Incremental grid growing: encoding high-dimensional structure into a two-dimensional feature map

Abstract

Knowledge of clusters and their relations is important in understanding high-dimensional input data with unknown distribution. Ordinary feature maps with fully connected, fixed grid topology cannot properly reflect the structure of clusters in the input space- there are no cluster boundaries on the map. Incremental feature map algorithms, where nodes and connections are added to or deleted from the map according to the input distribution, can overcome this problem. However, so far such algorithms have been limited to maps that can be drawn in 2-D only in the case of 2-dimensional input space. In the approach proposed in this paper, nodes are added incrementally to a regular, 2-dimensional grid, which is drawable at all times, irrespective of the dimensionality of the input space. The process results in a map that explicitly represents the cluster structure of the high-dimensional input.