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.

翻译：我们提出 " 稳妥性和共性 " 和 " 稳妥性 ",这是衡量多维投影(MDP)的集群间可靠性的两种新颖的衡量标准,具体而言,在原高空空间和低维投影空间之间保持了多高的集群间结构。衡量集群间可靠性至关重要,因为它直接影响到能够开展多高的集群任务(例如,从预测的视角确定原始空间内的集群关系);然而,尽管集群间任务很重要,但我们发现以前的指标,如可靠性和连续性,无法衡量多维度的可靠性。我们的衡量标准考虑了集群间可靠性的两个方面:稳妥度测量原始空间预测空间空间和低维度空间内预计空间组群集的集群范围,而协同性度则是相反的衡量标准。它们以任意的形状和位置抽取随机的集群,并评估其他空间内的集群被拉伸或分散的程度。此外,我们的计量标准可以量化点性扭曲,从而可以在预测中以可预见到跨集群的可靠性,我们称之为一个可靠性的地图。我们通过定量试验,我们核查我们的标准类比的用户在选择准确的准确的准确的准确的估测测算。