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 [12]. Let be the BMU of
vector . When a vector component *i* is varied by :

where is a unit vector along the *i*th 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 .

Tue May 27 12:40:37 EET DST 1997