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Unsupervised deep metric learning (UDML) focuses on learning a semantic representation space using only unlabeled data. This challenging problem requires accurately estimating the similarity between data points, which is used to supervise a…

This study aims to better understand the functional geometry of the motor cortex, starting from different sources of experimental evidence. Recent studies have proved that cells of the primary motor cortex (M1) are sensitive to short hand…

Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian…

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is…

The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are…

Geodesic regression has been proposed for fitting the geodesic curve. However, it cannot automatically choose the dimensionality of data. In this paper, we develop a Bayesian geodesic regression model on Riemannian manifolds (BGRM) model.…

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…

Functional magnetic resonance imaging or functional MRI (fMRI) is a non-invasive way to assess brain activity by detecting changes associated with blood flow. In this work, we propose a full Bayesian procedure to analyze fMRI data for…

Multiple sclerosis (MS) lesions occupy a small fraction of the brain volume, and are heterogeneous with regards to shape, size and locations, which poses a great challenge for training deep learning based segmentation models. We proposed a…

We explore the use of tools from Riemannian geometry for the analysis of symmetric positive definite matrices (SPD). An SPD matrix is a versatile data representation that is commonly used in chemical engineering (e.g.,…

Deep Metric Learning (DML) approaches learn to represent inputs to a lower-dimensional latent space such that the distance between representations in this space corresponds with a predefined notion of similarity. This paper investigates how…

In many pediatric fMRI studies, cardiac signals are often missing or of poor quality. A tool to extract Heart Rate Variation (HRV) waveforms directly from fMRI data, without the need for peripheral recording devices, would be highly…

We propose a novel two-phase approach to functional network estimation of multi-subject functional Magnetic Resonance Imaging (fMRI) data, which applies model-based image segmentation to determine a group-representative connectivity map. In…

Connectomics has emerged as a powerful tool in neuroimaging and has spurred recent advancements in statistical and machine learning methods for connectivity data. Despite connectomes inhabiting a matrix manifold, most analytical frameworks…

Multivariate Time Series (MTS) forecasting plays a vital role in various real-world applications, such as traffic management and predictive maintenance. Existing approaches typically model MTS data in either Euclidean or Riemannian space,…

In this paper, we address the challenging task of achieving multi-view dimensionality reduction. The goal is to effectively use the availability of multiple views for extracting a coherent low-dimensional representation of the data. The…

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…

Effectively representing medical concepts and patients is important for healthcare analytical applications. Representing medical concepts for healthcare analytical tasks requires incorporating medical domain knowledge and prior information…