  Self Organizing Map (SOM) has been applied into several classical modeling
tasks including clustering, classification, function approximation and
visualization of high dimensional spaces. The final products of a trained SOM
are a set of ordered (low dimensional) indices and their associated high
dimensional weight vectors. While in the above-mentioned applications, the
final high dimensional weight vectors play the primary role in the
computational steps, from a certain perspective, one can interpret SOM as a
nonparametric encoder, in which the final low dimensional indices of the
trained SOM are pointer to the high dimensional space. We showed how using a
one-dimensional SOM, which is not common in usual applications of SOM, one can
develop a nonparametric mapping from a high dimensional space to a continuous
one-dimensional numerical field. These numerical values, called contextual
numbers, are ordered in a way that in a given context, similar numbers refer to
similar high dimensional states. Further, as these numbers can be treated
similarly to usual continuous numbers, they can be replaced with their
corresponding high dimensional states within any data driven modeling problem.
As a potential application, we showed how using contextual numbers could be
used for the problem of high dimensional spatiotemporal dynamics.
