Related papers: Persistent Patterns in Eye Movements: A Topologica…
We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into…
Human emotion is expressed in many communication modalities and media formats and so their computational study is equally diversified into natural language processing, audio signal analysis, computer vision, etc. Similarly, the large…
Persistent homology (PH) encodes global information, such as cycles, and is thus increasingly integrated into graph neural networks (GNNs). PH methods in GNNs typically traverse an increasing sequence of subgraphs. In this work, we first…
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…
Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a…
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…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…
We address the problem of estimating topological features from data in high dimensional Euclidean spaces under the manifold assumption. Our approach is based on the computation of persistent homology of the space of data points endowed with…
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…
Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a…
Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers, but require extensive data and…
In this study, we present a novel molecular fingerprint generation method based on multiparameter persistent homology. This approach reveals the latent structures and relationships within molecular geometry, and detects topological features…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…
Geometry and topology constitute complementary descriptors of three-dimensional shape, yet existing benchmark datasets primarily capture geometric information while neglecting topological structure. This work addresses this limitation by…
Topological data analysis involves the statistical characterization of the shape of data. Persistent homology is a primary tool of topological data analysis, which can be used to analyze topological features and perform statistical…
Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point…
Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…