The elastic net formed by the SOM in the input space can be interpreted as an implicit lookup model of the phenomena that produced the training data. The lookup model can be used e.g. for sensitivity analysis . Let be the BMU of vector . When a vector component i is varied by :
where is a unit vector along the ith axis, the BMU changes to another map unit . Calculating gives the response of the model to the change. The quantization error can be used to estimate the reliability of the result.
If the idea of elastic net is taken a bit further the precision of the model can be increased. Let i be the BMU of a sample vector . From the neighbors of unit i, find the next best-matching unit j, and finally from units find the unit k closest to the sample vector. The three map units are adjacent and together define a plane in the input space. By calculating the projection of on that plane, a closer approximation of than the best-matching reference vector is obtained:
where is the unit-length normal vector of the plane. To ensure continuity of the projection, the must be constrained to be within the triangle .