The problem of using covariates to predict shapes of objects in a regression setting is important in many fields. A formal statistical approach, termed Geodesic regression model, is commonly used for modeling and analyzing relationships between Euclidean predictors and shape responses. Despite its popularity, this model faces several key challenges, including (i) misalignment of shapes due to pre-processing steps, (ii) difficulties in shape alignment due to imaging heterogeneity, and (iii) lack of spatial correlation in shape structures. This paper proposes a comprehensive geodesic factor regression model that addresses all these challenges. Instead of using shapes as extracted from pre-registered data, it takes a more fundamental approach, incorporating alignment step within the proposed regression model and learns them using both pre-shape and covariate data. Additionally, it specifies spatial correlation structures using low-dimensional representations, including latent factors on the tangent space and isotropic error terms. The proposed framework results in substantial improvements in regression performance, as demonstrated through simulation studies and a real data analysis on Corpus Callosum contour data obtained from the ADNI study.
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This content will become publicly available on December 1, 2024
Confounder Adjustment in Shape-on-Scalar Regression Model: Corpus Callosum Shape Alterations in Alzheimer’s Disease
Large-scale imaging studies often face challenges stemming from heterogeneity arising from differences in geographic location, instrumental setups, image acquisition protocols, study design, and latent variables that remain undisclosed. While numerous regression models have been developed to elucidate the interplay between imaging responses and relevant covariates, limited attention has been devoted to cases where the imaging responses pertain to the domain of shape. This adds complexity to the problem of imaging heterogeneity, primarily due to the unique properties inherent to shape representations, including nonlinearity, high-dimensionality, and the intricacies of quotient space geometry. To tackle this intricate issue, we propose a novel approach: a shape-on-scalar regression model that incorporates confounder adjustment. In particular, we leverage the square root velocity function to extract elastic shape representations which are embedded within the linear Hilbert space of square integrable functions. Subsequently, we introduce a shape regression model aimed at characterizing the intricate relationship between elastic shapes and covariates of interest, all while effectively managing the challenges posed by imaging heterogeneity. We develop comprehensive procedures for estimating and making inferences about the unknown model parameters. Through real-data analysis, our method demonstrates its superiority in terms of estimation accuracy when compared to existing approaches.
more » « less- Award ID(s):
- 1953087
- NSF-PAR ID:
- 10467690
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Stats
- Volume:
- 6
- Issue:
- 4
- ISSN:
- 2571-905X
- Page Range / eLocation ID:
- 980 to 989
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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 that can account for heterogeneity in PTSD, which is of paramount interest. We propose a comprehensive shape analysis framework representing brain sub-structures, such as the hippocampus, amygdala, and putamen, as parameterized surfaces and quantifying their shape differences using an elastic shape metric. Under this metric, we compute shape summaries (mean, covariance, PCA) of brain sub-structures and represent individual brain shapes by their principal scores under a shape-PCA basis. These representations are rich enough to allow visualizations of full 3D structures and help understand localized changes. In order to validate the elastic shape analysis, we use the principal components (PCs) to reconstruct the brain structures and perform further evaluation by performing a regression analysis to model PTSD and trauma severity using the brain shapes represented
via PCs and in conjunction with auxiliary exposure variables. We apply our method to data from the Grady Trauma Project (GTP), where the goal is to predict clinical measures of PTSD. The framework seamlessly integrates accurate morphological features and other clinical covariates to yield superior predictive performance when modeling PTSD outcomes. Compared to vertex-wise analysis and other widely applied shape analysis methods, the elastic shape analysis approach results in considerably higher reconstruction accuracy for the brain shape and reveals significantly greater predictive power. It also helps identify local deformations in brain shapes associated with PTSD severity. -
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Abstract Soil resource partitioning and dispersal limitation have been shown to shape the tree community structure of mature tropical forests, but are poorly studied in the context of forest succession. We examined the relative contributions of both ecological processes to the variation in the species composition of young tropical secondary forests at different spatial scales, and if the relative importance of these two ecological processes changed during succession. At the species level, we examined if the association between species abundances and soil fertility differed between early and late successional species and/or changed over the course of succession.
We used vegetation and soil data from 47 secondary forest sites with two plots each in a tropical agricultural landscape. A distance‐based redundancy analysis and variation partitioning were employed to examine the relative importance of spatial distance (proxy for dispersal limitation) and heterogeneity in soil nutrients (proxy for soil nutrient partitioning) at the landscape scale, and a linear regression to test their effects at the local scale. We examined interspecific variation in species’ responses to successional age and soil nutrients with a joint species distribution model.
Dispersal limitation and soil niche partitioning drove considerable variation in the composition of plant communities at local and landscape scales. The relative contribution of these two ecological processes changed with scale (local vs. landscape) and topography (lower slope vs. upper slope plots). At the species level, significant abundance–soil fertility associations were mostly positive. Most species became less responsive to soil nutrients over the first few decades of tropical forest succession, probably because light became the main limiting resource in older forests.
Synthesis. Our key finding is that spatial heterogeneity in soil resources and spatial distance jointly drive compositional variation within and across early successional forests. Our results highlight that a network of forest fragments enhances the resilience of ecological processes and the potential of secondary forests to restore and preserve biodiversity in human‐modified landscapes. To advance our understanding of ecological succession, we need to move beyond single‐factor and local‐scale studies and examine the effects of multiple variables on succession at different spatial scales. -
4D printed shape memory metamaterial for vibration bandgap switching and active elastic-wave guidingnull (Ed.)Acoustic/elastic metamaterials that rely on engineered microstructures instead of chemical composition enable a rich variety of extraordinary effective properties that are suited for various applications including vibration/noise isolation, high-resolution medical imaging, and energy harvesting and mitigation. However, the static nature of these elastic wave guides limits their potential for active elastic-wave guiding, as microstructure transformation remains a challenge to effectively apply in traditional elastic metamaterials due to the interplay of polarization and structural sensitivity. Here, a tunable, locally resonant structural waveguide is proposed and demonstrated for active vibration bandgap switching and elastic-wave manipulation between 1000–4000 Hz based on 3D printed building blocks of zinc-neutralized poly(ethylene- co -methacrylic acid) ionomer (Surlyn 9910). The ionomer exhibits shape memory behavior to enable rearrangement into new shape patterns through application of thermal stimuli that tunes mechanical performance in both space and time dimensions (4D metamaterial). The thermally induced shape-reorganization is programed to flip a series of frequency bands from passbands to bandgaps and vice versa . The continuously switched bandwidth can exceed 500 Hz. Consequently, altering the bandgap from “on” to “off” produces programmable elastic-wave propagation paths to achieve active wave guiding phenomena. An anisotropic cantilever-in-mass model is demonstrated to predict the self-adaptive dynamic responses of the printed structures with good agreement between the analytical work and experimental results. The tunable metamaterial-based waveguides illustrate the potential of 4D printed shape memory polymers in the designing and manufacturing of intelligent devices for elastic-wave control and vibration isolation.more » « less
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Abstract Proliferation of high‐resolution imaging data in recent years has led to substantial improvements in the two popular approaches for analyzing shapes of data objects based on landmarks and/or continuous curves. We provide an expository account of elastic shape analysis of parametric planar curves representing shapes of two‐dimensional (2D) objects by discussing its differences, and its commonalities, to the landmark‐based approach. Particular attention is accorded to the role of reparameterization of a curve, which in addition to rotation, scaling and translation, represents an important shape‐preserving transformation of a curve. The transition to the curve‐based approach moves the mathematical setting of shape analysis from finite‐dimensional non‐Euclidean spaces to infinite‐dimensional ones. We discuss some of the challenges associated with the infinite‐dimensionality of the shape space, and illustrate the use of geometry‐based methods in the computation of intrinsic statistical summaries and in the definition of statistical models on a 2D imaging dataset consisting of mouse vertebrae. We conclude with an overview of the current state‐of‐the‐art in the field.
This article is categorized under:
Image and Spatial Data < Data: Types and Structure
Computational Mathematics < Applications of Computational Statistics
