  In recent years, various kernels have been proposed in the context of
persistent homology to deal with persistence diagrams in supervised learning
approaches. In this paper, we consider the idea of variably scaled kernels, for
approximating functions and data, and we interpret it in the framework of
persistent homology. We call them Variably Scaled Persistence Kernels (VSPKs).
These new kernels are then tested in different classification experiments. The
obtained results show that they can improve the performance and the efficiency
of existing standard kernels.
