OM4AnI: A Novel Overlap Measure for Anomaly Identification in Multi-Class Scatterplots

Scatterplots are widely used across various domains to identify anomalies in datasets, particularly in multi-class settings, such as detecting misclassified or mislabeled data. However, scatterplot effectiveness often declines with large datasets due to limited display resolution. This paper introduces a novel Visual Quality Measure (VQM) - OM4AnI (Overlap Measure for Anomaly Identification) - which quantifies the degree of overlap for identifying anomalies, helping users estimate how effectively anomalies can be observed in multi-class scatterplots. OM4AnI begins by computing anomaly index based on each data point's position relative to its class cluster. The scatterplot is then discretized into a matrix representation by binning the display space into cell-level (pixel-level) grids and computing the coverage for each pixel. It takes into account the anomaly index of data points covering these pixels and visual features (marker shapes, marker sizes, and rendering orders). Building on this foundation, we sum all the coverage information in each cell (pixel) of matrix representation to obtain the final quality score with respect to anomaly identification. We conducted an evaluation to analyze the efficiency, effectiveness, sensitivity of OM4AnI in comparison with six representative baseline methods that are based on different computation granularity levels: data level, marker level, and pixel level. The results show that OM4AnI outperforms baseline methods by exhibiting more monotonic trends against the ground truth and greater sensitivity to rendering order, unlike the baseline methods. It confirms that OM4AnI can inform users about how effectively their scatterplots support anomaly identification. Overall, OM4AnI shows strong potential as an evaluation metric and for optimizing scatterplots through automatic adjustment of visual parameters.