## Neural Networks

#### Radial Basis Function Neural Networks

Radial basis function (RBF) neural networks (RBF-NN) have been introduced by Broomhead and Lowe in 1998 [ref]. Their model is inspired by the locally tuned response observed in biologic neurons that can be found in several parts of the nervous system, for example cells in the auditory systems which are selective to small bands of frequencies, in visual cortex, etc. Such locally tuned neurons show response characteristics bounded to a small range of the input space.

Radial basis function networks consist of a layer of units with radial basis activation function (RBF) and an output layer of linear summation unit(s). As the RBF, often Gaussian activation functions are used, therefore the corresponding units are called *Gaussian (kernel) units*. The number of the units has to be known in advance, however techniques for dynamic growth of the structures have been introduced.

#### Kohonen SOM

The Kohonen self-organizing network (SOM) [ref] is a single layer feed-forward network in which the output neurons are arranged in low dimensional structure that can be visualized easily. It is partly motivated by the way the visual, auditory or other sensory information is handled in separate parts of the cerebral cortex in human brain.

Each input of the network is distributed to all output neurons. There is a weight vector attached to each neuron having the same dimensionality as the input vectors. The number of input dimensions is usually much greater than the output grid dimension. Kohonen self-organizing networks are mainly used for dimensionality reduction rather than expansion, working similarly to PCA (primary component analysis) or ICA (independent component analysis).

Unlike the most of artificial neural networks, this neural network is trained by unsupervised training. This means that the neural network is given no information about the correct class of the input vector. Note, that the number of neurons remains the same through the whole learning process.

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