相关论文: Topological Brain Network Distances

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

The brain has no direct access to physical stimuli, but only to the spiking activity evoked in sensory organs. It is unclear how the brain can structure its representation of the world based on differences between those noisy, correlated…

Brain areas' functional repertoires are shaped by their incoming and outgoing structural connections. In empirically measured networks, most connections are short, reflecting spatial and energetic constraints. Nonetheless, a small number of…

This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…

Brain networks exhibit remarkable structural properties, including high local clustering, short path lengths, and heavy-tailed weight and degree distributions. While these features are thought to enable efficient information processing with…

A fundamental understanding of the network architecture of the brain is necessary for the further development of theories explicating circuit function. Perhaps as a derivative of its initial application to abstract informational systems,…

We define a metric---the network Gromov-Wasserstein distance---on weighted, directed networks that is sensitive to the presence of outliers. In addition to proving its theoretical properties, we supply network invariants based on optimal…

We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…

Mild cognitive impairment (MCI) is characterized by subtle changes in cognitive functions, often associated with disruptions in brain connectivity. The present study introduces a novel fine-grained analysis to examine topological…

Graph similarity metrics serve far-ranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful differences, yet are lightweight and scalable. Graph Relative…

Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…

Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological…

The graph parameters highway dimension and skeleton dimension were introduced to capture the properties of transportation networks. As many important optimization problems like Travelling Salesperson, Steiner Tree or $k$-Center arise in…

Neural network training is commonly based on SGD. However, the understanding of SGD's ability to converge to good local minima, given the non-convex nature of loss functions and the intricate geometric characteristics of loss landscapes,…

A fundamental problem in network science is the normalization of the topological or physical distance between vertices, that requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the…

Latent space models assume that network ties are more likely between nodes that are closer together in an underlying latent space. Euclidean space is a popular choice for the underlying geometry, but hyperbolic geometry can mimic more…

We study the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model under the assumptions of: i) variable…

Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…

We study typical distances in a geometric random graph on the hyperbolic plane. Introduced by Krioukov et al.~\cite{ar:Krioukov} as a model for complex networks, $N$ vertices are drawn randomly within a bounded subset of the hyperbolic…