As with the Combinatorial algorithm, the output variable must be
specified in advance by the person in charge of modeling, which
corresponds to the use of so-called explicit templates
[16,25]. In each layer, the F best models are used to successively
extend the input data sample.
In Multilayered Iterative (MIA) recurrent algorithm
the iteration rule remains unchanged from one layer to next. As
it shown the first layer tests the models, that can be derived from
the information contained in any two columns of the sample. The
second layer uses information from four columns; the third, from
any eight columns, etc. The exhaustive-search termination rule is
the same as for the Combinatorial
algorithm: in each layer the optimal models are selected by
the minimum of external
Output model: Yk+1 = d0
+ d1x1k + d2
x2k+ ... +dm xM
k xM-1 k
1 - data sampling;
2 - layers of partial
3 - form of partial
4 - choice of optimal
5 - additional
model definition by discriminating
F1 and F2 - number
of variables for data sampling extension.
MIA should be used when it is needed to handle a big number of
variables (up to 500). This algorithm also can be modified in such
way that at each layer a set of F best variables is selected and
at next layer only this variables are used. MIA may contain in some
cases the "multilayerness error" when effective variable are not
selected which is analogical to statistical error of control systems.
Multilayered GMDH algorithms can be used for solving of incorrect
and ill-defined modeling problems, i.e. in the cases when number
of observations is less than variables N < M. The regression analysis
methods are inapplicable in this case, because they give not possibility
to build the only model, which is adequate to process in this case.
Originally GMDH was proposed as addition to regression analysis
of two procedures:
1) for sets of model candidates generation: different algorithms
mainly differs one from another by the way of models candidates
2) for search of optimal model by external criterion.
Recent time two additional procedures are added:
3) preliminary handling of data sample by clusterization
algorithm. Initial data sample should be changed to the set of cluster
4) models received are used as active neurons in twice-multilayered
neuronet for additional increase
of modeling accuracy.