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Researcher profile

Zhengwu Zhang

Zhengwu Zhang contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
ApplicationsComputer VisionMachine LearningMethodologyComputationmath.FANeurons and Cognition

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Published work

7 published item(s)

preprint2026arXiv

Diffeomorphic Cortical Alignment via Direct Warping of Streamline Endpoints

Cortical surface registration is often driven by local geometric descriptors (e.g., sulcal depth and curvature). While this approach achieves geometric correspondence, it neglects the long-range wiring constraints imposed by white-matter anatomy. Diffusion MRI tractography offers these crucial constraints; however, prior connectivity-informed pipelines typically align precomputed connectivity matrices, making the optimization highly sensitive to connectivity estimation and its resolution. In this paper, we introduce a novel connectivity-based surface registration method that aligns cortical surfaces by operating directly on white-matter fiber-tract endpoints. We model tract endpoints as a point cloud on the product manifold $Ω\times Ω$, where $Ω$ represents the spherical domain of the inflated cortical hemispheres. Our alignment method iteratively (i) computes a small diffeomorphic warp for $Ω$ by minimizing connectivity mismatch, and (ii) updates the endpoints based on this warp. The method relies on a geometric framework that ensures output warps are diffeomorphisms and has a final goal that optimizes the matching of well-known fiber bundles. Experiments on Human Connectome Project (HCP) data demonstrate improved tract-level correspondence, achieving higher connectivity-level overlap coefficients on major fiber bundles and stronger robustness across grid resolutions for $Ω$ compared to state-of-the-art methods such as ENCORE and MSMAll.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

NeuroPMD: Neural Fields for Density Estimation on Product Manifolds

We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum likelihood framework, with a penalty term formed using manifold differential operators. The network architecture and estimation algorithm are carefully designed to handle the challenges of high-dimensional product manifold domains, effectively mitigating the curse of dimensionality that limits traditional kernel and basis expansion estimators, as well as overcoming the convergence issues encountered by non-specialized neural network methods. Extensive simulations and a real-world application to brain structural connectivity data highlight the clear advantages of our method over the competing alternatives.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Amplitude Mean of Functional Data on $\mathbb{S}^2$

Manifold-valued functional data analysis (FDA) recently becomes an active area of research motivated by the raising availability of trajectories or longitudinal data observed on non-linear manifolds. The challenges of analyzing such data come from many aspects, including infinite dimensionality and nonlinearity, as well as time-domain or phase variability. In this paper, we study the amplitude part of manifold-valued functions on $\mathbb{S}^2$, which is invariant to random time warping or re-parameterization. Utilizing the nice geometry of $\mathbb{S}^2$, we develop a set of efficient and accurate tools for temporal alignment of functions, geodesic computing, and sample mean calculation. At the heart of these tools, they rely on gradient descent algorithms with carefully derived gradients. We show the advantages of these newly developed tools over its competitors with extensive simulations and real data and demonstrate the importance of considering the amplitude part of functions instead of mixing it with phase variability in manifold-valued FDA.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Analyzing Brain Structural Connectivity as Continuous Random Functions

This work considers a continuous framework to characterize the population-level variability of structural connectivity. Our framework assumes the observed white matter fiber tract endpoints are driven by a latent random function defined over a product manifold domain. To overcome the computational challenges of analyzing such complex latent functions, we develop an efficient algorithm to construct a data-driven reduced-rank function space to represent the latent continuous connectivity. Using real data from the Human Connectome Project, we show that our method outperforms state-of-the-art approaches applied to the traditional atlas-based structural connectivity matrices on connectivity analysis tasks of interest. We also demonstrate how our method can be used to identify localized regions and connectivity patterns on the cortical surface associated with significant group differences. Code will be made available at https://github.com/sbci-brain.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Outlier Detection for Multi-Network Data

It has become routine in neuroscience studies to measure brain networks for different individuals using neuroimaging. These networks are typically expressed as adjacency matrices, with each cell containing a summary of connectivity between a pair of brain regions. There is an emerging statistical literature describing methods for the analysis of such multi-network data in which nodes are common across networks but the edges vary. However, there has been essentially no consideration of the important problem of outlier detection. In particular, for certain subjects, the neuroimaging data are so poor quality that the network cannot be reliably reconstructed. For such subjects, the resulting adjacency matrix may be mostly zero or exhibit a bizarre pattern not consistent with a functioning brain. These outlying networks may serve as influential points, contaminating subsequent statistical analyses. We propose a simple Outlier DetectIon for Networks (ODIN) method relying on an influence measure under a hierarchical generalized linear model for the adjacency matrices. An efficient computational algorithm is described, and ODIN is illustrated through simulations and an application to data from the UK Biobank. ODIN was successful in identifying moderate to extreme outliers. Removing such outliers can significantly change inferences in downstream applications.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Bayesian Hierarchical Modeling on Covariance Valued Data

Analysis of structural and functional connectivity (FC) of human brains is of pivotal importance for diagnosis of cognitive ability. The Human Connectome Project (HCP) provides an excellent source of neural data across different regions of interest (ROIs) of the living human brain. Individual specific data were available from an existing analysis (Dai et al., 2017) in the form of time varying covariance matrices representing the brain activity as the subjects perform a specific task. As a preliminary objective of studying the heterogeneity of brain connectomics across the population, we develop a probabilistic model for a sample of covariance matrices using a scaled Wishart distribution. We stress here that our data units are available in the form of covariance matrices, and we use the Wishart distribution to create our likelihood function rather than its more common usage as a prior on covariance matrices. Based on empirical explorations suggesting the data matrices to have low effective rank, we further model the center of the Wishart distribution using an orthogonal factor model type decomposition. We encourage shrinkage towards a low rank structure through a novel shrinkage prior and discuss strategies to sample from the posterior distribution using a combination of Gibbs and slice sampling. We extend our modeling framework to a dynamic setting to detect change points. The efficacy of the approach is explored in various simulation settings and exemplified on several case studies including our motivating HCP data. We extend our modeling framework to a dynamic setting to detect change points.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Discovering Common Change-Point Patterns in Functional Connectivity Across Subjects

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 accepted, this paper develops a formal statistical test for finding {\it change-points} in times series associated with FC. It represents short-term connectivity by a symmetric positive-definite matrix, and uses a Riemannian metric on this space to develop a graphical method for detecting change-points in a time series of such matrices. It also provides a graphical representation of estimated FC for stationary subintervals in between the detected change-points. Furthermore, it uses a temporal alignment of the test statistic, viewed as a real-valued function over time, to remove inter-subject variability and to discover common change-point patterns across subjects. This method is illustrated using data from Human Connectome Project (HCP) database for multiple subjects and tasks.

0 citations0 reviewsNo code linkedOpen access