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High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional space while preserving important relationships. TopoMap is another technique that excels at preserving the underlying structure of the data, leading to interpretable visualizations. In particular, TopoMap maps the high-dimensional data into a visual space, guaranteeing that the 0-dimensional persistence diagram of the Rips filtration of the visual space matches the one from the high-dimensional data. However, the original TopoMap algorithm can be slow and its layout can be too sparse for large and complex datasets. In this paper, we propose three improvements to TopoMap: 1) a more space-efficient layout, 2) a significantly faster implementation, and 3) a novel TreeMap-based representation that makes use of the topological hierarchy to aid the exploration of the projections. These advancements make TopoMap, now referred to as TopoMap++, a more powerful tool for visualizing high-dimensional data which we demonstrate through different use case scenarios.

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Exploring large virtual environments, such as cities, is a central task in several domains, such as gaming and urban planning. VR systems can greatly help this task by providing an immersive experience; however, a common issue with viewing and navigating a city in the traditional sense is that users can either obtain a local or a global view, but not both at the same time, requiring them to continuously switch between perspectives, losing context and distracting them from their analysis. In this article, our goal is to allow users to navigate to points of interest without changing perspectives. To accomplish this, we design an intuitive navigation interface that takes advantage of the strong sense of spatial presence provided by VR. We supplement this interface with a perspective that warps the environment, called UrbanRama, based on a cylindrical projection, providing a mix of local and global views. The design of this interface was performed as an iterative process in collaboration with architects and urban planners. We conducted a qualitative and a quantitative pilot user study to evaluate UrbanRama and the results indicate the effectiveness of our system in reducing perspective changes, while ensuring that the warping doesn't affect distance and orientation perception.

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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.

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Large scale shadows from buildings in a city play an important role in determining the environmental quality of public spaces. They can be both beneficial, such as for pedestrians during summer, and detrimental, by impacting vegetation and by blocking direct sunlight. Determining the effects of shadows requires the accumulation of shadows over time across different periods in a year. In this paper, we propose a simple yet efficient class of approach that uses the properties of sun movement to track the changing position of shadows within a fixed time interval. We use this approach to extend two commonly used shadow techniques, shadow maps and ray tracing, and demonstrate the efficiency of our approach. Our technique is used to develop an interactive visual analysis system, Shadow Profiler, targeted at city planners and architects that allows them to test the impact of shadows for different development scenarios. We validate the usefulness of this system through case studies set in Manhattan, a dense borough of New York City.

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Visual analytics systems can greatly help in the analysis of urban data allowing domain experts from academia and city governments to better understand cities, and thus enable better operations, informed planning and policies. Effectively designing these systems is challenging and requires bringing together methods from different domains. In this paper, we discuss the challenges involved in designing a visual analytics system to interactively explore large spatio-temporal data sets and give an overview of our research that combines visualization and data management to tackle these challenges.

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We present TopoAngler, a visualization framework that enables an interactive user-guided segmentation of fishes contained in a micro-CT scan. The inherent noise in the CT scan coupled with the often disconnected (and sometimes broken) skeletal structure of fishes makes an automatic segmentation of the volume impractical. To overcome this, our framework combines techniques from computational topology with an interactive visual interface, enabling the human-in-the-Ioop to effectively extract fishes from the volume. In the first step, the join tree of the input is used to create a hierarchical segmentation of the volume. Through the use of linked views, the visual interface then allows users to interactively explore this hierarchy, and gather parts of individual fishes into a coherent sub-volume, thus reconstructing entire fishes. Our framework was primarily developed for its application to CT scans of fishes, generated as part of the ScanAllFish project, through close collaboration with their lead scientist. However, we expect it to also be applicable in other biological applications where a single dataset contains multiple specimen; a common routine that is now widely followed in laboratories to increase throughput of expensive CT scanners.

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Cities are inherently dynamic. Interesting patterns of behavior typically manifest at several key areas of a city over multiple temporal resolutions. Studying these patterns can greatly help a variety of experts ranging from city planners and architects to human behavioral experts. Recent technological innovations have enabled the collection of enormous amounts of data that can help in these studies. However, techniques using these data sets typically focus on understanding the data in the context of the city, thus failing to capture the dynamic aspects of the city. The goal of this work is to instead understand the city in the context of multiple urban data sets. To do so, we define the concept of an "urban pulse" which captures the spatio-temporal activity in a city across multiple temporal resolutions. The prominent pulses in a city are obtained using the topology of the data sets, and are characterized as a set of beats. The beats are then used to analyze and compare different pulses. We also design a visual exploration framework that allows users to explore the pulses within and across multiple cities under different conditions. Finally, we present three case studies carried out by experts from two different domains that demonstrate the utility of our framework.

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Elucidation of transcriptional regulatory networks (TRNs) is a fundamental goal in biology, and one of the most important components of TRNs are transcription factors (TFs), proteins that specifically bind to gene promoter and enhancer regions to alter target gene expression patterns. Advances in genomic technologies as well as advances in computational biology have led to multiple large regulatory network models (directed networks) each with a large corpus of supporting data and gene-annotation. There are multiple possible biological motivations for exploring large regulatory network models, including: validating TF-target gene relationships, figuring out co-regulation patterns, and exploring the coordination of cell processes in response to changes in cell state or environment. Here we focus on queries aimed at validating regulatory network models, and on coordinating visualization of primary data and directed weighted gene regulatory networks. The large size of both the network models and the primary data can make such coordinated queries cumbersome with existing tools and, in particular, inhibits the sharing of results between collaborators. In this work, we develop and demonstrate a web-based framework for coordinating visualization and exploration of expression data (RNA-seq, microarray), network models and gene-binding data (ChIP-seq). Using specialized data structures and multiple coordinated views, we design an efficient querying model to support interactive analysis of the data. Finally, we show the effectiveness of our framework through case studies for the mouse immune system (a dataset focused on a subset of key cellular functions) and a model bacteria (a small genome with high data-completeness).

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The explosion in the volume of data about urban environments has opened up opportunities to inform both policy and administration and thereby help governments improve the lives of their citizens, increase the efficiency of public services, and reduce the environmental harms of development. However, cities are complex systems and exploring the data they generate is challenging. The interaction between the various components in a city creates complex dynamics where interesting facts occur at multiple scales, requiring users to inspect a large number of data slices over time and space. Manual exploration of these slices is ineffective, time consuming, and in many cases impractical. In this paper, we propose a technique that supports event-guided exploration of large, spatio-temporal urban data. We model the data as time-varying scalar functions and use computational topology to automatically identify events in different data slices. To handle a potentially large number of events, we develop an algorithm to group and index them, thus allowing users to interactively explore and query event patterns on the fly. A visual exploration interface helps guide users towards data slices that display interesting events and trends. We demonstrate the effectiveness of our technique on two different data sets from New York City (NYC): data about taxi trips and subway service. We also report on the feedback we received from analysts at different NYC agencies.

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We describe a framework to explore and visualize the movement of cloud systems. Using techniques from computational topology and computer vision, our framework allows the user to study this movement at various scales in space and time. Such movements could have large temporal and spatial scales such as the Madden Julian Oscillation (MJO), which has a spatial scale ranging from 1000 km to 10000 km and time of oscillation of around 40 days. Embedded within these larger scale oscillations are a hierarchy of cloud clusters which could have smaller spatial and temporal scales such as the Nakazawa cloud clusters. These smaller cloud clusters, while being part of the equatorial MJO, sometimes move at speeds different from the larger scale and in a direction opposite to that of the MJO envelope. Hitherto, one could only speculate about such movements by selectively analysing data and a priori knowledge of such systems. Our framework automatically delineates such cloud clusters and does not depend on the prior experience of the user to define cloud clusters. Analysis using our framework also shows that most tropical systems such as cyclones also contain multi-scale interactions between clouds and cloud systems. We show the effectiveness of our framework to track organized cloud system during one such rainfall event which happened at Mumbai, India in July 2005 and for cyclone Aila which occurred in Bay of Bengal during May 2009.

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The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.