An instantaneous topological mapping model for correlated stimuli

Topology-representing networks, such as the SOM and the growing neural gas (GNG) are powerful tools for the adaptive formation of maps of feature and state spaces for a broad range of applications. However, these algorithms suffer severe difficulties when their training inputs are strongly correlated. This makes them unsuitable for the online formation of maps of state spaces whose exploration occurs most naturally along trajectories, which is typical in many applications in the fields of robotics and process control. Based on investigations of the SOM and the GNG for these cases, we devise a new network model, the “instantaneous topological map” (ITM) that is able to overcome these difficulties and form maps from strongly correlated stimulus sequences in a fast and robust manner. This makes the ITM highly suitable for mapping of state spaces in control tasks in general and especially in robotics, where workspace limitations are complex and probably more easily explored than analyzed and coded by hand