Related papers: A Coupled Manifold Optimization Framework to Joint…

Autism Spectrum Disorder(ASD) is a set of neurodevelopmental conditions that affect patients' social abilities. In recent years, many studies have employed deep learning to diagnose this brain dysfunction through functional MRI (fMRI).…

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…

Understanding how neural systems efficiently process information through distributed representations is a fundamental challenge at the interface of neuroscience and machine learning. Recent approaches analyze the statistical and geometrical…

The objective of constrained motion planning is to connect start and goal configurations while satisfying task-specific constraints. Motion planning becomes inefficient or infeasible when the configurations lie in disconnected regions,…

Manifold learning using deep neural networks been shown to be an effective tool for building sophisticated prior image models that can be applied to noise reduction in low-dose CT. We propose a new iterative CT reconstruction algorithm,…

This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image…

We propose an asymptotic framework to analyze the performance of (personalized) federated learning algorithms. In this new framework, we formulate federated learning as a multi-criterion objective, where the goal is to minimize each…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

Aggregating multi-subject functional magnetic resonance imaging (fMRI) data is indispensable for generating valid and general inferences from patterns distributed across human brains. The disparities in anatomical structures and functional…

In neuroscience, understanding inter-individual differences has recently emerged as a major challenge, for which functional magnetic resonance imaging (fMRI) has proven invaluable. For this, neuroscientists rely on basic methods such as…

Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality," becoming ineffective as the dimension of the parameter space grows. One feature of a…

Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…

We propose a model for diagnosing Autism spectrum disorder (ASD) using multimodal magnetic resonance imaging (MRI) data. Our approach integrates brain connectivity data from diffusion tensor imaging (DTI) and functional MRI (fMRI),…

Predicting clinical variables from whole-brain neuroimages is a high dimensional problem that requires some type of feature selection or extraction. Penalized regression is a popular embedded feature selection method for high dimensional…

The fusion of complementary multimodal information is crucial in computational pathology for accurate diagnostics. However, existing multimodal learning approaches necessitate access to users' raw data, posing substantial privacy risks.…

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…

Autism spectrum disorder(ASD) is a lifelong neurodevelopmental condition that affects social communication and behavior. Investigating functional magnetic resonance imaging (fMRI)-based brain functional connectome can aid in the…

In the high-dimensional landscape, addressing the challenges of covariance regression with high-dimensional covariates has posed difficulties for conventional methodologies. This paper addresses these hurdles by presenting a novel approach…

Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a…

Discovering reliable and informative relationships among brain regions from functional magnetic resonance imaging (fMRI) signals is essential in phenotypic predictions. Most of the current methods fail to accurately characterize those…