Matrix variate receiver operating characteristic curve for binary classification

In recent years, the study of Receiver Operating Characteristic (ROC) curve analysis has gained significant attention as a means of accurately assessing test performance and determining optimal cutoff points. Traditionally, ROC models have been developed for bi-distributional univariate and multivariate data, such as Bi-normal, Bi-Exponential, Multivariate ROC models, and so forth. However, in current practical scenarios, the prevalence of high-dimensional matrix variate data poses a challenge for accurate test evaluation. To address this issue, this paper presents a novel ROC model that incorporates matrix variate normal distribution to effectively explain the accuracy of a test in the context of matrix data. Further, the accuracy measure, Area under the Curve (AUC) is derived, which helps in explaining the variability of the curve and provides the sensitivity at a particular value of specificity and vice versa. The proposed methodology is supported by a real data set and simulation studies.