Dealing with Multiple Requirements in Geometric Arrangements

UnDRground Tubes: Exploring Spatial Data with Multidimensional Projections and Set Visualization

In various scientific and industrial domains, analyzing multivariate spatial data, i.e., vectors associated with spatial locations, is common practice. To analyze those datasets, analysts may turn to methods such as Spatial Blind Source Separation (SBSS). Designed explicitly for spatial data analysis, SBSS finds latent components in the dataset and is superior to popular non-spatial methods, like PCA. However, when analysts try different tuning parameter settings, the amount of latent components complicates analytical tasks. Based on our years-long collaboration with SBSS researchers, we propose a visualization approach to tackle this challenge. The main component is UnDRground Tubes (UT), a general-purpose idiom combining ideas from set visualization and multidimensional projections. We describe the UT visualization pipeline and integrate UT into an interactive multiple-view system. We demonstrate its effectiveness through interviews with SBSS experts, a qualitative evaluation with visualization experts, and computational experiments. SBSS experts were excited about our approach. They saw many benefits for their work and potential applications for geostatistical data analysis more generally. UT was also well received by visualization experts. Our benchmarks show that UT projections and its heuristics are appropriate.

Mesoscopic structure graphs for interpreting uncertainty in non-linear embeddings

Probabilistic-based non-linear dimensionality reduction (PB-NL-DR) methods, such as t-SNE and UMAP, are effective in unfolding complex high-dimensional manifolds, allowing users to explore and understand the structural patterns of data. However, due to the trade-off between global and local structure preservation and the randomness during computation, these methods may introduce false neighborhood relationships, known as distortion errors and misleading visualizations. To address this issue, we first conduct a detailed survey to illustrate the design space of prior layout enrichment visualizations for interpreting DR results, and then propose a node-link visualization technique, ManiGraph. This technique rethinks the neighborhood fidelity between the high- and low-dimensional spaces by constructing dynamic mesoscopic structure graphs and measuring region-adapted trustworthiness. ManiGraph also addresses the overplotting issue in scatterplot visualization for large-scale datasets and supports examining in unsupervised scenarios. We demonstrate the effectiveness of ManiGraph in different analytical cases, including generic machine learning using 3D toy data illustrations and fashion-MNIST, a computational biology study using a single-cell RNA sequencing dataset, and a deep learning-enabled colorectal cancer study with histopathology-MNIST.

Visual Exploration of Relationships and Structure in Low-Dimensional Embeddings

In this work, we propose an interactive visual approach for the exploration and formation of structural relationships in embeddings of high-dimensional data. These structural relationships, such as item sequences, associations of items with groups, and hierarchies between groups of items, are defining properties of many real-world datasets. Nevertheless, most existing methods for the visual exploration of embeddings treat these structures as second-class citizens or do not take them into account at all. In our proposed analysis workflow, users explore enriched scatterplots of the embedding, in which relationships between items and/or groups are visually highlighted. The original high-dimensional data for single items, groups of items, or differences between connected items and groups are accessible through additional summary visualizations. We carefully tailored these summary and difference visualizations to the various data types and semantic contexts. During their exploratory analysis, users can externalize their insights by setting up additional groups and relationships between items and/or groups. We demonstrate the utility and potential impact of our approach by means of two use cases and multiple examples from various domains.

CriPAV: Street-Level Crime Patterns Analysis and Visualization

Extracting and analyzing crime patterns in big cities is a challenging spatiotemporal problem. The hardness of the problem is linked to two main factors, the sparse nature of the crime activity and its spread in large spatial areas. Sparseness hampers most time series (crime time series) comparison methods from working properly, while the handling of large urban areas tends to render the computational costs of such methods impractical. Visualizing different patterns hidden in crime time series data is another issue in this context, mainly due to the number of patterns that can show up in the time series analysis. In this article, we present a new methodology to deal with the issues above, enabling the analysis of spatiotemporal crime patterns in a street-level of detail. Our approach is made up of two main components designed to handle the spatial sparsity and spreading of crimes in large areas of the city. The first component relies on a stochastic mechanism from which one can visually analyze probable×intensive crime hotspots. Such analysis reveals important patterns that can not be observed in the typical intensity-based hotspot visualization. The second component builds upon a deep learning mechanism to embed crime time series in Cartesian space. From the embedding, one can identify spatial locations where the crime time series have similar behavior. The two components have been integrated into a web-based analytical tool called CriPAV (Crime Pattern Analysis and Visualization), which enables global as well as a street-level view of crime patterns. Developed in close collaboration with domain experts, CriPAV has been validated through a set of case studies with real crime data in São Paulo - Brazil. The provided experiments and case studies reveal the effectiveness of CriPAV in identifying patterns such as locations where crimes are not intense but highly probable to occur as well as locations that are far apart from each other but bear similar crime patterns.

Gaze-driven placement of items for proactive visual exploration

Recent advances in digital signage technology have improved the ability to visually select specific items within a group. Although this is due to the ability to dynamically update the display of items, the corresponding layout schemes remain a subject of research. This paper explores the sophisticated layout of items by respecting the underlying context of searching for favorite items. Our study begins by formulating the static placement of items as an optimization problem that incorporates aesthetic layout criteria as constraints. This is further extended to accommodate the dynamic placement of items for more proactive visual exploration based on the ongoing search context. Our animated layout is driven by analyzing the distribution of eye gaze through an eye-tracking device, by which we infer how the most attractive items lead to the finally wanted ones. We create a planar layout of items as a context map to establish association rules to dynamically replace existing items with new ones. For this purpose, we extract the set of important topics from a set of annotated texts associated with the items using matrix factorization. We also conduct user studies to evaluate the validity of the design criteria incorporated into both static and dynamic placement of items. After discussing the pros and cons of the proposed approach and possible themes for future research, we conclude this paper.

Content-Based Visual Summarization for Image Collections

With the surge of images in the information era, people demand an effective and accurate way to access meaningful visual information. Accordingly, effective and accurate communication of information has become indispensable. In this article, we propose a content-based approach that automatically generates a clear and informative visual summarization based on design principles and cognitive psychology to represent image collections. We first introduce a novel method to make representative and nonredundant summarizations of image collections, thereby ensuring data cleanliness and emphasizing important information. Then, we propose a tree-based algorithm with a two-step optimization strategy to generate the final layout that operates as follows: (1) an initial layout is created by constructing a tree randomly based on the grouping results of the input image set; (2) the layout is refined through a coarse adjustment in a greedy manner, followed by gradient back propagation drawing on the training procedure of neural networks. We demonstrate the usefulness and effectiveness of our method via extensive experimental results and user studies. Our visual summarization algorithm can precisely and efficiently capture the main content of image collections better than alternative methods or commercial tools.

TopoMap: A 0-dimensional Homology Preserving Projection of High-Dimensional Data

Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to preserve some dissimilarity (similarity) measure, such as the Euclidean distance for example. In fact, although adopting distinct mathematical formulations designed to favor different aspects of the data, most multidimensional projection methods strive to preserve dissimilarity measures that encapsulate geometric properties such as distances or the proximity relation between data objects. However, geometric relations are not the only interesting property to be preserved in a projection. For instance, the analysis of particular structures such as clusters and outliers could be more reliably performed if the mapping process gives some guarantee as to topological invariants such as connected components and loops. This paper introduces TopoMap, a novel projection technique which provides topological guarantees during the mapping process. In particular, the proposed method performs the mapping from a high-dimensional space to a visual space, while preserving the 0-dimensional persistence diagram of the Rips filtration of the high-dimensional data, ensuring that the filtrations generate the same connected components when applied to the original as well as projected data. The presented case studies show that the topological guarantee provided by TopoMap not only brings confidence to the visual analytic process but also can be used to assist in the assessment of other projection methods.

Multidimensional Projection for Visual Analytics: Linking Techniques with Distortions, Tasks, and Layout Enrichment

Visual analysis of multidimensional data requires expressive and effective ways to reduce data dimensionality to encode them visually. Multidimensional projections (MDP) figure among the most important visualization techniques in this context, transforming multidimensional data into scatter plots whose visual patterns reflect some notion of similarity in the original data. However, MDP come with distortions that make these visual patterns not trustworthy, hindering users to infer actual data characteristics. Moreover, the patterns present in the scatter plots might not be enough to allow a clear understanding of multidimensional data, motivating the development of layout enrichment methodologies to operate together with MDP. This survey attempts to cover the main aspects of MDP as a visualization and visual analytic tool. It provides detailed analysis and taxonomies as to the organization of MDP techniques according to their main properties and traits, discussing the impact of such properties for visual perception and other human factors. The survey also approaches the different types of distortions that can result from MDP mappings and it overviews existing mechanisms to quantitatively evaluate such distortions. A qualitative analysis of the impact of distortions on the different analytic tasks performed by users when exploring multidimensional data through MDP is also presented. Guidelines for choosing the best MDP for an intended task are also provided as a result of this analysis. Finally, layout enrichment schemes to debunk MDP distortions and/or reveal relevant information not directly inferable from the scatter plot are reviewed and discussed in the light of new taxonomies. We conclude the survey providing future research axes to fill discovered gaps in this domain.

PhotoRecomposer: Interactive Photo Recomposition by Cropping

We present a visual analysis method for interactively recomposing a large number of photos based on example photos with high-quality composition. The recomposition method is formulated as a matching problem between photos. The key to this formulation is a new metric for accurately measuring the composition distance between photos. We have also developed an earth-mover-distance-based online metric learning algorithm to support the interactive adjustment of the composition distance based on user preferences. To better convey the compositions of a large number of example photos, we have developed a multi-level, example photo layout method to balance multiple factors such as compactness, aspect ratio, composition distance, stability, and overlaps. By introducing an EulerSmooth-based straightening method, the composition of each photos is clearly displayed. The effectiveness and usefulness of the method has been demonstrated by the experimental results, user study, and case studies.

On Building Online Visualization Maps for News Data Streams by Means of Mathematical Optimization

In this article we develop a novel online framework to visualize news data over a time horizon. First, we perform a Natural Language Processing analysis, wherein the words are extracted, and their attributes, namely the importance and the relatedness, are calculated. Second, we present a Mathematical Optimization model for the visualization problem and a numerical optimization approach. The model represents the words using circles, the time-varying area of which displays the importance of the words in each time period. Word location in the visualization region is guided by three criteria, namely, the accurate representation of semantic relatedness, the spread of the words in the visualization region to improve the quality of the visualization, and the visual stability over the time horizon. Our approach is flexible, allowing the user to interact with the display, as well as incremental and scalable. We show results for three case studies using data from Danish news sources.