159 research outputs found
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
Predicting cognitive scores with graph neural networks through sample selection learning
Analyzing the relation between intelligence and neural activity is of the
utmost importance in understanding the working principles of the human brain in
health and disease. In existing literature, functional brain connectomes have
been used successfully to predict cognitive measures such as intelligence
quotient (IQ) scores in both healthy and disordered cohorts using machine
learning models. However, existing methods resort to flattening the brain
connectome (i.e., graph) through vectorization which overlooks its topological
properties. To address this limitation and inspired from the emerging graph
neural networks (GNNs), we design a novel regression GNN model (namely RegGNN)
for predicting IQ scores from brain connectivity. On top of that, we introduce
a novel, fully modular sample selection method to select the best samples to
learn from for our target prediction task. However, since such deep learning
architectures are computationally expensive to train, we further propose a
\emph{learning-based sample selection} method that learns how to choose the
training samples with the highest expected predictive power on unseen samples.
For this, we capitalize on the fact that connectomes (i.e., their adjacency
matrices) lie in the symmetric positive definite (SPD) matrix cone. Our results
on full-scale and verbal IQ prediction outperforms comparison methods in autism
spectrum disorder cohorts and achieves a competitive performance for
neurotypical subjects using 3-fold cross-validation. Furthermore, we show that
our sample selection approach generalizes to other learning-based methods,
which shows its usefulness beyond our GNN architecture
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
Logistic Regression and Classification with non-Euclidean Covariates
We introduce a logistic regression model for data pairs consisting of a
binary response and a covariate residing in a non-Euclidean metric space
without vector structures. Based on the proposed model we also develop a binary
classifier for non-Euclidean objects. We propose a maximum likelihood estimator
for the non-Euclidean regression coefficient in the model, and provide upper
bounds on the estimation error under various metric entropy conditions that
quantify complexity of the underlying metric space. Matching lower bounds are
derived for the important metric spaces commonly seen in statistics,
establishing optimality of the proposed estimator in such spaces. Similarly, an
upper bound on the excess risk of the developed classifier is provided for
general metric spaces. A finer upper bound and a matching lower bound, and thus
optimality of the proposed classifier, are established for Riemannian
manifolds. We investigate the numerical performance of the proposed estimator
and classifier via simulation studies, and illustrate their practical merits
via an application to task-related fMRI data.Comment: This revision contains the following updates: (1) The parameter space
is allowed to be unbounded; (2) Some upper bounds are tightene
A Riemannian Revisiting of Structure–Function Mapping Based on Eigenmodes
International audienceUnderstanding the link between brain structure and function may not only improve our knowledge of brain organization, but also lead to better quantification of pathology. To quantify this link, recent studies have attempted to predict the brain's functional connectivity from its structural connectivity. However, functional connectivity matrices live in the Riemannian manifold of the symmetric positive definite space and a specific attention must be paid to operate on this appropriate space. In this work we investigated the implications of using a distance based on an affine invariant Riemannian metric in the context of structure–function mapping. Specifically, we revisit previously proposed structure–function mappings based on eigendecomposition and test them on 100 healthy subjects from the Human Connectome Project using this adapted notion of distance. First, we show that using this Riemannian distance significantly alters the notion of similarity between subjects from a functional point of view. We also show that using this distance improves the correlation between the structural and functional similarity of different subjects. Finally, by using a distance appropriate to this manifold, we demonstrate the importance of mapping function from structure under the Riemannian manifold and show in particular that it is possible to outperform the group average and the so–called glass ceiling on the performance of mappings based on eigenmodes
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