A map determination method and apparatus for calculating the coefficients to give a minimum evaluation function quickly and reliably where a map is expressed as the linear sum of a function g.sub.i (X) and a coefficient c.sub.i while a map for transforming a N-dimensional vector (x.sub.0, x.sub.1, x.sub.2, x.sub.3) to a M-dimensional vector y is being decided. The coefficient ci for the map is obtained by giving a learning sample and a teaching sample, obtaining an evaluation function and solving a simultaneous linear equation for which the partial differential is zero.