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Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key…
Point clouds are popular 3D representations for real-life objects (such as in LiDAR and Kinect) due to their detailed and compact representation of surface-based geometry. Recent approaches characterise the geometry of point clouds by…
A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…
The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts…
This paper addresses the challenge of viewing and navigating Bayesian networks as their structural size and complexity grow. Starting with a review of the state of the art of visualizing Bayesian networks, an area which has largely been…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…
Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and they have recently found success as a tool to analyze networks…
In backbone networks carrying heavy traffic loads, unwanted and unusual end-to-end delay changes can happen, though possibly rarely. In order to understand and manage the network to potentially avoid such abrupt changes, it is crucial and…
Graphs have often been used to answer questions about the interaction between real-world entities by taking advantage of their capacity to represent complex topologies. Complex networks are known to be graphs that capture such non-trivial…
Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not…
Today's Internet maps, which are all collected from a small number of vantage points, are falling short of being accurate. We suggest here a paradigm shift for this task. DIMES is a distributed measurement infrastructure for the Internet…
This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…
Geometric data analysis relies on graphs that are either given as input or inferred from data. These graphs are often treated as "correct" when solving downstream tasks such as graph signal denoising. But real-world graphs are known to…
Many real-world networks, including social and information networks, are dynamic structures that evolve over time. Such dynamic networks are typically visualized using a sequence of static graph layouts. In addition to providing a visual…
Querying graph data with low latency is an important requirement in application domains such as social networks and knowledge graphs. Graph queries perform multiple hops between vertices. When data is partitioned and stored across multiple…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
The increasing number and complexity of planetary exploration space missions require new tools to access, visualize and analyse data to improve their scientific return. ASI Science Data Center (ASDC) addresses this request with the web-tool…
Multilayer relationships among entities and information about entities must be accompanied by the means to analyze, visualize, and obtain insights from such data. We present open-source software (muxViz) that contains a collection of…
We introduce a Geometry Informed Model for financial forecasting by embedding high dimensional market data onto constant curvature 2manifolds. Guided by the uniformization theorem, we model market dynamics as Brownian motion on spherical…