## Internal Generating and External Growing Cell Structures

Kohonen’s self organizing feature maps(SOFM) generate mappings from high-dimensional signal spaces to lower dimensional topological structures.Their main features are formation of topology preserving feature maps and approximation of the input probability distribution. However, SOFM have some drawbacks: e.g. a fixed number of neural units which makes them impractical for applications where the optimal number of units is not known in advance and a topology of fixed dimensionality which results in problems if this dimensionality does not match the dimensionality of the feature manifold.

Incremental artificial neural networks grow when they learn and shrink when they forget. Competitive Hebbian learning generates the network structure by addition and removal of cells and links. B. Fritzke introduced an incremental variable topology self organizing network, i. e., Growing Cell Structures(GCS) . The initial topology of GCS is a k-dimensional simplex(e.g., a line for k=1, a triangle for k=2, and a tetrahedron for k=3). During self-organization new cells will be added to the network and superfluous cells will be removed. The network must consist solely of k-dimensional simplices after each modification. Although the topology of GCS is much more flexible than that of the SOFM, the problem of fixed topology dimension remains.

Based on GCS and some ideas of J. Blackmore’s Incremental Grid Growing(IGG) neural network and J. Bruske’s Dynamic Cell Structures(DCS) we present here a new incremental self organizing neural network, i.e., Internal Generating and External Growing Cell Structures (IGEGCS). The goals are to overcome the fixed "simplex" structure of GCS, to speed up the convergency and to improve the topology preserving. The internal generating cell mechanism of IGEGCS takes place in the same way as in GCS for intrinsic maximum error nodes. For external growing cell from the boundary maximum error nodes there are two possibilities: Convex Weight External Growing and Concave Weight External Growings(see Figures as following). Depending upon whether internal generatings happen at the same time with external growing actions from the boundary maximum error nodes or whether they don't, there are three variations of IGEGCS: external growings only, external growings at the same time internal generatings happened, external growings at the same time disconnection between the boundary maximum error node and the langest distance node in its direct topology neighborhood(dtn) happened.The first results on two spirals problem show that IGEGCS is better than GCS in the topology preservings, the required number of cells and training epoches. Future works include further testing on IGEGCS with other benchmarks and its application in the fields of pattern classification and data visualization.

Left: Convex Weight External Growing, Right: Concave Weight External
Growing