Prototype based one-class learners such as Supervised Vector Quantization for One-Class Classification (SVQ-OCC) utilise squared Euclidean distance without metric adaptation and cannot adapt to the spatial structure of the data. Moreover, these learners are unable to capture relevant variation when the target distribution presents anisotropic structure in the feature space. This paper proposes One-Class Generalized Learning Vector Quantization (OC-GLVQ), whose discriminant substitutes the negative-class distance in GLVQ with a per-prototype visibility threshold, yielding a cost function that is jointly differentiable in prototypes, thresholds and metric parameters. A hierarchy of distance formulations from diagonal relevance weighting through global and local matrix projections to tangent subspace metrics is developed within the OC-GLVQ framework. The resulting classifiers adapt their geometry to the target distribution while retaining prototype-level interpretability. This paper identifies a gradient-magnitude mismatch between the prototypes and threshold parameters in high-dimensional settings and resolves it through a square-root reparameterisation. Experimental assessment on four practical datasets indicates the metric-adaptive variants consistently surpass both SVQ-OCC and Support Vector Data Description (SVDD), with local matrix adaptation yielding the strongest overall performance.