Related papers: Wavelet-Based Density Estimation for Persistent Ho…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for…
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine…
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic…
Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…
Observing critical phases in lattice models is challenging due to the need to analyze the finite time or size scaling of observables. We study how the computational topology technique of persistent homology can be used to characterize…
Persistent homology is a vital tool for topological data analysis. Previous work has developed some statistical estimators for characteristics of collections of persistence diagrams. However, tools that provide statistical inference for…
We present a new tool for data analysis: persistence discrete homology, which is well-suited to analyze filtrations of graphs. In particular, we provide a novel way of representing high-dimensional data as a filtration of graphs using…
Persistent homology computes topological invariants from point cloud data. Recent work has focused on developing statistical methods for data analysis in this framework. We show that, in certain models, parametric inference can be performed…
Persistent homology is a popular data analysis technique that is used to capture the changing topology of a filtration associated with some simplicial complex $K$. These topological changes are summarized in persistence diagrams. We propose…
This paper introduces an unsupervised method to estimate the class separability of text datasets from a topological point of view. Using persistent homology, we demonstrate how tracking the evolution of embedding manifolds during training…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric…
It is important to choose the geographical distributions of public resources in a fair and equitable manner. However, it is complicated to quantify the equity of such a distribution; important factors include distances to resource sites,…
High-accuracy prediction of the physical properties of amorphous materials is challenging in condensed-matter physics. A promising method to achieve this is machine-learning potentials, which is an alternative to computationally demanding…
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…
We present a topological pipeline for automated multiclass emotion recognition from eye-tracking data. Delay embeddings of gaze trajectories are analyzed using persistent homology. From the resulting persistence diagrams, we extract…
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…