The Effect of the Hypersphere Volume Anomaly on Generative Support Vector Decoders

Transforming the energy supply to a sustainable system requires the integration of numerous renewable generation. This in turn leads to a need for new algorithms to keep the increasing complexity manageable. Support vector decoders for the systematic generation of feasible schedules for the operational management of electrical generators and consumers have proven to be helpful here. Such a decoder models a system by using a hypersphere model in a high-dimensional Hilbert space. However, it has been known for some time that the volume of high-dimensional hyperspheres exhibits an anomaly regarding the development of the volume with growing dimensionality. This paper investigates the influence of this anomaly on the performance of models based on 1-class support vector descriptions that use a high-dimensional hypersphere for modeling. We show that there is an impact that affects a certain range of support vector models, but also allows for Pareto-optimal models when training for quick execution is an issue.