Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality reduction: distance preservation and topology preservation. Inspired by recent work in topological data analysis, we are on the quest for a dimensionality reduction technique that achieves the criterion of homology preservation, a specific version of topology preservation. Specifically, we are interested in using topology-inspired manifold landmarking and manifold tearing to aid such a process and evaluate their effectiveness.
Homology-Preserving Dimensionality Reduction via Manifold Landmarking and Tearing
L Yan, Y Zhao, P Rosen, C Scheidegger, B Wang
Visualization in Data Science (VDS at IEEE VIS 2018)
Parallel coordinates plots (PCPs) are a well-studied technique for exploring multi-attribute datasets. In many situations, users find them a flexible method to analyze and interact with data. Unfortunately, using PCPs becomes challenging as the number of data items grows large or multiple trends within the data mix in the visualization. The resulting overdraw can obscure important features. A number of modifications to PCPs have been proposed, including using color, opacity, smooth curves, frequency, density, and animation to mitigate this problem. However, these modified PCPs tend to have their own limitations in the kinds of relationships they emphasize. We propose a new data scalable design for representing and exploring data relationships in PCPs. The approach exploits the point/line duality property of PCPs and a local linear assumption of data to extract and represent relationship summarizations. This approach simultaneously shows relationships in the data and the consistency of those relationships. Our approach supports various visualization tasks, including mixed linear and nonlinear pattern identification, noise detection, and outlier detection, all in large data. We demonstrate these tasks on multiple synthetic and real-world datasets.
DSPCP: A data scalable approach for identifying relationships in parallel coordinates
H Nguyen, P Rosen
IEEE transactions on visualization and computer graphics 24 (3), 1301-1315
In visualization education, both science and humanities , the literature is often divided into two parts: the design aspect and the analysis of the visualization. However, we find limited discussion on how to motivate and engage visualization students in the classroom. In the field of Writing Studies, researchers develop tools and frameworks for student peer review of writing. Based on the literature review from the field of Writing Studies, this paper proposes a new framework to implement visualization peer review in the classroom to engage today’s students. This framework can be customized for incremental and double-blind review to inspire students and reinforce critical thinking about visualization.
Leveraging Peer Review in Visualization Education: A Proposal for a New Model
A. Friedman, P. Rosen
IEEE 2017 Pedagogy of Data Visualization Workshop
Correlation is a powerful measure of relationships assisting in estimating trends and making forecasts. Its use is widespread, being a critical data analysis component of fields including science, engineering, and business. Unfortunately, visualization methods used to identify and estimate correlation are designed to be general, supporting many visualization tasks. Due in large part to their generality, they do not provide the most efficient interface, in terms of speed and accuracy for correlation identifying. To address this shortcoming, we first propose a new correlation task-specific visual design called Correlation Coordinate Plots (CCPs). CCPs transform data into a powerful coordinate system for estimating the direction and strength of correlation. To extend the functionality of this approach to multiple attribute datasets, we propose two approaches. The first design is the Snowflake Visualization, a focus+context layout for exploring all pairwise correlations. The second design enhances the CCP by using principal component analysis to project multiple attributes. We validate CCP by applying it to real-world data sets and test its performance in correlation-specific tasks through an extensive user study that showed improvement in both accuracy and speed of correlation identification.
Correlation Coordinate Plots: Efficient Layouts for Correlation Tasks
H Nguyen, P Rosen
International Joint Conference on Computer Vision, Imaging and Computer Graphics
The topological notion of robustness introduces mathematically rigorous approaches to interpret vector field data. Robustness quantifies the structural stability of critical points with respect to perturbations and has been shown to be useful for increasing the visual interpretability of vector fields. However, critical points, which are essential components of vector field topology, are defined with respect to a chosen frame of reference. The classical definition of robustness, therefore, depends also on the chosen frame of reference. We define a new Galilean invariant robustness framework that enables the simultaneous visualization of robust critical points across the dominating reference frames in different regions of the data. We also demonstrate a strong connection between such a robustness-based framework with the one recently proposed by Bujack et al., which is based on the determinant of the Jacobian. Our results include notable observations regarding the definition of stable features within the vector field data.
Interpreting Galilean Invariant Vector Field Analysis via Extended Robustness
B Wang, R Bujack, P Rosen, P Skraba, H Bhatia, H Hagen
Topology-based Methods in Visualization (TopoInVis)
We present a new approach for accessing and visualizing point-based data in CAD applications. Instead of developing a traditional database around spatial data structures, our approach augments a data indexing engine to enable quick access to data. The primary advantage of an indexing engine is flexibility. The approach enables both range queries for accessing data spatially and resolution queries to access data at appropriate spatial resolutions. Our approach is robust to very large datasets, naturally supporting remote visualization and near-real-time input data streams. We demonstrate our approach on 2 large datasets, one 45M points, the other 53M points.
Using data indexing for remote visualization of point cloud data
P Rosen, LA Piegl
Computer-Aided Design and Applications 14 (6), 789-795
Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. We apply our method to synthetic and simulation datasets to demonstrate its effectiveness.
Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion
P Skraba, P Rosen, B Wang, G Chen, H Bhatia, V Pascucci
Transactions on Visualization and Computer Graphics
Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.
Robustness-based simplification of 2d steady and unsteady vector fields
P Skraba, B Wang, G Chen, P Rosen
IEEE transactions on visualization and computer graphics 21 (8), 930-944