Skeleton Regression: A Graph-Based Approach to Estimation with Manifold Structure

We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold. Our approach first constructs a graph representation, referred to as the skeleton, to capture the underlying geometric structure. We then define metrics on the skeleton graph and apply nonparametric regression techniques, along with feature transformations based on the graph, to estimate the regression function. In addition to the included nonparametric methods, we also discuss the limitations of some nonparametric regressors with respect to the general metric space such as the skeleton graph. The proposed regression framework allows us to bypass the curse of dimensionality and provides additional advantages that it can handle the union of multiple manifolds and is robust to additive noise and noisy observations. We provide statistical guarantees for the proposed method and demonstrate its effectiveness through simulations and real data examples.

TBI-GAN: An Adversarial Learning Approach for Data Synthesis on Traumatic Brain Segmentation

Brain network analysis for traumatic brain injury (TBI) patients is critical for its consciousness level assessment and prognosis evaluation, which requires the segmentation of certain consciousness-related brain regions. However, it is difficult to construct a TBI segmentation model as manually annotated MR scans of TBI patients are hard to collect. Data augmentation techniques can be applied to alleviate the issue of data scarcity. However, conventional data augmentation strategies such as spatial and intensity transformation are unable to mimic the deformation and lesions in traumatic brains, which limits the performance of the subsequent segmentation task. To address these issues, we propose a novel medical image inpainting model named TBI-GAN to synthesize TBI MR scans with paired brain label maps. The main strength of our TBI-GAN method is that it can generate TBI images and corresponding label maps simultaneously, which has not been achieved in the previous inpainting methods for medical images. We first generate the inpainted image under the guidance of edge information following a coarse-to-fine manner, and then the synthesized intensity image is used as the prior for label inpainting. Furthermore, we introduce a registration-based template augmentation pipeline to increase the diversity of the synthesized image pairs and enhance the capacity of data augmentation. Experimental results show that the proposed TBI-GAN method can produce sufficient synthesized TBI images with high quality and valid label maps, which can greatly improve the 2D and 3D traumatic brain segmentation performance compared with the alternatives.

Skeleton Clustering: Dimension-Free Density-based Clustering

We introduce a density-based clustering method called skeleton clustering that can detect clusters in multivariate and even high-dimensional data with irregular shapes. To bypass the curse of dimensionality, we propose surrogate density measures that are less dependent on the dimension but have intuitive geometric interpretations. The clustering framework constructs a concise representation of the given data as an intermediate step and can be thought of as a combination of prototype methods, density-based clustering, and hierarchical clustering. We show by theoretical analysis and empirical studies that the skeleton clustering leads to reliable clusters in multivariate and high-dimensional scenarios.