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We present a comprehensive survey on the use of annotations in information visualizations, highlighting their crucial role in improving audience understanding and engagement with visual data. Our investigation encompasses empirical studies on annotations, showcasing their impact on user engagement, interaction, comprehension, and memorability across various contexts. We also study the existing tools and techniques for creating annotations and their diverse applications, enhancing the understanding of both practical and theoretical aspects of annotations in data visualization. Additionally, we identify existing research gaps and propose potential future research directions, making our survey a valuable resource for researchers, visualization designers, and practitioners by providing a thorough understanding of the application of annotations in visualization.

The accuracy of recommender systems influences their trust and decision-making when using them. Providing additional information, such as visualizations, offers context that would otherwise be lacking. However, the role of visualizations in influencing trust and decisions with recommender systems is under-explored. To bridge this gap, we conducted a two-part human-subject experiment to investigate the impact of scatterplots on recommender system decisions. Our first study focuses on high-level decisions, such as selecting which recommender system to use. The second study focuses on low-level decisions, such as agreeing or disagreeing with a specific recommendation. Our results show scatterplots accompanied by higher levels of accuracy influence decisions and that participants tended to trust the recommendations more when scatterplots were accompanied by descriptive accuracy (e.g., \textit{high}, \textit{medium}, or \textit{low}) instead of numeric accuracy (e.g., \textit{90\%}). Furthermore, we observed scatterplots often assisted participants in validating their decisions. Based on the results, we believe that scatterplots and visualizations, in general, can aid in making informed decisions, validating decisions, and building trust in recommendation systems.

Version control systems are integral to software development, with GitHub emerging as a popular online platform due to its comprehensive project management tools, including issue tracking and pull requests. However, GitHub lacks a direct link between issues and commits, making it difficult for developers to understand how specific issues are resolved. Although GitHub's Insights page provides some visualization for repository data, the representation of issues and commits related data in a textual format hampers quick evaluation of issue management. This paper presents a prototype web application that generates visualizations to offer insights into issue timelines and reveals different factors related to issues. It focuses on the lifecycle of issues and depicts vital information to enhance users' understanding of development patterns in their projects. We demonstrate the effectiveness of our approach through case studies involving three open-source GitHub repositories. Furthermore, we conducted a user evaluation to validate the efficacy of our prototype in conveying crucial repository information more efficiently and rapidly.

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. In this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets., Comment: 9 pages paper + 2 page references, 8 figures, IEEE VIS 2024 paper to be published as a special issue of IEEE Transactions on Visualization and Computer Graphics (TVCG)

Peer review is a popular feedback mechanism in higher education that actively engages students and provides researchers with a means to assess student engagement. However, there is little empirical support for the durability of peer review, particularly when using data predictive modeling to analyze student comments. This study uses Na\"ive Bayes modeling to analyze peer review data obtained from an undergraduate visual literacy course over five years. We expand on the research of Friedman and Rosen and Beasley et al. by focusing on the Na\"ive Bayes model of students' remarks. Our findings highlight the utility of Na\"ive Bayes modeling, particularly in the analysis of student comments based on parts of speech, where nouns emerged as the prominent category. Additionally, when examining students' comments using the visual peer review rubric, the lie factor emerged as the predominant factor. Comparing Na\"ive Bayes model to Beasley's approach, we found both help instructors map directions taken in the class, but the Na\"ive Bayes model provides a more specific outline for forecasting with a more detailed framework for identifying core topics within the course, enhancing the forecasting of educational directions. Through the application of the Holdout Method and $\mathrm{k}$-fold cross-validation with continuity correction, we have validated the model's predictive accuracy, underscoring its effectiveness in offering deep insights into peer review mechanisms. Our study findings suggest that using predictive modeling to assess student comments can provide a new way to better serve the students' classroom comments on their visual peer work. This can benefit courses by inspiring changes to course content, reinforcement of course content, modification of projects, or modifications to the rubric itself., Comment: 8 pages, 6 figures, IEEE EDUCON 2024 conference

Designers often create visualizations to achieve specific high-level analytical or communication goals. These goals require people to naturally extract complex, contextualized, and interconnected patterns in data. While limited prior work has studied general high-level interpretation, prevailing perceptual studies of visualization effectiveness primarily focus on isolated, predefined, low-level tasks, such as estimating statistical quantities. This study more holistically explores visualization interpretation to examine the alignment between designers' communicative goals and what their audience sees in a visualization, which we refer to as their comprehension. We found that statistics people effectively estimate from visualizations in classical graphical perception studies may differ from the patterns people intuitively comprehend in a visualization. We conducted a qualitative study on three types of visualizations -- line graphs, bar graphs, and scatterplots -- to investigate the high-level patterns people naturally draw from a visualization. Participants described a series of graphs using natural language and think-aloud protocols. We found that comprehension varies with a range of factors, including graph complexity and data distribution. Specifically, 1) a visualization's stated objective often does not align with people's comprehension, 2) results from traditional experiments may not predict the knowledge people build with a graph, and 3) chart type alone is insufficient to predict the information people extract from a graph. Our study confirms the importance of defining visualization effectiveness from multiple perspectives to assess and inform visualization practices., Comment: Accepted for publication in ACM CHI 2024

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelX is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/}{https://pyt-team.github.io/.

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

Visual clustering is a common perceptual task in scatterplots that supports diverse analytics tasks (e.g., cluster identification). However, even with the same scatterplot, the ways of perceiving clusters (i.e., conducting visual clustering) can differ due to the differences among individuals and ambiguous cluster boundaries. Although such perceptual variability casts doubt on the reliability of data analysis based on visual clustering, we lack a systematic way to efficiently assess this variability. In this research, we study perceptual variability in conducting visual clustering, which we call Cluster Ambiguity. To this end, we introduce CLAMS, a data-driven visual quality measure for automatically predicting cluster ambiguity in monochrome scatterplots. We first conduct a qualitative study to identify key factors that affect the visual separation of clusters (e.g., proximity or size difference between clusters). Based on study findings, we deploy a regression module that estimates the human-judged separability of two clusters. Then, CLAMS predicts cluster ambiguity by analyzing the aggregated results of all pairwise separability between clusters that are generated by the module. CLAMS outperforms widely-used clustering techniques in predicting ground truth cluster ambiguity. Meanwhile, CLAMS exhibits performance on par with human annotators. We conclude our work by presenting two applications for optimizing and benchmarking data mining techniques using CLAMS. The interactive demo of CLAMS is available at clusterambiguity.dev., Comment: IEEE Transactions on Visualization and Computer Graphics (TVCG) (Proc. IEEE VIS 2023); equally contributed by Hyeon Jeon and Ghulam Jilani Quadri

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.

Annotations play a vital role in highlighting critical aspects of visualizations, aiding in data externalization and exploration, collaborative sensemaking, and visual storytelling. However, despite their widespread use, we identified a lack of a design space for common practices for annotations. In this paper, we evaluated over 1,800 static annotated charts to understand how people annotate visualizations in practice. Through qualitative coding of these diverse real-world annotated charts, we explored three primary aspects of annotation usage patterns: analytic purposes for chart annotations (e.g., present, identify, summarize, or compare data features), mechanisms for chart annotations (e.g., types and combinations of annotations used, frequency of different annotation types across chart types, etc.), and the data source used to generate the annotations. We then synthesized our findings into a design space of annotations, highlighting key design choices for chart annotations. We presented three case studies illustrating our design space as a practical framework for chart annotations to enhance the communication of visualization insights. All supplemental materials are available at {https://shorturl.at/bAGM1}.

Force-directed layouts belong to a popular class of methods used to position nodes in a node-link diagram. However, they typically lack direct consideration of global structures, which can result in visual clutter and the overlap of unrelated structures. In this paper, we use the principles of persistent homology to untangle force-directed layouts thus mitigating these issues. First, we devise a new method to use 0-dimensional persistent homology to efficiently generate an initial graph layout. The approach results in faster convergence and better quality graph layouts. Second, we provide a new definition and an efficient algorithm for 1-dimensional persistent homology features (i.e., tunnels/cycles) on graphs. We provide users the ability to interact with the 1-dimensional features by highlighting them and adding cycle-emphasizing forces to the layout. Finally, we evaluate our approach with 32 synthetic and real-world graphs by computing various metrics, e.g., co-ranking, edge crossing, etc., to demonstrate the efficacy of our proposed method.

Scatterplots are among the most widely used visualization techniques. Compelling scatterplot visualizations improve understanding of data by leveraging visual perception to boost awareness when performing specific visual analytic tasks. Design choices in scatterplots, such as graphical encodings or data aspects, can directly impact decision-making quality for low-level tasks like clustering. Hence, constructing frameworks that consider both the perceptions of the visual encodings and the task being performed enables optimizing visualizations to maximize efficacy. In this paper, we propose an automatic tool to optimize the design factors of scatterplots to reveal the most salient cluster structure. Our approach leverages the merge tree data structure to identify the clusters and optimize the choice of subsampling algorithm, sampling rate, marker size, and marker opacity used to generate a scatterplot image. We validate our approach with user and case studies that show it efficiently provides high-quality scatterplot designs from a large parameter space.

Every year we grow more dependent on wearable devices to gather personalized data, such as our movements, heart rate, respiration, etc. To capture this data, devices contain sensors, such as accelerometers and gyroscopes, that are able to measure changes in their surroundings and pass along the information for better informed decisions. Although these sensors should behave similarly in different devices, that is not always the case. In this case study, we analyze accelerometers from three different devices recording the same actions with an aim to determine whether the discrepancies are due to variability within or between devices. We found the most significant variation between devices with different specifications, such as sensitivity and sampling frequency. Nevertheless, variance in the data should be assumed, even if data is gathered from the same person, activity, and type of sensor.

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains. Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, we develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. We characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs in detail. Third, we evaluate the performance of CCNNs on tasks related to mesh shape analysis and graph learning. Our experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. Our findings demonstrate the advantages of incorporating higher-order relations into deep learning models in different applications.

Peer review is a widely utilized feedback mechanism for engaging students. As a pedagogical method, it has been shown to improve educational outcomes, but we have found limited empirical measurement of peer review in visualization courses. In addition to increasing engagement, peer review provides diverse feedback and reinforces recently-learned course concepts through critical evaluation of others' work. We discuss the construction and application of peer review in two visualization courses from different colleges at the University of South Florida. We then analyze student projects and peer review text via sentiment analysis to infer insights for visualization educators, including the focus of course content, engagement across student groups, student mastery of concepts, course trends over time, and expert intervention effectiveness. Finally, we provide suggestions for adapting peer review to other visualization courses to engage students and increase instructor understanding of the peer review process.

Accurately grading open-ended assignments in large or massive open online courses (MOOCs) is non-trivial. Peer review is a promising solution but can be unreliable due to few reviewers and an unevaluated review form. To date, no work has 1) leveraged sentiment analysis in the peer-review process to inform or validate grades or 2) utilized aspect extraction to craft a review form from what students actually communicated. Our work utilizes, rather than discards, student data from review form comments to deliver better information to the instructor. In this work, we detail the process by which we create our domain-dependent lexicon and aspect-informed review form as well as our entire sentiment analysis algorithm which provides a fine-grained sentiment score from text alone. We end by analyzing validity and discussing conclusions from our corpus of over 6800 peer reviews from nine courses to understand the viability of sentiment in the classroom for increasing the information from and reliability of grading open-ended assignments in large courses.

As cities continue to grow globally, air pollution is increasing at an alarming rate, causing a significant negative impact on public health. One way to affect the negative impact is to regulate the producers of such pollution through policy implementation and enforcement. CleanAirNowKC (CAN-KC) is an environmental justice organization based in Kansas City (KC), Kansas. As part of their organizational objectives, they have to date deployed nine PurpleAir air quality sensors in different locations about which the community has expressed concern. In this paper, we have implemented an interactive map that can help the community members to monitor air quality efficiently. The system also allows for reporting and tracking industrial emissions or toxic releases, which will further help identify major contributors to pollution. These resources can serve an important role as evidence that will assist in advocating for community-driven just policies to improve the air quality regulation in Kansas City.

We present an approach utilizing Topological Data Analysis to study the structure of face poses used in affective computing, i.e., the process of recognizing human emotion. The approach uses a conditional comparison of different emotions, both respective and irrespective of time, with multiple topological distance metrics, dimension reduction techniques, and face subsections (e.g., eyes, nose, mouth, etc.). The results confirm that our topology-based approach captures known patterns, distinctions between emotions, and distinctions between individuals, which is an important step towards more robust and explainable emotion recognition by machines.

Knowledge of human perception has long been incorporated into visualizations to enhance their quality and effectiveness. The last decade, in particular, has shown an increase in perception-based visualization research studies. With all of this recent progress, the visualization community lacks a comprehensive guide to contextualize their results. In this report, we provide a systematic and comprehensive review of research studies on perception related to visualization. This survey reviews perception-focused visualization studies since 1980 and summarizes their research developments focusing on low-level tasks, further breaking techniques down by visual encoding and visualization type. In particular, we focus on how perception is used to evaluate the effectiveness of visualizations, to help readers understand and apply the principles of perception of their visualization designs through a task-optimized approach. We concluded our report with a summary of the weaknesses and open research questions in the area.

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.

We present a comprehensive framework for evaluating line chart smoothing methods under a variety of visual analytics tasks. Line charts are commonly used to visualize a series of data samples. When the number of samples is large, or the data are noisy, smoothing can be applied to make the signal more apparent. However, there are a wide variety of smoothing techniques available, and the effectiveness of each depends upon both nature of the data and the visual analytics task at hand. To date, the visualization community lacks a summary work for analyzing and classifying the various smoothing methods available. In this paper, we establish a framework, based on 8 measures of the line smoothing effectiveness tied to 8 low-level visual analytics tasks. We then analyze 12 methods coming from 4 commonly used classes of line chart smoothing---rank filters, convolutional filters, frequency domain filters, and subsampling. The results show that while no method is ideal for all situations, certain methods, such as Gaussian filters and Topology-based subsampling, perform well in general. Other methods, such as low-pass cutoff filters and Douglas-Peucker subsampling, perform well for specific visual analytics tasks. Almost as importantly, our framework demonstrates that several methods, including the commonly used uniform subsampling, produce low-quality results, and should, therefore, be avoided, if possible.

Scatterplots are used for a variety of visual analytics tasks, including cluster identification, and the visual encodings used on a scatterplot play a deciding role on the level of visual separation of clusters. For visualization designers, optimizing the visual encodings is crucial to maximizing the clarity of data. This requires accurately modeling human perception of cluster separation, which remains challenging. We present a multi-stage user study focusing on four factors---distribution size of clusters, number of points, size of points, and opacity of points---that influence cluster identification in scatterplots. From these parameters, we have constructed two models, a distance-based model, and a density-based model, using the merge tree data structure from Topological Data Analysis. Our analysis demonstrates that these factors play an important role in the number of clusters perceived, and it verifies that the distance-based and density-based models can reasonably estimate the number of clusters a user observes. Finally, we demonstrate how these models can be used to optimize visual encodings on real-world data.

The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph. In this article, we use the PageRank function along with persistent homology to obtain a scalable graph descriptor and utilize it to compare the similarities between graphs. For a given graph $G(V,E)$, our descriptor can be computed in $O(|E|\alpha(|V|))$, where $\alpha$ is the inverse Ackermann function which makes it scalable and computable on massive graphs. We show the effectiveness of our method by utilizing it on multiple shape mesh datasets.

Peer review is a widely utilized pedagogical feedback mechanism for engaging students, which has been shown to improve educational outcomes. However, we find limited discussion and empirical measurement of peer review in visualization coursework. In addition to engagement, peer review provides direct and diverse feedback and reinforces recently-learned course concepts through critical evaluation of others' work. In this paper, we discuss the construction and application of peer review in a computer science visualization course, including: projects that reuse code and visualizations in a feedback-guided, continual improvement process and a peer review rubric to reinforce key course concepts. To measure the effectiveness of the approach, we evaluate student projects, peer review text, and a post-course questionnaire from 3 semesters of mixed undergraduate and graduate courses. The results indicate that course concepts are reinforced with peer review---82% reported learning more because of peer review, and 75% of students recommended continuing it. Finally, we provide a road-map for adapting peer review to other visualization courses to produce more highly engaged students.

Enhancement is an important step in post-processing digital images for personal use, in medical imaging, and for object recognition. Most existing manual techniques rely on region selection, similarity, and/or thresholding for editing, never really considering the topological structure of the image. In this paper, we leverage the contour tree to extract a hierarchical representation of the topology of an image. We propose 4 topology-aware transfer functions for editing features of the image using local topological properties, instead of global image properties. Finally, we evaluate our approach with grayscale and color images.

With the popularization of Topological Data Analysis, the Reeb graph has found new applications as a summarization technique in the analysis and visualization of large and complex data, whose usefulness extends beyond just the graph itself. Pairing critical points enables forming topological fingerprints, known as persistence diagrams, that provides insights into the structure and noise in data. Although the body of work addressing the efficient calculation of Reeb graphs is large, the literature on pairing is limited. In this paper, we discuss two algorithmic approaches for pairing critical points in Reeb graphs, first a multipass approach, followed by a new single-pass algorithm, called Propagate and Pair.

Reproducibility has been increasingly encouraged by communities of science in order to validate experimental conclusions, and replication studies represent a significant opportunity to vision scientists wishing contribute new perceptual models, methods, or insights to the visualization community. Unfortunately, the notion of replication of previous studies does not lend itself to how we communicate research findings. Simple put, studies that re-conduct and confirm earlier results do not hold any novelty, a key element to the modern research publication system. Nevertheless, savvy researchers have discovered ways to produce replication studies by embedding them into other sufficiently novel studies. In this position paper, we define three methods -- re-evaluation, expansion, and specialization -- for embedding a replication study into a novel published work. Within this context, we provide a non-exhaustive case study on replications of Cleveland and McGill's seminal work on graphical perception. As it turns out, numerous replication studies have been carried out based on that work, which have both confirmed prior findings and shined new light on our understanding of human perception. Finally, we discuss how publishing a true replication study should be avoided, while providing suggestions for how vision scientists and others can still use replication studies as a vehicle to producing visualization research publications.

Line charts are commonly used to visualize a series of data values. When the data are noisy, smoothing is applied to make the signal more apparent. Conventional methods used to smooth line charts, e.g., using subsampling or filters, such as median, Gaussian, or low-pass, each optimize for different properties of the data. The properties generally do not include retaining peaks (i.e., local minima and maxima) in the data, which is an important feature for certain visual analytics tasks. We present TopoLines, a method for smoothing line charts using techniques from Topological Data Analysis. The design goal of TopoLines is to maintain prominent peaks in the data while minimizing any residual error. We evaluate TopoLines for 2 visual analytics tasks by comparing to 5 popular line smoothing methods with data from 4 application domains.

We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst triangulated 2-manifolds. Our method relies on studying the lower-star filtration induced by the eigenfunctions of the Laplacian. This gives us a shape descriptor that inherits the rich information encoded in the eigenfunctions of the Laplacian. Moreover, the similarity between these descriptors can be easily computed using tools that are readily available in Topological Data Analysis. We provide experiments to illustrate the effectiveness of the proposed method.

The Reeb graph of a scalar function defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer graphics, and computational topology. The demand for analyzing large data sets has increased in the last decade. Hence the parallelization of topological computations needs to be more fully considered. We propose a parallel augmented Reeb graph algorithm on triangulated meshes with and without a boundary. That is, in addition to our parallel algorithm for computing a Reeb graph, we describe a method for extracting the original manifold data from the Reeb graph structure. We demonstrate the running time of our algorithm on standard datasets. As an application, we show how our algorithm can be utilized in mesh segmentation algorithms., Comment: 30 pages, 25 figures

Assessing the quality of 3D printed models before they are printed remains a challeng- ing problem, particularly when considering point cloud-based models. This paper introduces an approach to quality assessment, which uses techniques from the field of Topological Data Analy- sis (TDA) to compute a topological abstraction of the eventual printed model. Two main tools of TDA, Mapper and persistent homology, are used to analyze both the printed space and empty space created by the model. This abstraction enables investigating certain qualities of the model, with respect to print quality, and identifies potential anomalies that may appear in the final product.

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 generalized 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.

Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints. However, node-link diagrams may fail to convey insights regarding graph structures, even for moderately sized data of a few hundred nodes, due to visual clutter. We propose to apply the mapper construction -- a popular tool in topological data analysis -- to graph visualization, which provides a strong theoretical basis for summarizing the data while preserving their core structures. We develop a variation of the mapper construction targeting weighted, undirected graphs, called {\mog}, which generates homology-preserving skeletons of graphs. We further show how the adjustment of a single parameter enables multi-scale skeletonization of the input graph. We provide a software tool that enables interactive explorations of such skeletons and demonstrate the effectiveness of our method for synthetic and real-world data.

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets.

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint trees. In this paper, we study the parallel analysis of the construction of Mapper. We give a provably correct parallel algorithm to execute Mapper on multiple processors and discuss the performance results that compare our approach to a reference sequential Mapper implementation. We report the performance experiments that demonstrate the efficiency of our method.

We study the topological construction called Mapper in the context of simply connected domains, in particular on images. The Mapper construction can be considered as a generalization for contour, split, and joint trees on simply connected domains. A contour tree on an image domain assumes the height function to be a piecewise linear Morse function. This is a rather restrictive class of functions and does not allow us to explore the topology for most real world images. The Mapper construction avoids this limitation by assuming only continuity on the height function allowing this construction to robustly deal with a significant larger set of images. We provide a customized construction for Mapper on images, give a fast algorithm to compute it, and show how to simplify the Mapper structure in this case. Finally, we provide a simple procedure that guarantees the equivalence of Mapper to contour, join, and split trees on a simply connected domain.

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into metric spaces, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data. To validate our approach, we conduct several case studies on real world data sets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs. We also examine whether persistence-based similarity measure as a graph metric satisfies a set of well-established, desirable properties for graph metrics.

The current generation of radio and millimeter telescopes, particularly the Atacama Large Millimeter Array (ALMA), offers enormous advances in observing capabilities. While these advances represent an unprecedented opportunity to facilitate scientific understanding, the increased complexity in the spatial and spectral structure of these ALMA data cubes lead to challenges in their interpretation. In this paper, we perform a feasibility study for applying topological data analysis and visualization techniques never before tested by the ALMA community. Through techniques based on contour trees, we seek to improve upon existing analysis and visualization workflows of ALMA data cubes, in terms of accuracy and speed in feature extraction. We review our application development process in building effective analysis and visualization capabilities for the astrophysicists. We also summarize effective design practices by identifying domain-specific needs of simplicity, integrability, and reproducibility, in order to best target and service the large astrophysics community.