Related papers: Topological Signal Processing using the Weighted O…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…
Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…
Analyzing flight trajectory data sets poses challenges due to the intricate interconnections among various factors and the high dimensionality of the data. Topological Data Analysis (TDA) is a way of analyzing big data sets focusing on the…
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…
Software ecosystems have had a tremendous impact on computing and society, capturing the attention of businesses, researchers, and policy makers alike. Massive ecosystems like the JavaScript node package manager (npm) is evidence of how…
Topological Data Analysis (TDA) has emerged as a powerful tool for extracting meaningful features from complex data structures, driving significant advancements in fields such as neuroscience, biology, machine learning, and financial…
This paper introduces topological data analysis. Starting from notions of a metric space and some elementary graph theory, we take example sets of data and demonstrate some of their topological properties. We discuss simplicial complexes…
Multivariate time series prediction has applications in a wide variety of domains and is considered to be a very challenging task, especially when the variables have correlations and exhibit complex temporal patterns, such as seasonality…
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…
In recent years, graph neural networks (GNNs) have emerged as a potent tool for learning on graph-structured data and won fruitful successes in varied fields. The majority of GNNs follow the message-passing paradigm, where representations…
Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is…
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…
Identifying molecular signatures from complex disease patients with underlying symptomatic similarities is a significant challenge in the analysis of high dimensional multi-omics data. Topological data analysis (TDA) provides a way of…
In low-altitude surveillance and early warning systems, detecting weak moving targets remains a significant challenge due to low signal energy, small spatial extent, and complex background clutter. Existing methods struggle with extracting…
Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…
Soft gels, formed via the self-assembly of particulate organic materials, exhibit intricate multi-scale structures that provides them with flexibility and resilience when subjected to external stresses. This work combines molecular…
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…
Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However,…
In the framework of convolutional neural networks that lie at the heart of deep learning, downsampling is often performed with a max-pooling operation that only retains the element with maximum activation, while completely discarding the…
Anomaly detection in multivariate signals is a task of paramount importance in many disciplines (epidemiology, finance, cognitive sciences and neurosciences, oncology, etc.). In this perspective, Topological Data Analysis (TDA) offers a…