Hierarchical feature maps for non-linear component analysis

Based on earlier work on self-organizing maps with adaptive local neighborhood widths suitable for construction of principal manifolds, we propose an algorithm for hierarchical maps of heterogeneous high-dimensional data onto a structurally similar output space. Instead of a fixed output grid a network structure evolves that is locally orthogonal, but globally shaped by prominent data features. These features form principal manifolds in subspaces being determined by earlier hierarchical levels. The algorithm allows for an efficient separation of the interdependent learning tasks of acquiring optimal maps, learning parameters, and network structure