相关论文: Tropical Sufficient Statistics for Persistent Homo…

Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…

This paper is a survey of persistent homology, primarily as it is used in topological data analysis. It includes the theory of persistence modules, as well as stability theorems for persistence barcodes, generalized persistence,…

Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…

In this paper we introduce a statistic, the persistent homology transform (PHT), to model surfaces in $\mathbb{R}^3$ and shapes in $\mathbb{R}^2$. This statistic is a collection of persistence diagrams - multiscale topological summaries…

In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…

Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…

In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…

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…

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…

This work presents a new method to quantify connectivity in transportation networks. Inspired by the field of topological data analysis, we propose a novel approach to explore the robustness of road network connectivity in the presence of…

Towards building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a topological ring. This requires building the theory of…

We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called persistence complex is used to reveal…

Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…

In medical image analysis, feature engineering plays an important role in the design and performance of machine learning models. Persistent homology (PH), from the field of topological data analysis (TDA), demonstrates robustness and…

Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…

Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents…

Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to the dark matter halo catalogs from the Quijote…

This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or,…

Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…

In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…