Anuj Srivastava

• Florida State University

Human mobility analysis at urban-scale requires models to represent the complex nature of human movements, which in turn are affected by accessibility to nearby points of interest, underlying socioeconomic factors of a place, and local transport choices for people living in a geographic region. In this work, we represent human mobility and the asso...

Brain networks are typically represented by adjacency matrices, where each node corresponds to a brain region. In traditional brain network analysis, nodes are assumed to be matched across individuals, but the methods used for node matching often overlook the underlying connectivity information. This oversight can result in inaccurate node alignmen...

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering these questions can provide key insights in explaining and advancing success of machine learning algorithms in co...

We propose a novel framework for the statistical analysis of genus-zero 4D surfaces, i.e., 3D surfaces that deform and evolve over time. This problem is particularly challenging due to the arbitrary parameterizations of these surfaces and their varying deformation speeds, necessitating effective spatiotemporal registration. Traditionally, 4D surfac...

Clinical assessments for neuromuscular disorders, such as Spinal Muscular Atrophy (SMA) and Duchenne Muscular Dystrophy (DMD), continue to rely on subjective measures to monitor treatment response and disease progression. We introduce a novel method using wearable sensors to objectively assess motor function during daily activities in 19 patients w...

This paper addresses the critical and challenging task of developing emulators for simulating human operational motions in industrial workplaces. We conceptualize human motion as a sequence of human body shapes. Leveraging statistical shape theory, we develop statistical generative models for sequences of human (body) shapes of human workers in wor...

Functional data contains two components: shape (or amplitude) and phase. This paper focuses on a branch of functional data analysis (FDA), namely Shape-Based FDA, that isolates and focuses on shapes of functions. Specifically, this paper focuses on Scalar-on-Shape (ScoSh) regression models that incorporate the shapes of predictor functions and disc...

Wasserstein distances form a family of metrics on spaces of probability measures that have recently seen many applications. However, statistical analysis in these spaces is complex due to the nonlinearity of Wasserstein spaces. One potential solution to this problem is Linear Optimal Transport (LOT). This method allows one to find a Euclidean embed...

Shape graphs are complex geometrical structures commonly found in biological and anatomical systems. A shape graph is a collection of nodes, some connected by curvilinear edges with arbitrary shapes. Their high complexity stems from the large number of nodes and edges and the complex shapes of edges. With an eye for statistical analysis, one seeks...

We propose the first comprehensive approach for modeling and analyzing the spatiotemporal shape variability in tree-like 4D objects, i.e., 3D objects whose shapes bend, stretch, and change in their branching structure over time as they deform, grow, and interact with their environment. Our key contribution is the representation of tree-like 3D shap...

This paper provides developments in statistical shape analysis of shape graphs , and demonstrates them using such complex objects as Retinal Blood Vessel (RBV) networks and neurons. The shape graphs are represented by sets of nodes and edges (articulated curves) connecting some nodes. The goals are to utilize nodes (locations, connectivity) and e...

We express our gratitude to the authors of five comment articles for their valuable contributions, feedback, and recommendations on our discussion document (Wu et al. Test, 2023). All the reviewers acknowledged the value of our proposed research direction, which focuses on shape-based functional data analysis. They also provided insightful suggesti...

Background Over the past 30 years, MRI has become a ubiquitous tool for accurately visualizing the development of the brain’s subcortical structures. However, the quantification of subcortical structures is still in its infancy due to challenges in shape extraction, representation, and modeling. Method A simple and efficient framework of longitudi...

How can one analyze detailed 3D biological objects, such as neuronal and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and computing geodesic deformations between the shapes of such tree-like 3D objects. A hierarchical organization o...

Functional data analysis (FDA) is a fast-growing area of research and development in statistics. While most FDA literature imposes the classical $$\mathbb {L}^2$$ L 2 Hilbert structure on function spaces, there is an emergent need for a different, shape-based approach for analyzing functional data. This paper reviews and develops fundamental geomet...

This paper focuses on the statistical analysis of shapes of data objects called shape graphs, a set of nodes connected by articulated curves with arbitrary shapes. A critical need here is a constrained registration of points (nodes to nodes, edges to edges) across objects. This, in turn, requires optimization over the permutation group, made challe...

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 learning and for predicting images of objects for novel, continuous 3D rotations. The approach uses two distinct concepts: (1) Geometric Style-GAN (Geom-SGAN), which maps i...

Estimating signals underlying noisy data is a significant problem in statistics and engineering. Numerous estimators are available in the literature, depending on the observation model and estimation criterion. This paper introduces a framework that estimates the shape of the unknown signal and the signal itself. The approach utilizes a peak-persis...

This paper provides theoretical and computational developments in statistical shape analysis of shape graphs, and demonstrates them using analysis of complex data from retinal blood-vessel (RBV) networks. The shape graphs are represented by a set of nodes and edges (planar articulated curves) connecting some of these nodes. The goals are to utilize...

Graph-based representations are becoming increasingly popular for representing and analyzing video data, especially in object tracking and scene understanding applications. Accordingly, an essential tool in this approach is to generate statistical inferences for graphical time series associated with videos. This paper develops a Kalman-smoothing me...

It is well-known that morphological features in the brain undergo changes due to traumatic events and associated disorders such as post-traumatic stress disorder (PTSD). However, existing approaches typically offer group-level comparisons, and there are limited predictive approaches for modeling behavioral outcomes based on brain shape features tha...

Over the past 30 years, magnetic resonance imaging has become a ubiquitous tool for accurately visualizing the change and development of the brain’s subcortical structures (e.g., hippocampus). Although subcortical structures act as information hubs of the nervous system, their quantification is still in its infancy due to many challenges in shape e...

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered. Also, different deforming objects, hereinaft...

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 approach based on Fisher-Rao metric and square-root velocity functions (SRVFs) has been shown to have good performance. However, this SRVF method has two limitations: (1) it is...

Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 5,002,387 cases and 127,258 deaths as of October 31, 2021. The aggressive transmission dynamics of SARS-CoV-2 motivate an investigation of COVID-19 at the national and regional levels in Colombia. We...

Data Science for Motion and Time Analysis Motion and time analysis has been a popular tool in operations research for analyzing work performance in manufacturing and service operations. The current practice in motion and time analysis involves many labor-intensive steps such as stop-watching, videotaping, and manual data analysis. It is too ineffic...

Elastic Riemannian metrics have been used successfully for statistical treatments of functional and curve shape data. However, this usage suffers from a significant restriction: the function boundaries are assumed to be fixed and matched. Functional data often comes with unmatched boundaries, {\it e.g.}, in dynamical systems with variable evolution...

Shape analysis of objects in images is a critical area of research, and several approaches, including those that utilize elastic Riemannian metrics, have been proposed. While elastic techniques for shape analysis of curves are pretty advanced, the corresponding results for higher-dimensional objects (surfaces and disks) are less developed. This pap...

How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and computing geodesic deformations between the shapes of such tree-like 3D objects. A hierarchical organization of...

We investigate the problem of statistical analysis of interval-valued time series data – two nonintersecting real-valued functions, representing lower and upper limits, over a period of time. Specifically, we pay attention to the two concepts of phase (or horizontal) variability and amplitude (or vertical) variability, and propose a phase-amplitude...

Predictive modeling involving brain morphological features and other covariates is of paramount interest in such heterogeneous mental disorders as PTSD. We propose a comprehensive shape analysis framework representing brain substructures, such as the hippocampus, amygdala, and putamen, as parameterized surfaces and quantifying their shape differenc...

Empirically multidimensional discriminator (critic) output can be advantageous, while a solid explanation for it has not been discussed. In this paper, (i) we rigorously prove that high-dimensional critic output has advantage on distinguishing real and fake distributions; (ii) we also introduce an square-root velocity transformation (SRVT) block wh...

Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e., a non-linear shift along the time axis, which makes standard methods not directly applicable. The key challenge is that these observations are not “al...

An important hypothesis in animal cell biology is that an animal’s acute exercise regimen affects some subcellular structures, for example mitochondrial morphology, in its muscle tissue. This paper investigates that hypothesis using a nonparametric metric‐based energy test for comparing mitochondrial populations. It explores two shape spaces—the el...

Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 4,240,982 cases and 106,544 deaths as of June 30, 2021. This motivates an investigation of the SARS-CoV-2 transmission dynamics at the national and regional level using case incidence data. Mathemati...

Mexico has experienced one of the highest COVID-19 mortality rates in the world. A delayed implementation of social distancing interventions in late March 2020 and a phased reopening of the country in June 2020 has facilitated sustained disease transmission in the region. In this study we systematically generate and compare 30-day ahead forecasts u...

Complex analyses involving multiple, dependent random quantities often lead to graphical models—a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical analyses for graphical data, especially towards generative modeling, one needs mathematical representations and...

This paper develops a generative statistical model for representing, modeling, and comparing the morphological evolution of biological cells undergoing motility. It uses the elastic shape analysis to separate cell kinematics (overall location, rotation, speed, etc.) from its morphology and represents morphological changes using transported square-r...

There is increasing evidence on the importance of brain morphology in predicting and classifying mental disorders. However, the vast majority of current shape approaches rely heavily on vertex-wise analysis that may not successfully capture complexities of subcortical structures. Additionally, the past works do not include interactions between thes...

Elastic Riemannian metrics have been used successfully in the past for statistical treatments of functional and curve shape data. However, this usage has suffered from an important restriction: the function boundaries are assumed fixed and matched. Functional data exhibiting unmatched boundaries typically arise from dynamical systems with variable...

This article develops an agent-level stochastic simulation model, termed RAW-ALPS, for simulating the spread of an epidemic in a community. The mechanism of transmission is agent-to-agent contact, using parameters reported for the COVID-19 pandemic. When unconstrained, the agents follow independent random walks and catch infections due to physical...

This paper develops statistical tools for testing differences in shapes of chromosomes resulting from certain gene knockouts (KO), specifically RIF1 gene KO (RKO) and the cohesin subunit RAD21 gene KO (CKO). It utilizes a two-sample test for comparing shapes of KO chromosomes with wild type (WT) at two levels: (1) Coarse shape analysis, where one c...

The study of the three-dimensional (3D) structure of chromosomes-the largest macromolecules in biology-is one of the most challenging to date in structural biology. Here, we develop a novel representation of 3D chromosome structures, as sequences of shape letters from a finite shape alphabet, which provides a compact and efficient way to analyze en...

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of subjects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered onto each others. Also, different deforming...

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of subjects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary spatial and temporal parameterizations. Thus, they need to be spatially registered and temporally aligned ont...

The ongoing coronavirus pandemic reached Mexico in late February 2020. Since then Mexico has observed a sustained elevation in the number of COVID-19 deaths. Mexicos delayed response to the COVID-19 pandemic until late March 2020 hastened the spread of the virus in the following months. However, the government followed a phased reopening of the cou...

Estimation of a probability density function (pdf) from its samples, while satisfying certain shape constraints, is an important problem that lacks coverage in the literature. This paper introduces a novel geometric, deformable template constrained density estimator (dtcode) for estimating pdfs constrained to have a given number of modes. Our appro...

The motion-and-time analysis has been a popular research topic in operations research, especially for analyzing work performances in manufacturing and service operations. It is regaining attention as continuous improvement tools for lean manufacturing and smart factory. This paper develops a framework for data-driven analysis of work motions and st...

The study of the 3-dimensional (3D) structure of chromosomes -- the largest macromolecules in biology -- is one of the most challenging to date in structural biology. Here, we develop a novel representation of chromosomes, as sequences of shape letters from a finite shape alphabet, which provides a compact and efficient way to analyze ensembles of...

Structures of brain arterial networks (BANs) - that are complex arrangements of individual arteries, their branching patterns, and inter-connectivities - play an important role in characterizing and understanding brain physiology. One would like tools for statistically analyzing the shapes of BANs, i.e. quantify shape differences, compare populatio...

UNSTRUCTURED The growth rates of COVID-19 across different geographical regions (e.g., states in a nation, countries in a continent) follow different shapes and patterns. The overall summaries at coarser spatial scales that are obtained by simply averaging individual curves (across regions) obscure nuanced variability and blurs the spatial heteroge...

The growth rates of COVID-19 across different geographical regions (e.g., states in a nation, countries in a continent) follow different shapes and patterns. The overall summaries at coarser spatial scales that are obtained by simply averaging individual curves (across regions) obscure nuanced variability and blurs the spatial heterogeneity at fine...

Functional variables are often used as predictors in regression problems. A commonly used parametric approach, called scalar-on-function regression, uses the L2 inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability, causing phases to have disprop...

This paper develops an agent-level simulation model, termed ALPS, for simulating the spread of an infectious disease in a confined community. The mechanism of transmission is agent-to-agent contact, using parameters reported for Corona COVID-19 pandemic. The main goal of the ALPS simulation is analyze effects of preventive measures -- imposition an...

Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the current literature offers only topological methods. This paper introduces a far-reaching geometric approach for an...

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 help in assessing the plant's health, understanding its growth patterns, and modeling relations between plant species and between plants and their environment. In this artic...

Rapid advances in cost-effective and non-invasive depth sensors, and the development of reliable and real-time 3D skeletal data estimation algorithms, have opened up a new application area in computer vision - statistical analysis of human kinematic data for fast, automated assessment of body movements. These assessments can play important roles in...

Complex analyses involving multiple, dependent random quantities often lead to graphical models: a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical analyses for graphical data, one needs mathematical representations and metrics for matching and comparing gra...

Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis, which makes standard methods not directly applicable. The key challenge is that these observations are not "alig...

Functional variables are often used as predictors in regression problems. A commonly-used parametric approach, called {\it scalar-on-function regression}, adopts the standard $\ltwo$ inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability because p...

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. This paper aims to statistically analyze the dynamic nature of FC by representing the collective time-series data, over a set of brain regions, as a trajectory on the spac...

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 relates to the similarity of fMRI responses across different brain regions when the brain is simply resting or performing a task. While the dynamic nature of FC is well accept...

The problem of three-dimensional (3D) chromosome structure inference from Hi-C data sets is important and challenging. While bulk Hi-C data sets contain contact information derived from millions of cells and can capture major structural features shared by the majority of cells in the sample, they do not provide information about local variability b...

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 help in assessing the plant's health, understanding its growth patterns, and modeling relations between plant species and between plants and their environment. In this article,...

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 relates to the similarity of fMRI responses across different brain regions when the brain is simply resting or performing a task. While the dynamic nature of FC is well accept...

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. This paper aims to statistically analyze the dynamic nature of FC by representing the collective time-series data, over a set of brain regions, as a trajectory on the spac...

In this article, we review the past development, current trends, and possible future directions within the broad field of pattern recognition. We consider three main building blocks of pattern recognition systems: feature extraction, dimensionality reduction, and classifier learning. In each case, we discuss both the classical and the contemporary...

The problem of estimating probability densities underlying given i.i.d. samples is a fundamental problem in statistics. Taking a Bayesian nonparametric approach, we put forth a geometric solution that uses different actions of the diffeomorphism (domain warping) group on the set of positive pdfs to explore this space more efficiently. This represen...

We study regression using functional predictors in situations where these functions contains both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can significantly degrade both model estimation and prediction performance. The current techniques either ignore the phas...

Statistical analysis of dynamic systems, such as videos and dynamic functional connectivity, is often translated into a problem of analyzing trajectories of relevant features, particularly covariance matrices. As an example, in video-based action recognition, a natural mathematical representation of activity videos is as parameterized trajectories...

Spillover indices computed from VAR models are intended to measure the connectedness between the variables in the system. The generalized spillover index ([Formula presented]) computed using the generalized forecast error variance decomposition is often considerably larger than the conventional spillover index computed from specific Cholesky decomp...

Neuron morphology plays a central role in characterizing cognitive health and functionality of brain structures. The problem of quantifying neuron shapes and capturing statistical variability of shapes is difficult because neurons differ both in geometry and in topology. This paper develops a mathematical representation of neuronal trees, restricti...

This paper presents a shape preserving incremental learning algorithm that employs a novel shape-based metric called the Fisher-Rao Amplitude-Phase Distance (FRAPD) metric. The combined amplitude and phase distance metric is achieved on a function space from the Fisher-Rao elastic registration. We utilize an exhaustive search method for selecting t...

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. Popular approaches for comparing populations (on Euclidean domains) mostly involve a two-step procedure: (1) estimate probability density functions (pdf s) from their res...