Related papers: Learning Simplicial Complexes from Persistence Dia…
Recent advances in pretraining 3D point cloud encoders (e.g., Point-BERT, Point-MAE) have produced powerful models, whose abilities are typically evaluated on geometric or semantic tasks. At the same time, topological descriptors have been…
We present a new approach, the Topograph, which reconstructs underlying physics processes, including the intermediary particles, by leveraging underlying priors from the nature of particle physics decays and the flexibility of message…
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines…
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in $\mathbb{R}^n$, we may obtain a global representation as a cell complex with vertices given by a representative subset of the point cloud. The vertex…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
Algebraic topology has been widely applied to point cloud data to capture geometric shapes and topological structures. However, its application to genome sequence analysis remains rare. In this work, we propose topological sequence analysis…
Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a…
Hypergraphs are mathematical models for many problems in data sciences. In recent decades, the topological properties of hypergraphs have been studied and various kinds of (co)homologies have been constructed (cf. [3, 4, 12]). In this…
Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \textit{steady} and…
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of…
In recent years there has been noticeable interest in the study of the "shape of data". Among the many ways a "shape" could be defined, topology is the most general one, as it describes an object in terms of its connectivity structure:…
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…
Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an…
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.
Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here we showcase…
Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…
We explore the role of torsion in hybrid deep learning models that incorporate topological data analysis, focusing on autoencoders. While most TDA tools use field coefficients, this conceals torsional features present in integer homology.…
Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…
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…