A PLS‐CM and ASCA Procedure to Explore the Overlap of Two Classes

Class‐modeling (CM) and discriminant analysis (DA) are commonly applied to binary classification. DA enforces exclusive assignments of unknowns by constructing optimal delimiters, which may convey unwarranted certainty. Conversely, CM defines two class regions in the predictor space (2‐class model), allowing individuals to be assigned to one class, both, or none. This work focuses on CM, particularly on the uncertainty derived from overlapping regions and its interpretation. Overlapping may be due to an inadequate model or may indicate that predictors do not provide enough information to discriminate between classes. A procedure using soft partial least squares class modeling (PLS‐CM) is proposed and optimized. The chosen metric of performance, diagonal modified confusion entropy, DMCEN, which measures the reduction in entropy achieved by applying CM, is minimized regarding key parameters: number of latent variables, Q and T 2 confidence levels, and probability thresholds for class assignment. Subsequently, ANOVA–simultaneous component analysis (ASCA) is applied to shed light on the reason underlying class overlap. The procedure has been applied to two case studies, one related to cardiovascular disease (CVD) and the other to diabetes. In the CVD case, 77 out of 297 individuals were assigned to both classes. ASCA indicates that predictor variables lack differential information (healthy vs sick) for them, suggesting that classification ambiguity is data‐driven rather than method‐related. The same applies to 42 out of 825 individuals in the diabetes case. PLS‐CM together with ASCA provides thresholds for identifying individuals who cannot be clearly classified as healthy or sick, which discriminant methods cannot address.