Simplicial map neural networks (SMNNs) are topology-based neural networks
with interesting properties such as universal approximation capability and
robustness to adversarial examples under appropriate conditions. However, SMNNs
present some bottlenecks for their possible application in high dimensions.
First, no SMNN training process has been defined so far. Second, SMNNs require
the construction of a convex polytope surrounding the input dataset. In this
paper, we propose a SMNN training procedure based on a support subset of the
given dataset and a method based on projection to a hypersphere as a
replacement for the convex polytope construction. In addition, the
explainability capacity of SMNNs is also introduced for the first time in this
paper