Multiclass threshold-based classification and model evaluation

In this paper, we introduce a threshold-based framework for multiclass classification that generalizes the standard argmax rule. This is done by replacing the probabilistic interpretation of softmax outputs with a geometric one on the multidimensional simplex, where the classification depends on a multidimensional threshold. This change of perspective enables for any trained classification network an textita posteriori optimization of the classification score by means of threshold tuning, as usually carried out in the binary setting, thus allowing for a further refinement of the prediction capability of any network. Our experiments show indeed that multidimensional threshold tuning yields performance improvements across various networks and datasets. Moreover, we derive a multiclass ROC analysis based on ROC clouds -- the attainable (FPR,TPR) operating points induced by a single multiclass threshold -- and summarize them via a Distance From Point (DFP) score to (0,1). This yields a coherent alternative to standard One-vs-Rest (OvR) curves and aligns with the observed tuning gains.