Related papers: Joint Geometric and Topological Analysis of Hierar…

Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukeherjee, and Boyer showed that…

Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We show that a computational problem closely related to a core task in TDA --…

Accurate bone strength prediction is essential for assessing fracture risk, particularly in aging populations and individuals with osteoporosis. Bone imaging has evolved from X-rays and DXA to clinical computed tomography (CT), and now to…

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and…

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…

We develop a framework for comparing data manifolds, aimed, in particular, towards the evaluation of deep generative models. We describe a novel tool, Cross-Barcode(P,Q), that, given a pair of distributions in a high-dimensional space,…

In this paper, we propose a sensitivity-free and multi-objective structural design methodology called data-driven topology design. It is schemed to obtain high-performance material distributions from initially given material distributions…

Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…

Deep learning methods have achieved a lot of success in various applications involving converting wearable sensor data to actionable health insights. A common application areas is activity recognition, where deep-learning methods still…

Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important…

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…

The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these…

The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures. Motivated by insights from the Topological Data Analysis…

Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an…

High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…

Manifold learning is used for dimensionality reduction, with the goal of finding a projection subspace to increase and decrease the inter- and intraclass variances, respectively. However, a bottleneck for subspace learning methods often…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…