Multiclass Classification Without Labels via Posterior Simplex Geometry

A recent study published on arXiv expands the Classification without Labels (CWoLa) concept from binary to multiclass scenarios. Often, in classification tasks, dependable instance-level labels are lacking; however, weakly enriched unlabeled datasets—derived from various cuts, sources, populations, or experimental conditions—alter latent class proportions without disclosing them. In binary situations (K=2), CWoLa demonstrates that a classifier trained to differentiate between two impure mixtures with varying class proportions can identify an optimal class discriminator without knowledge of those proportions. The authors broaden this approach to multiclass learning involving multiple unlabeled mixtures (K>2), where the learner only knows the mixture identity, lacking both latent class labels and class-prior matrices. They establish that in a multiclass mixture model, the Bayes-optimal mixture classifier g* assigns data points to a (K-1)-simplex within the mixture-posterior space. The vertices of this simplex, totaling K, represent pure classes, allowing for classification without labeled data. The paper can be found on arXiv under ID 2607.24943.