相关论文: Topological Data Analysis of Decision Boundaries w…

One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded…

We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

Topological data analysis (TDA), as a relatively recent approach, has demonstrated great potential in capturing the intrinsic and robust structural features of complex data. While persistent homology, as a core tool of TDA, focuses on…

In recent years, many techniques have been developed to improve the performance and efficiency of data center networks. While these techniques provide high accuracy, they are often designed using heuristics that leverage domain-specific…

Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides…

We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to…

Uncovering latent community structure in complex networks is a field that has received an enormous amount of attention. Unfortunately, whilst potentially very powerful, unsupervised methods for uncovering labels based on topology alone has…

We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…

Neuro-symbolic reasoning systems face fundamental challenges in maintaining semantic coherence while satisfying physical and logical constraints. Building upon our previous work on Ontology Neural Networks, we present an enhanced framework…

This paper has three main goals : (1) To give an axiomatic formulation of the construction of "reduced \v{C}ech complexes", complexes using fewer than the usual number of intersections but still computing cohomology of an appropriate class…

This study proposes a new approach that investigates differences in topological characteristics of visual networks, which are constructed using fMRI BOLD time-series corresponding to visual datasets of COCO, ImageNet, and SUN. A publicly…

The so called \v{C}ech and Vietoris-Rips simplicial filtrations are designed to capture information about the topological structure of metric datasets. These filtrations are two of the workhorses in the field of topological data analysis.…

The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training process, and interpret their outputs. In this paper, we propose a novel approach to investigate…

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…

Topological data analysis computes and analyses topological features of the point clouds by constructing and studying a simplicial representation of the underlying topological structure. The enthusiasm that followed the initial successes of…

Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions…

The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…