  Simplicial map neural networks (SMNNs) are topology-based neural networks
with interesting properties such as universal approximation ability and
robustness to adversarial examples under appropriate conditions. However, SMNNs
present some bottlenecks for their possible application in high-dimensional
datasets. First, SMNNs have precomputed fixed weight and no SMNN training
process has been defined so far, so they lack generalization ability. Second,
SMNNs require the construction of a convex polytope surrounding the input
dataset. In this paper, we overcome these issues by proposing an SMNN training
procedure based on a support subset of the given dataset and replacing the
construction of the convex polytope by a method based on projections to a
hypersphere. In addition, the explainability capacity of SMNNs and an effective
implementation are also newly introduced in this paper.
