Related papers: Visualising high-dimensional state spaces with "Tu…
3D scatterplots are a well-established plotting technique that can be used to represent data with three or more dimensions. On paper and computer monitors they are essentially two-dimensional projections of the three-dimensional Cartesian…
Data visualizations summarize high-dimensional distributions in two or three dimensions. Dimensionality reduction entails a loss of information, and what is preserved differs between methods. Existing methods preserve the local or the…
The challenge of navigation in environments with dynamic objects continues to be a central issue in the study of autonomous agents. While predictive methods hold promise, their reliance on precise state information makes them less practical…
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…
We generalize the method introduced in Phys. Rev. B 101, 041108 (2020) of extracting information about topological order from the ground state of a strongly correlated two-dimensional system represented by an infinite projected entangled…
Dimensionality reduction methods such as t-SNE and UMAP are popular methods for visualizing data with a potential (latent) clustered structure. They are known to group data points at the same time as they embed them, resulting in…
Trajectory-user linking (TUL) aims to match anonymous trajectories to the most likely users who generated them, offering benefits for a wide range of real-world spatio-temporal applications. However, existing TUL methods are limited by high…
This paper studies the problem of image-goal navigation which involves navigating to the location indicated by a goal image in a novel previously unseen environment. To tackle this problem, we design topological representations for space…
The theory of homologies introduces cell complexes to provide an algebraic description of spaces up to topological equivalence. Attractors in state space can be studied using Branched Manifold Analysis through Homologies: this strategy…
Point feature labeling is a classical problem in cartography and GIS that has been extensively studied for geospatial point data. At the same time, word clouds are a popular visualization tool to show the most important words in text data…
We propose a way -- universal wave function overlap -- to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data should fully characterize the topological orders…
In this paper, we present a simple yet effective Boolean map based representation that exploits connectivity cues for visual tracking. We describe a target object with histogram of oriented gradients and raw color features, of which each…
Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…
While the topological order in two dimensions has been studied extensively since the discover of the integer and fractional quantum Hall systems, topological states in 3 spatial dimensions are much less understood. In this paper, we propose…
We present a practical application of parallel symbolic computation in General Relativity: the calculation of curvature invariants for large dimension. We discuss the structure of the calculations, an implementation of the technique and…
We propose a new approach, named PolyMapper, to circumvent the conventional pixel-wise segmentation of (aerial) images and predict objects in a vector representation directly. PolyMapper directly extracts the topological map of a city from…
Implicit neural representations (INRs) have emerged as a powerful tool for compressing large-scale volume data. This opens up new possibilities for in situ visualization. However, the efficient application of INRs to distributed data…
Despite the remarkable success of large large-scale neural networks, we still lack unified notation for thinking about and describing their representational spaces. We lack methods to reliably describe how their representations are…
High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…