Related papers: A Persistent Homology Approach to Time Series Clas…

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

Persistent homology, a powerful mathematical tool for data analysis, summarizes the shape of data through tracking topological features across changes in different scales. Classical algorithms for persistent homology are often constrained…

Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales.…

Topological data analysis (TDA), as a relatively recent approach, has demonstrated great potential in capturing the intrinsic and robust structural features of complex data. While persistent homology, as a core tool of TDA, focuses on…

Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…

Topological Data Analysis (TDA) is a rapidly growing field, which studies methods for learning underlying topological structures present in complex data representations. TDA methods have found recent success in extracting useful geometric…

Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…

A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) and signal processing (e.g.,…

We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances…

Topological Data Analysis (TDA) has been successfully used for various tasks in signal/image processing, from visualization to supervised/unsupervised classification. Often, topological characteristics are obtained from persistent homology…

\emph{Topological data analysis} (TDA) has recently emerged as a new technique to extract meaningful discriminitve features from high dimensional data. In this paper, we investigate the possibility of applying TDA to improve the…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

Topological Data Analysis (TDA) gives practioners the ability to analyse the global structure of cybersecurity data. We use TDA for anomaly detection in host-based logs collected with the open-source Logging Made Easy (LME) project. We…

Persistent homology is an area within topological data analysis (TDA) that can uncover different dimensional holes (connected components, loops, voids, etc.) in data. The holes are characterized, in part, by how long they persist across…

We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pronounced topological…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…

This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…

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 semiconductor manufacturing, wafer map defect pattern provides critical information for facility maintenance and yield management, so the classification of defect patterns is one of the most important tasks in the manufacturing process.…

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…