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

Taxonomy of ANNs

Artificial neural networks (ANN) are adaptive models that can establish almost any relationship between data. They can be regarded as black boxes to build mappings between a set of input and output vectors. ANNs are quite promising in solving problems where traditional models fail, especially for modeling complex phenomena which show a non-linear relationship.

Neural networks can be roughly divided into three categories:

  • Signal transfer networks. In signal transfer networks, the input signal is transformed into an output signal. Note that the dimensionality of the signals may change during this process. The signal is propagated through the network and is thus changed by the internal mechanism of the network. Most network models are based on some kind of predefined basis functions (e.g. Gaussian peaks, as in the case of radial basis function networks (RBF networks), or sigmoid function (in the case of multi-layer perceptrons).
  • State transition networks. Examples: Hopfield networks, and Boltzmann machines.
  • Competitive learning networks. In competitive networks (sometimes also called self-organizing maps, or SOMs) all the neurons of the network compete for the input signal. The neuron which "wins" gets the chance to move towards the input signal in n-dimensional space. Example: Kohonen feature map.

What these types of networks have in common is that they "learn" by adapting their network parameters. In general, the learning algorithms try to minimize the error of the model. This is often a type of gradient descent approach - with all its pitfalls.