wGMDH :: Initialization

Initialization

A pool of nodes is used to limit the search to a beam, rather than traversing the vast space of all possible solutions. We designate the pool at the i-th iteration as $S_{i}$ .

The nodes are organized in layers, starting from the 0-th layer consisting of the regressor nodes. By $N_{i}^{l}(N_{j}^{m},N_{k}^{m})$ , we designate the i-th node in the l-th layer, connected to nodes $N_{j}^{m}$ and $N_{k}^{m}$ as inputs. By $L_{i}$ , we denote the i-th layer, being defined as

$L_{i}=\left\{N_{1}^{i},N_{1}^{i},\cdots,N_{n}^{i}\right\}$

where n is the number of nodes per layer, i.e. the width of the beam.

The algorithm starts with the pool of nodes empty, and the zeroth layer, a layer of regressor nodes, existing outside the pool.

$S_{0}=\varnothing\newline L_{0}=\left \{ N_{1}^{0},N_{2}^{0},\cdots ,N_{K}^{0}\right \}$

Then it proceeds to the first iteration.

Algorithms