Vector quantization and projection neural network

Abstract

Classical data analysis techniques are generally linear. They fail to reduce the dimension of data sets where dependence between observed variables is non-linear. However, for numerous scientific, industrial and economic areas, it should be desirable to obtain a low-dimensional parametric representation of the data set. Model fitting is a way to obtain a usable representation of an observed phenomenon, but it requires expert knowledge about the phenomenon. Moreover, hidden relations between observables could be not revealed. Kohonen maps are shown to be an alternative techniques, able to map even strongly non-linear data sets [l]. Unfortunately, they have an a priori fixed shape and neighbourhood structure, thus their use requires some informations about the shape and the dimension of the underlying parameters space. We propose here a new self-organizing neural network, composed of two connections layers. The first one quantizes an input data set, and the second one progressively constructs the projected shape and neighbourhood on an output space of any chosen dimension. We illustrate the algorithm for various applications.