Geometric Image of Statistical Learning (Morphogenetic Neuron)

Abstract

We present a neural model called Morphogenetic Neuron. This model generates a geometric image of the data given by a table of features. A point in the n-dimensional geometric space is a set of the values of the attributes of the features. In each point we compute a value of a field by a linear superposition of the values of the attributes in the point. The coefficients of the linear superposition are the same for all the points and are invariant for any symmetric transformations of the geometric space. The morphogenetic neuron can compute the coefficients by data without recursive methods, to reproduce the wanted function by samples (classification , learning and so on) . Non-linear primitive functions cannot be represented in the morphogenetic geometric space. Primitive non-linear functions are considered as new coordinates for which the dimensions of the space are incremented. The geometry in general is non Euclidean and its structure is determined by the positions of the points in the space. The type of geometry is one of the main difference respects to the classical statistical learning and other neuron models. Connection between statistic properties and coefficients are founded.