Assigning discriminable and harmonic colors to samples according to their class labels and spatial distribution can generate attractive visualizations and facilitate data exploration. However, as the number of classes increases, it is challenging to generate a high-quality color assignment result that accommodates all classes simultaneously. A practical solution is to organize classes into a hierarchy and then dynamically assign colors during exploration. However, existing color assignment methods fall short in generating high-quality color assignment results and dynamically aligning them with hierarchical structures. To address this issue, we develop a dynamic color assignment method for hierarchical data, which is formulated as a multi-objective optimization problem. This method simultaneously considers color discriminability, color harmony, and spatial distribution at each hierarchical level. By using the colors of parent classes to guide the color assignment of their child classes, our method further promotes both consistency and clarity across hierarchical levels. We demonstrate the effectiveness of our method in generating dynamic color assignment results with quantitative experiments and a user study.

Fuzzy clusters, where ambiguous samples belong to multiple clusters, are common in real-world applications. Analyzing such ambiguous samples in large-scale datasets is crucial for practical applications, such as diagnosing machine learning models. A promising method to support such analysis is through hierarchical cluster-aware grid visualizations, which offer high space efficiency and clear cluster perception. However, existing cluster-aware grid layout methods cannot clarify ambiguity among fuzzy clusters, which limits their effectiveness in fuzzy cluster analysis. To tackle this issue, we introduce a hierarchical fuzzy-cluster-aware grid layout method that supports hierarchical exploration of large-scale datasets. Throughout the hierarchical exploration, it is crucial to facilitate fuzzy cluster analysis while maintaining visual continuity for users. To achieve this, we propose a two-step optimization strategy for enhancing cluster perception, clarifying ambiguity, and preserving stability during the exploration. The first step is to create cluster-aware partitions, where each partition corresponds to a cluster. This step focuses on enhancing cluster perception and maintaining the previous shapes and positions of clusters to preserve stability at the cluster level. The second step is to generate a grid layout for each partition. In addition to placing similar samples together, this step also places ambiguous samples near the boundaries to clarify ambiguity and reveal the root causes of their occurrences and maintains the relative positions of the samples in the same cluster to preserve stability at the sample level. Several quantitative experiments and a use case are conducted to demonstrate the effectiveness and usefulness of our method in analyzing large-scale datasets, especially in fuzzy cluster analysis.

Temporal action localization aims to identify the boundaries and categories of actions in videos, such as scoring a goal in a football match. Single-frame supervision has emerged as a labor-efficient way to train action localizers as it requires only one annotated frame per action. However, it often suffers from poor performance due to the lack of precise boundary annotations. To address this issue, we propose a visual analysis method that aligns similar actions and then propagates a few user-provided annotations (e.g., boundaries, category labels) to similar actions via the generated alignments. Our method models the alignment between actions as a heaviest path problem and the annotation propagation as a quadratic optimization problem. As the automatically generated alignments may not accurately match the associated actions and could produce inaccurate localization results, we develop a storyline visualization to explain the localization results of actions and their alignments. This visualization facilitates users in correcting wrong localization results and misalignments. The corrections are then used to improve the localization results of other actions. The effectiveness of our method in improving localization performance is demonstrated through quantitative evaluation and a case study.

Grid visualizations are widely used in many applications to visually explain a set of data and their proximity relationships. However, existing layout methods face difficulties when dealing with the inherent cluster structures within the data. To address this issue, we propose a cluster-aware grid layout method that aims to better preserve cluster structures by simultaneously considering proximity, compactness, and convexity in the optimization process. Our method utilizes a hybrid optimization strategy that consists of two phases. The global phase aims to balance proximity and compactness within each cluster, while the local phase ensures the convexity of cluster shapes. We evaluate the proposed grid layout method through a series of quantitative experiments and two use cases, demonstrating its effectiveness in preserving cluster structures and facilitating analysis tasks.

The modeling of the behavior of the external ear with a beamformer is proposed. The output of a beamformer is a weighted combination of the data received at any array of spatially distributed sensors. The beamformer weights and array geometry determine its spatial and temporal filtering characteristics. A least squares procedure for choosing the weights so the beamformer response approximates the measured response of the external ear is described. The effectiveness of this model is demonstrated by designing a beamformer of several hundred weights which duplicates and interpolates the measured external ear response of a cat over broad ranges of frequency and direction.>