Artificial neural network
The mathematical structure modeled on the human neural network and which is designed to attack number of statistical troubles, particularly in the areas of pattern recognition, learning multivariate analysis, and memory. The essential feature of such a structure is a network of the simple processing elements (arti?cial neurons) which are coupled together (either in the hardware or the software), so that they can cooperate with each other. From the set of 'inputs' and an associated set of parameters, the arti?cial neurons create an 'output' which provides a possible solution to the problem under analysis. In number of neural networks the relationship between the input received by the neuron and its output is determined by a general linear model. The most ordinary form is the feed-forward network which is basically an extension of idea of the perception. In this type of network the vertices can be numbered such that all the connections go from a vertex to one with the higher number; the vertices are set in layers, with connections only to the higher layers. This is explained in the figure drawn below. Each neuron sums its inputs to form a entire input and applies the function fj to xj to give the desired output yj. The links have weights wij which multiply signals travelling along with them by that factor. Number of ideas and activities familiar to statisticians can be expressed in a neural-network notation, consisting regression analysis, generalized additive models, and discriminate investigation. In any practical problem which occurs the statistical equivalent of specifying architecture of the suitable network is specifying a suitable model, and training the network to do well with reference to the training set is equivalent to estimating the parameters of the model provides a set of data.