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The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains…
A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to…
The Morse-Smale complex is a standard tool in visual data analysis. The classic definition is based on a continuous view of the gradient of a scalar function where its zeros are the critical points. These points are connected via gradient…
Network visualization allows a quick glance at how nodes (or actors) are connected by edges (or ties). A conventional network diagram of "contact tree" maps out a root and branches that represent the structure of nodes and edges, often…
The chemical sciences are producing an unprecedented amount of large, high-dimensional data sets containing chemical structures and associated properties. However, there are currently no algorithms to visualize such data while preserving…
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis,…
We study three representations of hierarchies of partitions: dendrograms (direct representations), saliency maps, and minimum spanning trees. We provide a new bijection between saliency maps and hierarchies based on quasi-flat zones as used…
With the increasing amount of data being visualized in large information spaces, methods providing data-driven context have become indispensable. Off-screen visualization techniques, therefore, have been extensively researched for their…
Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…
With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…
A central problem in topological data analysis is that of computing the homology of a given simplicial complex. Said complexes can have arbitrary large number of simplices, as can happen, for example, if the space is the Rips-Vietoris or…
Classification of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from real-world networks. In this paper we present a computationally tractable…
For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often…
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…
Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology.…
In this paper, we exploit minimal sensing information gathered from biologically inspired sensor networks to perform exploration and mapping in an unknown environment. A probabilistic motion model of mobile sensing nodes, inspired by motion…
We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in…
In recent years, cosmic shear has emerged as a powerful tool to study the statistical distribution of matter in our Universe. Apart from the standard two-point correlation functions, several alternative methods like peak count statistics…
We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called persistence complex is used to reveal…