SOM of SOMs.
This paper proposes an extension of the self-organizing map (SOM), in which the mapping objects themselves are self-organizing maps. Thus a "SOM of SOMs" is presented, which we refer to as a SOM(2). A SOM(2) has a hierarchical structure consisting of a single parent SOM and a set of child SOMs. Each child SOM is trained to represent the distribution of a data class in a manifold, while the parent SOM generates a self-organizing map of the group of manifolds modeled by the child SOMs. Thus a SOM(2) is an architecture that organizes a product manifold represented as (child SOM) x (parent SOM). Such a product manifold is called a fiber bundle in terms of the topology. This extension of a SOM is easily generalized to any combination of SOM families, including cases of neural gas (NG) in which, for example, " NG(2) (=NG x NG) as an NG of NGs" and "NG x SOM as a SOM of NGs" are possible. Furthermore, a SOM(2) can be extended to a SOM(n), such as SOM(3)=SOM x SOM x SOM defined as a "SOM of SOM(2)". In this paper, the algorithms for the SOM(2) and its variations are introduced, and some simulation results are reported.
Furukawa
Tetsuo
T
Department of Brain Science and Engineering, Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, Kitakyushu, Japan. furukawa@brain.kyutech.ac.jp
D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D007091:Image Processing, Computer-Assisted; D055641:Mathematical Concepts; D008606:Mental Processes / Q000502:physiology; D016571:Neural Networks, Computer; D009473:Neuronal Plasticity / Q000502:physiology; D010363:Pattern Recognition, Automated; D012371:Robotics