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In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
Topological Data Analysis (TDA) is a novel, and relatively new approach to analysing high-dimensional data sets. It does this by focussing on global properties like the shape and connectivity of the data giving it a significant advantage…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…
Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…
Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…
Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…
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…
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…
Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…
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…
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…
Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology,…
Topological data analysis (TDA) uncovers crucial properties of objects in medical imaging. Methods based on persistent homology have demonstrated their advantages in capturing topological features that traditional deep learning methods…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
TDA (topological data analysis) is a relatively new area of research related to importing classical ideas from topology into the realm of data analysis. Under the umbrella term TDA, there falls, in particular, the notion of persistent…
Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is…