185 citations · 894 across the 21 of their papers we have counts for
22 papers
Learning Pose Image Manifolds Using Geometry-Preserving GANs and Elasticae
Shenyuan Liang, Pavan Turaga, Anuj Srivastava
This paper investigates the challenge of learning image manifolds, specifically pose manifolds, of 3D objects using limited training data. It proposes a DNN approach to manifold le…
Data-Driven, Soft Alignment of Functional Data Using Shapes and Landmarks
Xiaoyang Guo, Wei Wu, Anuj Srivastava
Alignment or registration of functions is a fundamental problem in statistical analysis of functions and shapes. While there are several approaches available, a more recent approac…
Regression Models Using Shapes of Functions as Predictors
Kyungmin Ahn, J. Derek Tucker, Wei Wu +1
Functional variables are often used as predictors in regression problems. A commonly-used parametric approach, called {\it scalar-on-function regression}, uses the $\ltwo$ inner pr…
Analyzing Dynamical Brain Functional Connectivity As Trajectories on Space of Covariance Matrices
Mengyu Dai, Zhengwu Zhang, Anuj Srivastava
Human brain functional connectivity (FC) is often measured as the similarity of functional MRI responses across brain regions when a brain is either resting or performing a task. T…
Statistical Analysis and Modeling of the Geometry and Topology of Plant Roots
Guan Wang, Hamid Laga, Jinyuan Jia +2
The root is an important organ of a plant since it is responsible for water and nutrient uptake. Analyzing and modelling variabilities in the geometry and topology of roots can hel…
Discovering Common Change-Point Patterns in Functional Connectivity Across Subjects
Mengyu Dai, Zhengwu Zhang, Anuj Srivastava
This paper studies change-points in human brain functional connectivity (FC) and seeks patterns that are common across multiple subjects under identical external stimulus. FC relat…
Elastic Functional Principal Component Regression
J. Derek Tucker, John Lewis, Anuj Srivastava
We study regression using functional predictors in situations where these functions contain both phase and amplitude variability. In other words, the functions are misaligned due t…
Robust Comparison of Kernel Densities on Spherical Domains
Zhengwu Zhang, Eric Klassen, Anuj Srivastava
While spherical data arises in many contexts, including in directional statistics, the current tools for density estimation and population comparison on spheres are quite limited.…
Shape-Constrained Univariate Density Estimation
Sutanoy Dasgupta, Debdeep Pati, Ian H. Jermyn +1
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and cha…
Trend and Variable-Phase Seasonality Estimation from Functional Data
Liang-Hsuan Tai, Anuj Srivastava, Kyle A. Gallivan
The problem of estimating trend and seasonal variation in time-series data has been studied over several decades, although mostly using single time series. This paper studies the p…
Nonparametric Spherical Regression Using Diffeomorphic Mappings
Michael Rosenthal, Wei Wu, Eric Klassen +1
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The rest…
A Two-Step Geometric Framework For Density Modeling
Sutanoy Dasgupta, Debdeep Pati, Anuj Srivastava
We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation…
Numerical Inversion of SRNF Maps for Elastic Shape Analysis of Genus-Zero Surfaces
Hamid Laga, Qian Xie, Ian H. Jermyn +1
Recent developments in elastic shape analysis (ESA) are motivated by the fact that it provides comprehensive frameworks for simultaneous registration, deformation, and comparison o…
Phase-Amplitude Separation and Modeling of Spherical Trajectories
Zhengwu Zhang, Eric Klassen, Anuj Srivastava
This paper studies the problem of separating phase-amplitude components in sample paths of a spherical process (longitudinal data on a unit two-sphere). Such separation is essentia…
Elastic Functional Coding of Riemannian Trajectories
Rushil Anirudh, Pavan Turaga, Jingyong Su +1
Visual observations of dynamic phenomena, such as human actions, are often represented as sequences of smoothly-varying features . In cases where the feature spaces can be structur…
Functional Data Analysis of Amplitude and Phase Variation
J. S. Marron, James O. Ramsay, Laura M. Sangalli +1
The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with seve…
Gauge Invariant Framework for Shape Analysis of Surfaces
Alice Barbara Tumpach, Hassen Drira, Mohamed Daoudi +1
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riem…
Video-Based Action Recognition Using Rate-Invariant Analysis of Covariance Trajectories
Zhengwu Zhang, Jingyong Su, Eric Klassen +2
Statistical classification of actions in videos is mostly performed by extracting relevant features, particularly covariance features, from image frames and studying time series as…
Bayesian Clustering of Shapes of Curves
Zhengwu Zhang, Debdeep Pati, Anuj Srivastava
Unsupervised clustering of curves according to their shapes is an important problem with broad scientific applications. The existing model-based clustering techniques either rely o…
Statistical analysis of trajectories on Riemannian manifolds: Bird migration, hurricane tracking and video surveillance
Jingyong Su, Sebastian Kurtek, Eric Klassen +1
We consider the statistical analysis of trajectories on Riemannian manifolds that are observed under arbitrary temporal evolutions. Past methods rely on cross-sectional analysis, w…
Generative Models for Functional Data using Phase and Amplitude Separation
J. Derek Tucker, Wei Wu, Anuj Srivastava
Constructing generative models for functional observations is an important task in statistical functional analysis. In general, functional data contains both phase (or x or horizon…
Registration of Functional Data Using Fisher-Rao Metric
Anuj Srivastava, Wei Wu, Sebastian Kurtek +2
We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This fra…