Related papers: Multimapper: Data Density Sensitive Topological Vi…

In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a…

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…

Reeb spaces, as well as their discretized versions called Mappers, are common descriptors used in Topological Data Analysis, with plenty of applications in various fields of science, such as computational biology and data visualization,…

Color maps are a commonly used visualization technique in which data are mapped to optical properties, e.g., color or opacity. Color maps, however, do not explicitly convey structures (e.g., positions and scale of features) within data.…

In this short paper, a neural network that is able to form a low dimensional topological hidden representation is explained. The neural network can be trained as an autoencoder, a classifier or mix of both, and produces different low…

High-throughput technologies to collect field data have made observations possible at scale in several branches of life sciences. The data collected can range from the molecular level (genotypes) to physiological (phenotypic traits) and…

Advancing research in fields such as Simultaneous Localization and Mapping (SLAM) and autonomous navigation critically depends on the availability of reliable and reproducible multimodal datasets. While several influential datasets have…

Mapper algorithm can be used to build graph-based representations of high-dimensional data capturing structurally interesting features such as loops, flares or clusters. The graph can be further annotated with additional colouring of…

Ball Mapper is an widely used tool in topological data analysis for summarizing the structure of high-dimensional data through metric-based coverings and graph representations. A central computational bottleneck in Ball Mapper is the…

In Geographical Information search, map visualization can challenge the user because results can consist of a large set of heterogeneous items, increasing visual complexity. We propose a novel visualization model to address this issue. Our…

Density map is an effective visualization technique for depicting the scalar field distribution in 2D space. Conventional methods for constructing density maps are mainly based on Euclidean distance, limiting their applicability in urban…

Large-scale vector mapping is important for transportation, city planning, and survey and census. We propose GraphMapper, a unified framework for end-to-end vector map extraction from satellite images. Our key idea is a novel unified…

Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these…

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

We propose DeepExplorer, a simple and lightweight metric-free exploration method for topological mapping of unknown environments. It performs task and motion planning (TAMP) entirely in image feature space. The task planner is a recurrent…

Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…

Visual scenes are naturally organized in a hierarchy, where a coarse semantic is recursively comprised of several fine details. Exploring such a visual hierarchy is crucial to recognize the complex relations of visual elements, leading to a…

This paper addresses the problem of very large-scale image retrieval, focusing on improving its accuracy and robustness. We target enhanced robustness of search to factors such as variations in illumination, object appearance and scale,…

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…

Reeb graphs are an important tool for abstracting and representing the topological structure of a function defined on a manifold. We have identified three properties for faithfully representing Reeb graphs in a visualization: they should be…