Distortion-Aware Brushing for Reliable Cluster Analysis in Multidimensional Projections

TL;DR

This work tackles the unreliability of cluster analysis in multidimensional data when visualized through distorted MD projections. It introduces Distortion-aware brushing, a lens-based interaction that dynamically relocates points to reflect true MD proximity, enabling 2D brushes to align with MD clusters. Through two user studies, it shows that the method yields higher clustering accuracy under distortions at the cost of longer task times, and demonstrates practical benefits in geospatial clustering and interactive labeling. The approach combines robust MD-density based seed selection, persistent MD-aware relocation, and contextualization to improve reliability while remaining usable for real-world data exploration.

Abstract

Brushing is a common interaction technique in 2D scatterplots, allowing users to select clustered points within a continuous, enclosed region for further analysis or filtering. However, applying conventional brushing to 2D representations of multidimensional (MD) data, i.e., Multidimensional Projections (MDPs), can lead to unreliable cluster analysis due to MDP-induced distortions that inaccurately represent the cluster structure of the original MD data. To alleviate this problem, we introduce a novel brushing technique for MDPs called Distortion-aware brushing. As users perform brushing, Distortion-aware brushing corrects distortions around the currently brushed points by dynamically relocating points in the projection, pulling data points close to the brushed points in MD space while pushing distant ones apart. This dynamic adjustment helps users brush MD clusters more accurately, leading to more reliable cluster analysis. Our user studies with 24 participants show that Distortion-aware brushing significantly outperforms previous brushing techniques for MDPs in accurately separating clusters in the MD space and remains robust against distortions. We further demonstrate the effectiveness of our technique through two use cases: (1) conducting cluster analysis of geospatial data and (2) interactively labeling MD clusters.

Figures (9)

• Figure 1: Comparison between existing brushing techniques (\ref{['sec:mdpbrushrel']}) and Distortion-aware brushing in identifying clusters within multidimensional (MD) data through its 2D projection. (a) Previous brushing techniques work by defining a continuous 2D region via direct manipulation (e.g., lassoing). As projections may not accurately reflect original MD data distribution due to distortions, users cannot precisely identify MD clusters.. (b) Distortion-aware brushing supports users to precisely extract MD clusters by resolving distortions based on point relocation.
• Figure 2: Overall workflow of Distortion-aware brushing (\ref{['sec:workflow']}). The technique features a lens with inner and outer boundaries depicted as bold blue and red closed lines, respectively. Users' actions are explained with blue text and arrows, while the machine's actions are detailed in orange. Data points are represented as small circles, i.e., dots, where seed and brushed points are highlighted using thick dotted and solid borders. Seed and brushed points are also highlighted in blue color. The opacity of data points depicts MD density in [patternparamsolid, background-color=myorange!40] Step 1 and represents MD closeness to the seed or brushed points in the following steps.
• Figure 3: Illustration on how Distortion-aware brushing relocates points in [patternparamsolid, background-color=myorange!40] Step 3 and [patternparamsolid, background-color=myorange!40] Step 4. The machine first examines the MD closeness of unbrushed points to the brushed points (or seed points in [patternparamsolid, background-color=myorange!40] Step 3) (3-a), then relocates those points in the projection to reflect that MD closeness.
• Figure 4: The example projections (i.e., stimuli) used in our experiments with different amounts of distortions. In study 1 (\ref{['sec:comparisonstudy']}, we treat the amount of distortions as an independent variable, namely DistortionAmount. In study 2 (\ref{['sec:detailstudy']}), it is controlled as a confounding variable.
• Figure 5: Study 1 results demonstrating the robustness of brushing techniques against the amount of distortions. Overall, Distortion-aware brushing significantly outperforms baseline techniques in terms of task completion time, but requires participants more time to complete the task. Please refer to \ref{['sec:study1results']} and \ref{['sec:study1discuss']} for detailed analysis results and discussions, respectively.