相关论文: Topological Brain Network Distances

Considerable efforts in modern statistical physics is devoted to the study of networked systems. One of the most important example of them is the brain, which creates and continuously develops complex networks of correlated dynamics. An…

Small-world networks, i.e. networks displaying both a high clustering coefficient and a small characteristic path length, are obliquitous in nature. Since their identification, the "small-worldness" metric, as proposed by Humphries and…

Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally…

The Gromov-Hausdorff distance ($d_\mathrm{GH}$) provides a natural way of quantifying the dissimilarity between two given metric spaces. It is known that computing $d_\mathrm{GH}$ between two finite metric spaces is NP-hard, even in the…

We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into…

Neurons in the brain are organized such that nearby cells tend to share similar functions. AI models lack this organization, and past efforts to introduce topography have often led to trade-offs between topography and task performance. In…

Calibrating neural networks is of utmost importance when employing them in safety-critical applications where the downstream decision making depends on the predicted probabilities. Measuring calibration error amounts to comparing two…

The Gromov-Hausdorff (GH) distance is a natural way to measure distance between two metric spaces. We prove that it is $\mathrm{NP}$-hard to approximate the Gromov-Hausdorff distance better than a factor of $3$ for geodesic metrics on a…

The network architecture of the human brain has become a feature of increasing interest to the neuroscientific community, largely because of its potential to illuminate human cognition, its variation over development and aging, and its…

Recent studies on Graph Neural Networks(GNNs) provide both empirical and theoretical evidence supporting their effectiveness in capturing structural patterns on both homophilic and certain heterophilic graphs. Notably, most real-world…

Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for…

Graph distance metric learning serves as the foundation for many graph learning problems, e.g., graph clustering, graph classification and graph matching. Existing research works on graph distance metric (or graph kernels) learning fail to…

Brain extraction is a fundamental step for most brain imaging studies. In this paper, we investigate the problem of skull stripping and propose complementary segmentation networks (CompNets) to accurately extract the brain from T1-weighted…

Providing human-understandable insights into the inner workings of neural networks is an important step toward achieving more explainable and trustworthy AI. Existing approaches to such mechanistic interpretability typically require…

In topological data analysis (TDA), persistence diagrams have been a succesful tool. To compare them, Wasserstein and Bottleneck distances are commonly used. We address the shortcomings of these metrics and show a way to investigate them in…

As a relatively new field, network neuroscience has tended to focus on aggregate behaviours of the brain averaged over many successive experiments or over long recordings in order to construct robust brain models. These models are limited…

Recently, cross-spectral image patch matching based on feature relation learning has attracted extensive attention. However, performance bottleneck problems have gradually emerged in existing methods. To address this challenge, we make the…

The course was given at Peking University, Fall 2019. We discuss the following subjects: (1) Introduction to general topology, hyperspaces, metric and pseudometric spaces, graph theory. (2) Graphs in metric spaces, minimum spanning tree,…

An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This…

The segregation of brain fiber tractography data into distinct and anatomically meaningful clusters can help to comprehend the complex brain structure and early investigation and management of various neural disorders. We propose a novel…