The contour depth methodology enables non-parametric summarization of contour ensembles by extracting their representatives, confidence bands, and outliers for visualization (via contour boxplots) and robust downstream procedures. We address two shortcomings of these methods. Firstly, we significantly expedite the computation and recomputation of Inclusion Depth (ID), introducing a linear-time algorithm for epsilon ID, a variant used for handling ensembles with contours with multiple intersections. We also present the inclusion matrix, which contains the pairwise inclusion relationships between contours, and leverage it to accelerate the recomputation of ID. Secondly, extending beyond the single distribution assumption, we present the Relative Depth (ReD), a generalization of contour depth for ensembles with multiple modes. Building upon the linear-time eID, we introduce CDclust, a clustering algorithm that untangles ensemble modes of variation by optimizing ReD. Synthetic and real datasets from medical image segmentation and meteorological forecasting showcase the speed advantages, illustrate the use case of progressive depth computation and enable non-parametric multimodal analysis. To promote research and adoption, we offer the contour-depth Python package.

Exploration and analysis of high-dimensional data are important tasks in many fields that produce large and complex data, like the financial sector, systems biology, or cultural heritage. Tailor-made visual analytics software is developed for each specific application, limiting their applicability in other fields. However, as diverse as these fields are, their characteristics and requirements for data analysis are conceptually similar. Many applications share abstract tasks and data types and are often constructed with similar building blocks. Developing such applications, even when based mostly on existing building blocks, requires significant engineering efforts. We developed ManiVault, a flexible and extensible open-source visual analytics framework for analyzing high-dimensional data. The primary objective of ManiVault is to facilitate rapid prototyping of visual analytics workflows for visualization software developers and practitioners alike. ManiVault is built using a plugin-based architecture that offers easy extensibility. While our architecture deliberately keeps plugins self-contained, to guarantee maximum flexibility and re-usability, we have designed and implemented a messaging API for tight integration and linking of modules to support common visual analytics design patterns. We provide several visualization and analytics plugins, and ManiVault's API makes the integration of new plugins easy for developers. ManiVault facilitates the distribution of visualization and analysis pipelines and results for practitioners through saving and reproducing complete application states. As such, ManiVault can be used as a communication tool among researchers to discuss workflows and results. A copy of this paper and all supplemental material is available at osf.io/9k6jw, and source code at github.com/ManiVaultStudio.

During training sessions, sailors rely on feedback provided by the coaches to reinforce their skills and improve their performance. Nowadays, the incorporation of sensors on the boats enables coaches to potentially provide more informed feedback to the sailors. A common exercise during practice sessions, consists of two boats of the same class, sailing side by side in a straight line with different boat handling techniques. Coaches try to understand which techniques are that make one boat go faster than the other. The analysis of the obtained data from the boats is challenging given its multi-dimensional, time-varying and spatial nature. At present, coaches only rely on aggregated statistics reducing the complexity of the data, hereby losing local and temporal information. We describe a new domain characterization and present a visualization design that allows coaches to analyse the data, structuring their analysis and explore the data from different perspectives. A central element of the tool is the glyph design to intuitively represent and aggregate multiple aspects of the sensor data. We have conducted multiple user studies with naive users, sailors and coaches to evaluate the design and potential of the overall tool. (Figure presented.).

High-dimensional imaging is becoming increasingly relevant in many fields from astronomy and cultural heritage to systems biology. Visual exploration of such high-dimensional data is commonly facilitated by dimensionality reduction. However, common dimensionality reduction methods do not include spatial information present in images, such as local texture features, into the construction of low-dimensional embeddings. Consequently, exploration of such data is typically split into a step focusing on the attribute space followed by a step focusing on spatial information, or vice versa. In this paper, we present a method for incorporating spatial neighborhood information into distance-based dimensionality reduction methods, such as t-Distributed Stochastic Neighbor Embedding (t-SNE). We achieve this by modifying the distance measure between high-dimensional attribute vectors associated with each pixel such that it takes the pixel's spatial neighborhood into account. Based on a classification of different methods for comparing image patches, we explore a number of different approaches. We compare these approaches from a theoretical and experimental point of view. Finally, we illustrate the value of the proposed methods by qualitative and quantitative evaluation on synthetic data and two real-world use cases.