Measuring and Explaining the Inter-Cluster Reliability of Multidimensional Projections
This work addresses a crucial gap for users in data visualization and analysis by enabling reliable interpretation of inter-cluster structures in projections, though it is incremental as it builds on existing projection techniques.
The paper tackles the problem of measuring inter-cluster reliability in multidimensional projections, proposing Steadiness and Cohesiveness metrics that capture distortions affecting cluster relationships, with quantitative experiments showing they outperform previous metrics like Trustworthiness and Continuity.
We propose Steadiness and Cohesiveness, two novel metrics to measure the inter-cluster reliability of multidimensional projection (MDP), specifically how well the inter-cluster structures are preserved between the original high-dimensional space and the low-dimensional projection space. Measuring inter-cluster reliability is crucial as it directly affects how well inter-cluster tasks (e.g., identifying cluster relationships in the original space from a projected view) can be conducted; however, despite the importance of inter-cluster tasks, we found that previous metrics, such as Trustworthiness and Continuity, fail to measure inter-cluster reliability. Our metrics consider two aspects of the inter-cluster reliability: Steadiness measures the extent to which clusters in the projected space form clusters in the original space, and Cohesiveness measures the opposite. They extract random clusters with arbitrary shapes and positions in one space and evaluate how much the clusters are stretched or dispersed in the other space. Furthermore, our metrics can quantify pointwise distortions, allowing for the visualization of inter-cluster reliability in a projection, which we call a reliability map. Through quantitative experiments, we verify that our metrics precisely capture the distortions that harm inter-cluster reliability while previous metrics have difficulty capturing the distortions. A case study also demonstrates that our metrics and the reliability map 1) support users in selecting the proper projection techniques or hyperparameters and 2) prevent misinterpretation while performing inter-cluster tasks, thus allow an adequate identification of inter-cluster structure.