A granular computing framework for self-organizing maps

Abstract

When using granular computing for problem solving, one can focus on a specific level of understanding without looking at unwanted details of subsequent (more precise) levels. We present a granular computing framework for growing hierarchical self-organizing maps. This approach is ideal since the maps are arranged in a hierarchical manner and each is a complete abstraction of a pattern within data. The framework allows us to precisely define the connections between map levels. Formulating a neuron as a granule, the actions of granule construction and decomposition correspond to the growth and absorption of neurons in the previous model. In addition, we investigate the effects of updating granules with new information on both coarser and finer granules that have a derived relationship. Called bidirectional update propagation, the method ensures pattern consistency among data abstractions. An algorithm for the construction, decomposition, and updating of the granule-based self-organizing map is introduced. With examples, we demonstrate the effectiveness of this framework for abstracting patterns on many levels.