Multi-scale metrics and self-organizing maps: a computational approach to the structure of sensory maps

Abstract: This paper introduces the concept of a bi-scale metric for use in the cooperative phase of the self-organizing map (SOM) algorithm. Use of a bi-scale metric allows segmentation of the map into a number of regions, corresponding to anticipated cluster structure in the data. Such a situation occurs, for example, in the somatotopic maps which inspired the SOM algo- rithm, where clusters of data may correspond to body surface regions whose general structure is known. When a bi-scale metric is appropriately applied, issues with map neurons that are not activated by any point in the training data are reduced or eliminated. The paper also presents results of simulation studies on the plasticity of bi-scale metric maps when they are retrained af- ter loss of groups of map neurons or after changes in training data (such as would occur in a somatotopic map when a body surface region like a finger is lost/removed). The paper further considers situations where tri-scale met- rics may be useful, and an alternative approach suggested by neurobiology, where some map regions adapt more slowly to stimuli because they have a lower learning rate parameter.