Paul Rosen

Mathilde Papillon, Mustafa Hajij, Helen Jenne et al.

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.

Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou et al.

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.

Hyeon Jeon, Ghulam Jilani Quadri, Hyunwook Lee et al.

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.

Md Dilshadur Rahman, Ghulam Jilani Quadri, Bhavana Doppalapudi et al.

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}.

Md Dilshadur Rahman, Bhavana Doppalapudi, Ghulam Jilani Quadri et al.

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.

Md Dilshadur Rahman, Devin Lange, Ghulam Jilani Quadri et al.

Annotation is a central mechanism in visualization design that enables people to communicate key insights. Prior research has provided essential accounts of the visual forms annotations take, but less attention has been paid to the decisions behind them. This paper examines how annotations are designed in practice and how educators reflect on those practices. We conducted a two-phase qualitative study: interviews with ten practitioners from diverse backgrounds revealed the heuristics they draw on when creating annotations, and interviews with seven visualization educators offered complementary perspectives situated within broader concerns of clarity, guidance, and viewer agency. These studies provide a systematic account of annotation design knowledge in professional settings, highlighting the considerations, trade-offs, and contextual judgments that shape the use of annotations. By making this tacit expertise explicit, our work complements prior form-focused studies, strengthens understanding of annotation as a design activity, and points to opportunities for improved tool and guideline support.

Rifat Ara Proma, Paul Rosen

Simplifying line charts for responsive displays typically applies a single algorithm uniformly across devices, despite the availability of multiple techniques that preserve different signal characteristics (e.g., peaks, trends, periodicity). We investigate whether users benefit from algorithmic choice when adapting charts across screen sizes. In a within-subjects study (N=30), participants simplified nine datasets under three conditions: single pre-assigned technique (C1), multiple techniques (C2), and multiple techniques with manual point selection (C3), each with control over simplification level. We found that users adapted technique selections across datasets rather than devices, leveraging dataset-level strategies rather than per-device optimization. Additionally, interaction complexity did not always increase engagement uniformly, suggesting that responsive simplification tools should balance algorithmic flexibility with progressive disclosure and strong defaults. Supplemental materials are available at https://osf.io/yjp76/?view_only=b77b5e97f0cc4f689fbf48ad0d965af3.

Mustafa Hajij, Mathilde Papillon, Florian Frantzen et al.

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/.

Sudhanva Manjunath Athreya, Paul Rosen

Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of Latent Embeddings), a method for analyzing and interpreting deep neural networks through persistent homology. HOLE extracts topological features from neural activations and presents them using a suite of visualization techniques, including Sankey diagrams, heatmaps, dendrograms, and blob graphs. These tools facilitate the examination of representation structure and quality across layers. We evaluate HOLE on standard datasets using a range of discriminative models, focusing on representation quality, interpretability across layers, and robustness to input perturbations and model compression. The results indicate that topological analysis reveals patterns associated with class separation, feature disentanglement, and model robustness, providing a complementary perspective for understanding and improving deep learning systems.

Md Rahat-uz- Zaman, Bei Wang, Paul Rosen

Deep neural networks (DNNs) achieve state-of-the-art performance in many vision tasks, yet understanding their internal behavior remains challenging, particularly how different layers and activation channels contribute to class separability. We introduce ChannelExplorer, an interactive visual analytics tool for analyzing image-based outputs across model layers, emphasizing data-driven insights over architecture analysis for exploring class separability. ChannelExplorer summarizes activations across layers and visualizes them using three primary coordinated views: a Scatterplot View to reveal inter- and intra-class confusion, a Jaccard Similarity View to quantify activation overlap, and a Heatmap View to inspect activation channel patterns. Our technique supports diverse model architectures, including CNNs, GANs, ResNet and Stable Diffusion models. We demonstrate the capabilities of ChannelExplorer through four use-case scenarios: (1) generating class hierarchy in ImageNet, (2) finding mislabeled images, (3) identifying activation channel contributions, and(4) locating latent states' position in Stable Diffusion model. Finally, we evaluate the tool with expert users.

Zachariah Beasley, Alon Friedman, Paul Rosen

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.

Zachariah J. Beasley, Les A. Piegl, Paul Rosen

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.

Rifat Ara Proma, Matthew Sumpter, Humberto Lugo et al.

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.

Hamza Elhamdadi, Shaun Canavan, Paul Rosen

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.

Ghulam Jilani Quadri, Paul Rosen

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.

Alon Friedman, Paul Rosen

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.

Paul Rosen, Ghulam Jilani Quadri

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.

Ghulam Jilani Quadri, Paul Rosen

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.

Mustafa Hajij, Elizabeth Munch, Paul Rosen

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 $O(|E|α(|V|))$, where $α$ 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.

Zachariah Beasley, Alon Friedman, Les Piegl et al.

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.

Junyi Tu, Paul Rosen

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.

Ghulam Jilani Quadri, Paul Rosen

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.

Paul Rosen, Ashley Suh, Christopher Salgado et al.

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.

Yunhao Zhang, Haowen Liu, Paul Rosen et al.

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.

Mustafa Hajij, Paul Rosen

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.

Paul Rosen, Mustafa Hajij, Bei Wang

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.

Mustafa Hajij, Basem Assiri, Paul Rosen

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.

Alejandro Robles, Mustafa Hajij, Paul Rosen

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.

Paul Rosen, Anil Seth, Betsy Mills et al.

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.

Jonathan Beezley, Mavin Martin, Paul Rosen et al.

We introduce several useful utilities in development for the creation and analysis of real wildland fire simulations using WRF and SFIRE. These utilities exist as standalone programs and scripts as well as extensions to other well known software. Python web scrapers automate the process of downloading and preprocessing atmospheric and surface data from common sources. Other scripts simplify the domain setup by creating parameter files automatically. Integration with Google Earth allows users to explore the simulation in a 3D environment along with real surface imagery. Postprocessing scripts provide the user with a number of output data formats compatible with many commonly used visualization suites allowing for the creation of high quality 3D renderings. As a whole, these improvements build toward a unified web application that brings a sophisticated wildland fire modeling environment to scientists and users alike.