Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

ANN - Mapping of Spaces

Newcomers in the field of multivariate data analysis and neural networks often think that an artificial neural network (ANN) is a type of a black magic box which can be used to enter data and get a solution back. Although this view is potentially dangerous, there is also a grain of truth in it. We could therefore regard an ANN as an abstract machine which creates a non-linear mapping between an n-dimensional input data space and a p-dimension output space. n is usually much larger than p; with p often being in the range of 1 to 3 (since the human interpreter is restricted to a maximum dimensionality of 3 or perhaps 4).

This non-linear mapping is set up during the learning process of a neural network. The "art" of training a neural network is to control the training in such a way that the resulting mapping represents the underlying relationship within the data, avoiding any adjustment for noise, or errors in the data.