BayesAHDD: A new Bayesian rule-based adaptive hypersphere data description for few-shot one-class classification

Few-shot one-class classification (FS-OCC) is a challenging classification problem that involves learning from a very limited number of training samples, all from a single class. Recently, several data description methods have been proposed to address the FS-OCC problem. Unlike conventional one-class classification problems, the few-shot setting requires the model to generalize to novel tasks with previously unseen positive classes. Most existing methods learn decision boundaries in the feature space without explicitly modeling the underlying data distributions, which limits the generalization ability of the learned representations. To address this issue, we propose Bayesian Rule-based Adaptive Hypersphere Data Description (BayesAHDD), a probabilistic framework that represents data with multivariate Gaussian distributions and performs classification according to the Bayes decision rule. Based on the assumption that negative samples are more dispersed in the feature space, BayesAHDD models the negative class by scaling the positive class variance vector element-wise using a learnable vector. To address the challenges of exploding gradients and numerical overflow, we impose a lower bound on the positive class variance vector and introduce a trainable parameter that integrates the class prior probability ratio with the normalization constants of the Gaussian class-conditional densities. Experimental results on both benchmark and domain-specific datasets show that BayesAHDD consistently outperforms existing baselines and state-of-the-art FS-OCC methods. Moreover, quantitative analysis demonstrates that the learned feature representations exhibit superior discriminative ability compared to those produced by previous approaches.