We present a novel type of circular treemap, where we intentionally allocate extra space for additional visual variables. With this extended visual design space, we encode hierarchically structured data along with their uncertainties in a combined diagram. We introduce a hierarchical and force-based circle-packing algorithm to compute Bubble Treemaps, where each node is visualized using nested contour arcs. Bubble Treemaps do not require any color or shading, which offers additional design choices. We explore uncertainty visualization as an application of our treemaps using standard error and Monte Carlo-based statistical models. To this end, we discuss how uncertainty propagates within hierarchies. Furthermore, we show the effectiveness of our visualization using three different examples: the package structure of Flare, the S&P 500 index, and the US consumer expenditure survey.
a b s t r a c tAugmented Reality is a promising paradigm for intraoperative assistance. Yet, apart from technical issues, a major obstacle to its clinical application is the man-machine interaction. Visualization of unnecessary, obsolete or redundant information may cause confusion and distraction, reducing usefulness and acceptance of the assistance system.We propose a system capable of automatically filtering available information based on recognized phases in the operating room. Our system offers a specific selection of available visualizations which suit the surgeon's needs best. The system was implemented for use in laparoscopic liver and gallbladder surgery and evaluated in phantom experiments in conjunction with expert interviews.
0 0 0 (a) Regular PCA 0 0 0 (b) s = 0.5 0 0 0 (c) s = 0.8 0 0 0 (d) s = 1.0 Fig. 1. Data uncertainty can have a significant influence on the outcome of dimensionality reduction techniques. We propose a generalization of principal component analysis (PCA) that takes into account the uncertainty in the input. The top row shows the dataset with varying degrees of uncertainty and the corresponding principal components, whereas the bottom row shows the projection of the dataset, using our method, onto the first principal component. In Figures (a) and (b), with relatively low uncertainty, the blue and the orange distributions are comprised by the red and the green distributions. In Figures (c) and (d), with a larger amount of uncertainty, the projection changes drastically: now the orange and blue distributions encompass the red and the green distributions.Abstract-We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.