Related papers: Stable Homology-Based Cycle Centrality Measures
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…
We present the application of topological data analysis (TDA) to study unweighted complex networks via their persistent homology. By endowing appropriate weights that capture the inherent topological characteristics of such a network, we…
We present mathematical models based on persistent homology for analyzing force distributions in particulate systems. We define three distinct chain complexes: digital, position, and interaction, motivated by different capabilities of…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
A very interesting matter of Network Science is assessing how complex a given network is. In other words, by how much does such a network departs from any general patterns which could be evoked for its description. Among other choices,…
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…
Topological methods are very rarely used in structural health monitoring (SHM), or indeed in structural dynamics generally, especially when considering the structure and topology of observed data. Topological methods can provide a way of…
The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures. Motivated by insights from the Topological Data Analysis…
Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…
This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on…
The association between tie strength and social structure is a fundamental topic in the social sciences. We study this association by analyzing tie strength in higher-order networks, an increasingly relevant model which can encode group…
Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…
By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…
In network analysis, a measure of node centrality provides a scale indicating how central a node is within a network. The coreness is a popular notion of centrality that accounts for the maximal smallest degree of a subgraph containing a…
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…
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…
We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…
Hierarchy and centrality are two popular notions used to characterize the importance of entities in complex systems. Indeed, many complex systems exhibit a natural hierarchical structure, and centrality is a fundamental characteristic…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…