Self-organizing hierarchical feature maps

Abstract

The topological feature map (TFM) algorithm introduced by T. Kohenen (1982) implements two important properties: a vector quantization (VQ) and a topology-preserving mapping. A tree-structured TFM (TSTFM) is presented as a computationally inexpensive alternative to the TFM algorithm. The computational complexity of the TSTFM is <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O </e1> (log <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</e1> ) rather than <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</e1> ( <e1 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</e1> ) for the TFM. In addition, the TSTFM has some new properties that prove to be useful for VQ and in the context of visual perception: increased performance in VQ compared to the tree-structured VQ of A. Buzo et al. (1980) and hierarchical mapping of code vectors