arXiv subjects

Barbara B. Bendlin

Publications and source records attributed to Barbara B. Bendlin.

4 recordsLinked to original sources

arXiv2026

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex

Compositional data -- vectors encoding relative proportions -- arise across scientific domains, including ecology, geochemistry, and genomics. The features in these data often come with known hierarchical structure (e.g., taxonomies, phylogenies, ontologies), yet existing methods either ignore this structure, discard the intrinsic Aitchison geometry, are designed for binary trees, or yield incomplete coordinate systems. We describe PolyILR, a canonical orthonormal decomposition of the Aitchison tangent space aligned with any tree topology. Our construction defines a weighted local geometry at each internal node capturing full branching structure, then lifts these to a global orthonormal basis where every coordinate corresponds to a specific tree location. On microbiome and single-cell benchmarks, PolyILR yields stable, interpretable features and enables inference at multiscale tree resolution. We also establish a novel theoretical connection to softmax classifiers, suggesting possible applications to probabilistic modeling.

cs.LG↗

arXiv2024

Association of neighborhood disadvantage with cognitive function and cortical disorganization in an unimpaired cohort

Neighborhood disadvantage is associated with worse health and cognitive outcomes. Morphological similarity network (MSN) is a promising approach to elucidate cortical network patterns underlying complex cognitive functions. We hypothesized that MSNs could capture changes in cortical patterns related to neighborhood disadvantage and cognitive function. This cross-sectional study included cognitively unimpaired participants from two large Alzheimers studies at University of Wisconsin-Madison. Neighborhood disadvantage status was obtained using the Area Deprivation Index (ADI). Cognitive performance was assessed on memory, processing speed and executive function. Morphological Similarity Networks (MSN) were constructed for each participant based on the similarity in distribution of cortical thickness of brain regions, followed by computation of local and global network features. Association of ADI with cognitive scores and MSN features were examined using linear regression and mediation analysis. ADI showed negative association with category fluency,implicit learning speed, story recall and modified pre-clinical Alzheimers cognitive composite scores, indicating worse cognitive function among those living in more disadvantaged neighborhoods. Local network features of frontal and temporal regions differed based on ADI status. Centrality of left lateral orbitofrontal region showed a partial mediating effect between association of neighborhood disadvantage and story recall performance. Our preliminary findings suggest differences in local cortical organization by neighborhood disadvantage, which partially mediated the relationship between ADI and cognitive performance, providing a possible network-based mechanism to, in-part, explain the risk for poor cognitive functioning associated with disadvantaged neighborhoods.

q-bio.NC↗

arXiv2019

Dilated Convolutional Neural Networks for Sequential Manifold-valued Data

Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often, sizable empirical improvements are possible when the geometry of such data spaces are incorporated into the design of the model, architecture, and the algorithms. Motivated by neuroimaging applications, we study formulations where the data are {\em sequential manifold-valued measurements}. This case is common in brain imaging, where the samples correspond to symmetric positive definite matrices or orientation distribution functions. Instead of a recurrent model which poses computational/technical issues, and inspired by recent results showing the viability of dilated convolutional models for sequence prediction, we develop a dilated convolutional neural network architecture for this task. On the technical side, we show how the modules needed in our network can be derived while explicitly taking the Riemannian manifold structure into account. We show how the operations needed can leverage known results for calculating the weighted Fréchet Mean (wFM). Finally, we present scientific results for group difference analysis in Alzheimer's disease (AD) where the groups are derived using AD pathology load: here the model finds several brain fiber bundles that are related to AD even when the subjects are all still cognitively healthy.

cs.CV↗

arXiv2013

Diffeomorphic Metric Mapping and Probabilistic Atlas Generation of Hybrid Diffusion Imaging based on BFOR Signal Basis

We propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI), denoted as LDDMM-HYDI. We then propose a Bayesian model for estimating the white matter atlas from HYDIs. We adopt the work given in Hosseinbor et al. (2012) and represent the q-space diffusion signal with the Bessel Fourier orientation reconstruction (BFOR) signal basis. The BFOR framework provides the representation of mDWI in the q-space and thus reduces memory requirement. In addition, since the BFOR signal basis is orthonormal, the L2 norm that quantifies the differences in the q-space signals of any two mDWI datasets can be easily computed as the sum of the squared differences in the BFOR expansion coefficients. In this work, we show that the reorientation of the $q$-space signal due to spatial transformation can be easily defined on the BFOR signal basis. We incorporate the BFOR signal basis into the LDDMM framework and derive the gradient descent algorithm for LDDMM-HYDI with explicit orientation optimization. Additionally, we extend the previous Bayesian atlas estimation framework for scalar-valued images to HYDIs and derive the expectation-maximization algorithm for solving the HYDI atlas estimation problem. Using real HYDI datasets, we show the Bayesian model generates the white matter atlas with anatomical details. Moreover, we show that it is important to consider the variation of mDWI reorientation due to a small change in diffeomorphic transformation in the LDDMM-HYDI optimization and to incorporate the full information of HYDI for aligning mDWI.

cs.CV↗