623 research outputs found
Riemannian Geometry of Functional Connectivity Matrices for Multi-Site Attention-Deficit/Hyperactivity Disorder Data Harmonization
Riemannian geometry; Attention-deficit/hyperactivity disorder; Functional connectivityGeometria riemanniana; Trastorn per dèficit d'atenció/hiperactivitat; Connectivitat funcionalGeometrÃa riemanniana; Trastorno por déficit de atención/hiperactividad; Conectividad funcionalThe use of multi-site datasets in neuroimaging provides neuroscientists with more statistical power to perform their analyses. However, it has been shown that the imaging-site introduces variability in the data that cannot be attributed to biological sources. In this work, we show that functional connectivity matrices derived from resting-state multi-site data contain a significant imaging-site bias. To this aim, we exploited the fact that functional connectivity matrices belong to the manifold of symmetric positive-definite (SPD) matrices, making it possible to operate on them with Riemannian geometry. We hereby propose a geometry-aware harmonization approach, Rigid Log-Euclidean Translation, that accounts for this site bias. Moreover, we adapted other Riemannian-geometric methods designed for other domain adaptation tasks and compared them to our proposal. Based on our results, Rigid Log-Euclidean Translation of multi-site functional connectivity matrices seems to be among the studied methods the most suitable in a clinical setting. This represents an advance with respect to previous functional connectivity data harmonization approaches, which do not respect the geometric constraints imposed by the underlying structure of the manifold. In particular, when applying our proposed method to data from the ADHD-200 dataset, a multi-site dataset built for the study of attention-deficit/hyperactivity disorder, we obtained results that display a remarkable correlation with established pathophysiological findings and, therefore, represent a substantial improvement when compared to the non-harmonization analysis. Thus, we present evidence supporting that harmonization should be extended to other functional neuroimaging datasets and provide a simple geometric method to address it
An Explainable Geometric-Weighted Graph Attention Network for Identifying Functional Networks Associated with Gait Impairment
One of the hallmark symptoms of Parkinson's Disease (PD) is the progressive
loss of postural reflexes, which eventually leads to gait difficulties and
balance problems. Identifying disruptions in brain function associated with
gait impairment could be crucial in better understanding PD motor progression,
thus advancing the development of more effective and personalized therapeutics.
In this work, we present an explainable, geometric, weighted-graph attention
neural network (xGW-GAT) to identify functional networks predictive of the
progression of gait difficulties in individuals with PD. xGW-GAT predicts the
multi-class gait impairment on the MDS Unified PD Rating Scale (MDS-UPDRS). Our
computational- and data-efficient model represents functional connectomes as
symmetric positive definite (SPD) matrices on a Riemannian manifold to
explicitly encode pairwise interactions of entire connectomes, based on which
we learn an attention mask yielding individual- and group-level explainability.
Applied to our resting-state functional MRI (rs-fMRI) dataset of individuals
with PD, xGW-GAT identifies functional connectivity patterns associated with
gait impairment in PD and offers interpretable explanations of functional
subnetworks associated with motor impairment. Our model successfully
outperforms several existing methods while simultaneously revealing
clinically-relevant connectivity patterns. The source code is available at
https://github.com/favour-nerrise/xGW-GAT .Comment: Accepted by the 26th International Conference on Medical Image
Computing and Computer Assisted Intervention (MICCAI 2023). MICCAI
Student-Author Registration (STAR) Award. 11 pages, 2 figures, 1 table,
appendix. Source Code: https://github.com/favour-nerrise/xGW-GA
Geodesic Distance Function Learning via Heat Flow on Vector Fields
Learning a distance function or metric on a given data manifold is of great
importance in machine learning and pattern recognition. Many of the previous
works first embed the manifold to Euclidean space and then learn the distance
function. However, such a scheme might not faithfully preserve the distance
function if the original manifold is not Euclidean. Note that the distance
function on a manifold can always be well-defined. In this paper, we propose to
learn the distance function directly on the manifold without embedding. We
first provide a theoretical characterization of the distance function by its
gradient field. Based on our theoretical analysis, we propose to first learn
the gradient field of the distance function and then learn the distance
function itself. Specifically, we set the gradient field of a local distance
function as an initial vector field. Then we transport it to the whole manifold
via heat flow on vector fields. Finally, the geodesic distance function can be
obtained by requiring its gradient field to be close to the normalized vector
field. Experimental results on both synthetic and real data demonstrate the
effectiveness of our proposed algorithm
Tangent functional connectomes uncover more unique phenotypic traits
Functional connectomes (FCs) contain pairwise estimations of functional
couplings based on pairs of brain regions activity. FCs are commonly
represented as correlation matrices that are symmetric positive definite (SPD)
lying on or inside the SPD manifold. Since the geometry on the SPD manifold is
non-Euclidean, the inter-related entries of FCs undermine the use of
Euclidean-based distances. By projecting FCs into a tangent space, we can
obtain tangent functional connectomes (tangent-FCs). Tangent-FCs have shown a
higher predictive power of behavior and cognition, but no studies have
evaluated the effect of such projections with respect to fingerprinting. We
hypothesize that tangent-FCs have a higher fingerprint than regular FCs.
Fingerprinting was measured by identification rates (ID rates) on test-retest
FCs as well as on monozygotic and dizygotic twins. Our results showed that
identification rates are systematically higher when using tangent-FCs.
Specifically, we found: (i) Riemann and log-Euclidean matrix references
systematically led to higher ID rates. (ii) In tangent-FCs, Main-diagonal
regularization prior to tangent space projection was critical for ID rate when
using Euclidean distance, whereas barely affected ID rates when using
correlation distance. (iii) ID rates were dependent on condition and fMRI scan
length. (iv) Parcellation granularity was key for ID rates in FCs, as well as
in tangent-FCs with fixed regularization, whereas optimal regularization of
tangent-FCs mostly removed this effect. (v) Correlation distance in tangent-FCs
outperformed any other configuration of distance on FCs or on tangent-FCs
across the fingerprint gradient (here sampled by assessing test-retest,
Monozygotic and Dizygotic twins). (vi)ID rates tended to be higher in task
scans compared to resting-state scans when accounting for fMRI scan length.Comment: 29 pages, 10 figures, 2 table
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