562 research outputs found
Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)
This paper presents a computational framework for the Principal Geodesic
Analysis of merge trees (MT-PGA), a novel adaptation of the celebrated
Principal Component Analysis (PCA) framework [87] to the Wasserstein metric
space of merge trees [92]. We formulate MT-PGA computation as a constrained
optimization problem, aiming at adjusting a basis of orthogonal geodesic axes,
while minimizing a fitting energy. We introduce an efficient, iterative
algorithm which exploits shared-memory parallelism, as well as an analytic
expression of the fitting energy gradient, to ensure fast iterations. Our
approach also trivially extends to extremum persistence diagrams. Extensive
experiments on public ensembles demonstrate the efficiency of our approach -
with MT-PGA computations in the orders of minutes for the largest examples. We
show the utility of our contributions by extending to merge trees two typical
PCA applications. First, we apply MT-PGA to data reduction and reliably
compress merge trees by concisely representing them by their first coordinates
in the MT-PGA basis. Second, we present a dimensionality reduction framework
exploiting the first two directions of the MT-PGA basis to generate
two-dimensional layouts of the ensemble. We augment these layouts with
persistence correlation views, enabling global and local visual inspections of
the feature variability in the ensemble. In both applications, quantitative
experiments assess the relevance of our framework. Finally, we provide a
lightweight C++ implementation that can be used to reproduce our results
Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)
This paper presents a computational framework for the Wasserstein
auto-encoding of merge trees (MT-WAE), a novel extension of the classical
auto-encoder neural network architecture to the Wasserstein metric space of
merge trees. In contrast to traditional auto-encoders which operate on
vectorized data, our formulation explicitly manipulates merge trees on their
associated metric space at each layer of the network, resulting in superior
accuracy and interpretability. Our novel neural network approach can be
interpreted as a non-linear generalization of previous linear attempts [79] at
merge tree encoding. It also trivially extends to persistence diagrams.
Extensive experiments on public ensembles demonstrate the efficiency of our
algorithms, with MT-WAE computations in the orders of minutes on average. We
show the utility of our contributions in two applications adapted from previous
work on merge tree encoding [79]. First, we apply MT-WAE to merge tree
compression, by concisely representing them with their coordinates in the final
layer of our auto-encoder. Second, we document an application to dimensionality
reduction, by exploiting the latent space of our auto-encoder, for the visual
analysis of ensemble data. We illustrate the versatility of our framework by
introducing two penalty terms, to help preserve in the latent space both the
Wasserstein distances between merge trees, as well as their clusters. In both
applications, quantitative experiments assess the relevance of our framework.
Finally, we provide a C++ implementation that can be used for reproducibility.Comment: arXiv admin note: text overlap with arXiv:2207.1096
Comparing Morse Complexes Using Optimal Transport: An Experimental Study
Morse complexes and Morse-Smale complexes are topological descriptors popular
in topology-based visualization. Comparing these complexes plays an important
role in their applications in feature correspondences, feature tracking,
symmetry detection, and uncertainty visualization. Leveraging recent advances
in optimal transport, we apply a class of optimal transport distances to the
comparative analysis of Morse complexes. Contrasting with existing comparative
measures, such distances are easy and efficient to compute, and naturally
provide structural matching between Morse complexes. We perform an experimental
study involving scientific simulation datasets and discuss the effectiveness of
these distances as comparative measures for Morse complexes. We also provide an
initial guideline for choosing the optimal transport distances under various
data assumptions.Comment: IEEE Visualization Conference (IEEE VIS) Short Paper, accepted, 2023;
supplementary materials:
http://www.sci.utah.edu/~beiwang/publications/GWMC_VIS_Short_BeiWang_2023_Supplement.pd
A Comparative Study of the Perceptual Sensitivity of Topological Visualizations to Feature Variations
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. Topology-based visualizations reveal and explicitly communicate
structures underlying data. Although we have a good understanding of what types
of features are captured by topological visualizations, our understanding of
people's perception of those features is not. This paper evaluates the
sensitivity of topology-based isocontour, Reeb graph, and persistence diagram
visualizations compared to a reference color map visualization for
synthetically generated scalar fields on 2-manifold triangular meshes embedded
in 3D. In particular, we built and ran a human-subject study that evaluated the
perception of data features characterized by Gaussian signals and measured how
effectively each visualization technique portrays variations of data features
arising from the position and amplitude variation of a mixture of Gaussians.
For positional feature variations, the results showed that only the Reeb graph
visualization had high sensitivity. For amplitude feature variations,
persistence diagrams and color maps demonstrated the highest sensitivity,
whereas isocontours showed only weak sensitivity. These results take an
important step toward understanding which topology-based tools are best for
various data and task scenarios and their effectiveness in conveying
topological variations as compared to conventional color mapping
Feature-Based Uncertainty Visualization
While uncertainty in scientific data attracts an increasing research interest in the visualization community, two critical issues remain insufficiently studied: (1) visualizing the impact of the uncertainty of a data set on its features and (2) interactively exploring 3D or large 2D data sets with uncertainties. In this study, a suite of feature-based techniques is developed to address these issues. First, a framework of feature-level uncertainty visualization is presented to study the uncertainty of the features in scalar and vector data. The uncertainty in the number and locations of features such as sinks or sources of vector fields are referred to as feature-level uncertainty while the uncertainty in the numerical values of the data is referred to as data-level uncertainty. The features of different ensemble members are indentified and correlated. The feature-level uncertainties are expressed as the transitions between corresponding features through new elliptical glyphs. Second, an interactive visualization tool for exploring scalar data with data-level and two types of feature-level uncertainties — contour-level and topology-level uncertainties — is developed. To avoid visual cluttering and occlusion, the uncertainty information is attached to a contour tree instead of being integrated with the visualization of the data. An efficient contour tree-based interface is designed to reduce users’ workload in viewing and analyzing complicated data with uncertainties and to facilitate a quick and accurate selection of prominent contours. This thesis advances the current uncertainty studies with an in-depth investigation of the feature-level uncertainties and an exploration of topology tools for effective and interactive uncertainty visualizations. With quantified representation and interactive capability, feature-based visualization helps people gain new insights into the uncertainties of their data, especially the uncertainties of extracted features which otherwise would remain unknown with the visualization of only data-level uncertainties
Comparative Uncertainty Visualization for High-Level Analysis of Scalar- and Vector-Valued Ensembles
With this thesis, I contribute to the research field of uncertainty visualization, considering parameter dependencies in multi valued fields and the uncertainty of automated data analysis. Like uncertainty visualization in general, both of these fields are becoming more and more important due to increasing computational power, growing importance and availability of complex models and collected data, and progress in artificial intelligence. I contribute in the following application areas:
Uncertain Topology of Scalar Field Ensembles.
The generalization of topology-based visualizations to multi valued data involves many challenges. An example is the comparative visualization of multiple contour trees, complicated by the random nature of prevalent contour tree layout algorithms. I present a novel approach for the comparative visualization of contour trees - the Fuzzy Contour Tree.
Uncertain Topological Features in Time-Dependent Scalar Fields.
Tracking features in time-dependent scalar fields is an active field of research, where most approaches rely on the comparison of consecutive time steps. I created a more holistic visualization for time-varying scalar field topology by adapting Fuzzy Contour Trees to the time-dependent setting.
Uncertain Trajectories in Vector Field Ensembles.
Visitation maps are an intuitive and well-known visualization of uncertain trajectories in vector field ensembles. For large ensembles, visitation maps are not applicable, or only with extensive time requirements. I developed Visitation Graphs, a new representation and data reduction method for vector field ensembles that can be calculated in situ and is an optimal basis for the efficient generation of visitation maps. This is accomplished by bringing forward calculation times to the pre-processing.
Visually Supported Anomaly Detection in Cyber Security.
Numerous cyber attacks and the increasing complexity of networks and their protection necessitate the application of automated data analysis in cyber security. Due to uncertainty in automated anomaly detection, the results need to be communicated to analysts to ensure appropriate reactions. I introduce a visualization system combining device readings and anomaly detection results: the Security in Process System. To further support analysts I developed an application agnostic framework that supports the integration of knowledge assistance and applied it to the Security in Process System. I present this Knowledge Rocks Framework, its application and the results of evaluations for both, the original and the knowledge assisted Security in Process System. For all presented systems, I provide implementation details, illustrations and applications
Contrasting Climate Ensembles: A Model-based Visualization Approach for Analyzing Extreme Events
AbstractThe use of increasingly sophisticated means to simulate and observe natural phenomena has led to the production of larger and more complex data. As the size and complexity of this data increases, the task of data analysis becomes more challeng- ing. Determining complex relationships among variables requires new algorithm development. Addressing the challenge of handling large data necessitates that algorithm implementations target high performance computing platforms. In this work we present a technique that allows a user to study the interactions among multiple variables in the same spatial extents as the underlying data. The technique is implemented in an existing parallel analysis and visualization framework in order that it be applicable to the largest datasets. The foundation of our approach is to classify data points via inclusion in, or distance to, multivariate representations of relationships among a subset of the variables of a dataset. We abstract the space in which inclusion is calculated and through various space transformations we alleviate the necessity to consider variables’ scales and distributions when making comparisons. We apply this approach to the problem of highlighting variations in climate model ensembles
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