12 research outputs found
The State-of-the-Art of Set Visualization
Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net
Multi-Perspective, Simultaneous Embedding
We describe MPSE: a Multi-Perspective Simultaneous Embedding method for
visualizing high-dimensional data, based on multiple pairwise distances between
the data points. Specifically, MPSE computes positions for the points in 3D and
provides different views into the data by means of 2D projections (planes) that
preserve each of the given distance matrices. We consider two versions of the
problem: fixed projections and variable projections. MPSE with fixed
projections takes as input a set of pairwise distance matrices defined on the
data points, along with the same number of projections and embeds the points in
3D so that the pairwise distances are preserved in the given projections. MPSE
with variable projections takes as input a set of pairwise distance matrices
and embeds the points in 3D while also computing the appropriate projections
that preserve the pairwise distances. The proposed approach can be useful in
multiple scenarios: from creating simultaneous embedding of multiple graphs on
the same set of vertices, to reconstructing a 3D object from multiple 2D
snapshots, to analyzing data from multiple points of view. We provide a
functional prototype of MPSE that is based on an adaptive and stochastic
generalization of multi-dimensional scaling to multiple distances and multiple
variable projections. We provide an extensive quantitative evaluation with
datasets of different sizes and using different number of projections, as well
as several examples that illustrate the quality of the resulting solutions
Analysis and Visualisation of Edge Entanglement in Multiplex Networks
Cette thèse présente une nouvelle méthodologie pour analyser des réseaux. Nous développons l'intrication d'un réseau multiplex, qui se matérialise sous forme d'une mesure d'intensité et d'homogénéité, et d'une abstraction, le réseau d'interaction des catalyseurs, auxquels sont associés des indices d'intrication. Nous présentons ensuite la mise en place d'outils spécifiques pour l'analyse visuelle des réseaux complexes qui tirent profit de cette méthodologie. Ces outils présente une vue double de deux réseaux,qui inclue une un algorithme de dessin, une interaction associant brossage d'une sélection et de multiples liens pré-attentifs. Nous terminons ce document par la présentation détaillée d'applications dans de multiples domaines.When it comes to comprehension of complex phenomena, humans need to understand what interactions lie within them.These interactions are often captured with complex networks. However, the interaction pluralism is often shallowed by traditional network models. We propose a new way to look at these phenomena through the lens of multiplex networks, in which catalysts are drivers of the interaction through substrates. To study the entanglement of a multiplex network is to study how edges intertwine, in other words, how catalysts interact. Our entanglement analysis results in a full set of new objects which completes traditional network approaches: the entanglement homogeneity and intensity of the multiplex network, and the catalyst interaction network, with for each catalyst, an entanglement index. These objects are very suitable for embedment in a visual analytics framework, to enable comprehension of a complex structure. We thus propose of visual setting with coordinated multiple views. We take advantage of mental mapping and visual linking to present simultaneous information of a multiplex network at three different levels of abstraction. We complete brushing and linking with a leapfrog interaction that mimics the back-and-forth process involved in users' comprehension. The method is validated and enriched through multiple applications including assessing group cohesion in document collections, and identification of particular associations in social networks.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF
Large bichromatic point sets admit empty monochromatic 4-gons
We consider a variation of a problem stated by Erd˝os
and Szekeres in 1935 about the existence of a number
fES(k) such that any set S of at least fES(k) points in
general position in the plane has a subset of k points
that are the vertices of a convex k-gon. In our setting
the points of S are colored, and we say that a (not necessarily
convex) spanned polygon is monochromatic if
all its vertices have the same color. Moreover, a polygon
is called empty if it does not contain any points of
S in its interior. We show that any bichromatic set of
n ≥ 5044 points in R2 in general position determines
at least one empty, monochromatic quadrilateral (and
thus linearly many).Postprint (published version
Simulation and Modeling of Nanomaterials
This Special Issue focuses on computational detailed studies (simulation, modeling, and calculations) of the structures, main properties, and peculiarities of the various nanomaterials (nanocrystals, nanoparticles, nanolayers, nanofibers, nanotubes, etc.) based on various elements, including organic and biological components, such as amino acids and peptides. For many practical applications in nanoelectronics., such materials as ferroelectrics and ferromagnetics, having switching parameters (polarization, magnetization), are highly requested, and simulation of dynamics and kinetics of their switching are a very important task. An important task for these studies is computer modeling and computational research of the properties on the various composites of the other nanostructures with polymeric ferroelectrics and with different graphene-like 2-dimensional structures. A wide range of contemporary computational methods and software are used in all these studies