Voronoi treemaps are used to depict nodes and their hierarchical relationships simultaneously. However, in addition to the hierarchical structure, data attributes, such as co-occurring features or similarities, frequently exist. Examples include geographical attributes like shared borders between countries or contextualized semantic information such as embedding vectors derived from large language models. In this work, we introduce a Voronoi treemap algorithm that leverages data similarity to generate neighborhood-preserving treemaps. First, we extend the treemap layout pipeline to consider similarity during data preprocessing. We then use a Kuhn-Munkres matching of similarities to centroidal Voronoi tessellation (CVT) cells to create initial Voronoi diagrams with equal cell sizes for each level. Greedy swapping is used to improve the neighborhoods of cells to match the data's similarity further. During optimization, cell areas are iteratively adjusted to their respective sizes while preserving the existing neighborhoods. We demonstrate the practicality of our approach through multiple real-world examples drawn from infographics and linguistics. To quantitatively assess the resulting treemaps, we employ treemap metrics and measure neighborhood preservation.

Density plots effectively summarize large numbers of points, which would otherwise lead to severe overplotting in, for example, a scatter plot. However, when applied to line-based datasets, such as trajectories or time series, density plots alone are insufficient, as they disrupt path continuity, obscuring smooth trends and rare anomalies. We propose a bin-based illumination model that decouples structure from density to enhance flow and reveal sparse outliers while preserving the original colormap. We introduce a bin-based outlierness metric to rank trajectories. Guided by this ranking, we construct a structural normal map and apply locally-adaptive lighting in the luminance channel to highlight chosen patterns-from dominant trends to atypical paths-with acceptable color distortion. Our interactive method enables analysts to prioritize main trends, focus on outliers, or strike a balance between the two. We demonstrate our method on several real-world datasets, showing it reveals details missed by simpler alternatives, achieves significantly lower CIEDE2000 color distortion than standard shading, and supports interactive updates for up to 10,000 lines.

Line-based density plots are used to reduce visual clutter in line charts with a multitude of individual lines. However, these traditional density plots are often perceived ambiguously, which obstructs the user's identification of underlying trends in complex datasets. Thus, we propose a novel image space coloring method for line-based density plots that enhances their interpretability. Our method employs color not only to visually communicate data density but also to highlight similar regions in the plot, allowing users to identify and distinguish trends easily. We achieve this by performing hierarchical clustering based on the lines passing through each region and mapping the identified clusters to the hue circle using circular MDS. Additionally, we propose a heuristic approach to assign each line to the most probable cluster, enabling users to analyze density and individual lines. We motivate our method by conducting a small-scale user study, demonstrating the effectiveness of our method using synthetic and real-world datasets, and providing an interactive online tool for generating colored line-based density plots.

Abstract Euler diagrams are a popular technique to visualize set‐typed data. However, creating diagrams using simple shapes remains a challenging problem for many complex, real‐life datasets. To solve this, we propose RectEuler: a flexible, fully‐automatic method using rectangles to create Euler‐like diagrams. We use an efficient mixed‐integer optimization scheme to place set labels and element representatives (e.g., text or images) in conjunction with rectangles describing the sets. By defining appropriate constraints, we adhere to well‐formedness properties and aesthetic considerations. If a dataset cannot be created within a reasonable time or at all, we iteratively split the diagram into multiple components until a drawable solution is found. Redundant encoding of the set membership using dots and set lines improves the readability of the diagram. Our web tool lets users see how the layout changes throughout the optimization process and provides interactive explanations. For evaluation, we perform quantitative and qualitative analysis across different datasets and compare our method to state‐of‐the‐art Euler diagram generation methods.

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data points. Existing methods focus on the projection of multidimensional data points, and the neighborhood information is ignored. Our method is able to analyze the shape and directional information of the local subspace to gain more insights into the global structure of the data through the perception of local structures. Local subspaces are fitted by multidimensional ellipses that are spanned by basis vectors. An accurate and efficient vector transformation method is proposed based on analytical differentiation of multidimensional projections formulated as implicit functions. The results are visualized as glyphs and analyzed using a full set of specifically-designed interactions supported in our efficient web-based visualization tool. The usefulness of our method is demonstrated using various multi- and high-dimensional benchmark datasets. Our implicit differentiation vector transformation is evaluated through numerical comparisons; the overall method is evaluated through exploration examples and use cases.

Deep learning has recently attracted significant attention in the field of hyperspectral images (HSIs) classification. However, the construction of an efficient deep neural network mostly relies on a large number of labeled samples being available. To address this problem, this paper proposes a unified deep network, combined with active transfer learning (TL) that can be well-trained for HSIs classification using only minimally labeled training data. More specifically, deep joint spectral-spatial feature is first extracted through hierarchical stacked sparse autoencoder (SSAE) networks. Active TL is then exploited to transfer the pretrained SSAE network and the limited training samples from the source domain to the target domain, where the SSAE network is subsequently fine-tuned using the limited labeled samples selected from both source and target domains by the corresponding active learning (AL) strategies. The advantages of our proposed method are threefold: 1) the network can be effectively trained using only limited labeled samples with the help of novel AL strategies; 2) the network is flexible and scalable enough to function across various transfer situations, including cross data set and intraimage; and 3) the learned deep joint spectral-spatial feature representation is more generic and robust than many joint spectral-spatial feature representations. Extensive comparative evaluations demonstrate that our proposed method significantly outperforms many state-of-the-art approaches, including both traditional and deep network-based methods, on three popular data sets.