed of two distinct terms: Functional segregation and gradients. Overlooking their differences is one reason for the observed similarity between gradient estimates in the literature and ICA maps. Functional segregation manifests as a low-rank property of the data (ROIs) and can be found by outer-product decomposition. Gradients on the other hand, are continuously-varying connectivity patterns, are not low-rank, and may appear sparse in D. This leads to a "low rank + sparse" potential decomposition of D into three components: a low-rank matrix L, a sparse matrix S, and a noise matrix N: D=L+S+N. The matrix L is intended to capture the global, low-rank features. This allows the sparse matrix S to represent the continuous connectivity patterns among brain nodes. We used the Stable Principal Component Pursuit framework to achieve this decomposition (Zhou, 2010). The matrix S is then subjected to nonlinear manifold learning techniques, e.g., ISOMAP (Global) (Tenenbaum, 2000) and UMAP (Local/Global) (McInnes, 2018) to estimate the gradients. In order to evaluate the quality of gradient estimation, a reverse process was then used to reconstruct the sparse matrix S, including distance matrix estimation in the low-dimensional space, converting this to a connectivity matrix, and then aligning it with the original S using a global histogram matching approach.
Results:
When our framework is applied globally, it uncovers an organizational structure that differs from that revealed by low-rank approaches, emphasizing a fine-grained global organization of brain connectivity patterns. Figure 1 displays the global gradients of four ROIs in simulation, demonstrating that the gradients align with the smoothing kernel applied to each ROI, reflecting the consistency between local and global gradients. Figure 2 presents the results from group-averaged HCP resting-state fMRI data (Van Essen, 2013) showcasing the global gradients of the brain and their clustering results projected onto the brain versus ICA maps.
Conclusions:
We introduced a novel global framework for gradient estimation of brain connectivity that integrates the strengths of both linear low-rank and nonlinear approaches. This framework provides gradient maps that are consistent with those derived locally while remaining distinct from the global low-rank maps. A key advantage of our framework is its versatility-it allows for gradient estimation both within specific ROIs and across the entire brain, mapping all regions to a unified embedding space. This capability is particularly promising for enabling researchers to explore connectivity gradients at multiple levels of granularity and to explore the hierarchical and multidimensional organization of the brain.
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural) 1
Methods Development 2
Keywords:
Cortex
Design and Analysis
FUNCTIONAL MRI
Machine Learning
Other - Gradients
1|2Indicates the priority used for review
Abstract Information
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Provide references using APA citation style.
Margulies, D. S. (2016). Situating the default-mode network along a principal gradient of macroscale cortical organization. Proceedings of the National Academy of Sciences, 12574--12579.
McInnes, L. a. (2018). Umap: Uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426, 1--63.
Tenenbaum, J. B. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 2319--2323.
Van Essen, D. C.-M. (2013). The WU-Minn human connectome project: an overview. Neuroimage, 62--79.
Zhou, Z. a. (2010). Stable principal component pursuit. IEEE International Symposium on Information Theory (pp. 1518--1522). IEEE.