In this paper we propose a strategy, the Tree-based Topology-Oriented SOM (TTO-SOM) by which we can impose an arbitrary, user-defined, tree-like topology onto the codebooks. Such an imposition enforces a neighborhood phenomenon which is based on the user-defined tree, and consequently renders the so-called bubble of activity to be drastically different from the ones defined in the prior literature. The map learnt as a consequence of training with the TTO-SOM is able to infer both the distribution of the data and its structured topology interpreted via the perspective of the user-defined tree. The TTO-SOM also reveals multi-resolution capabilities, which are helpful for representing the original data set with different numbers of points, whithout the necessity of recomputing the whole tree. The ability to extract an skeleton, which is a “stick-like” representation of the image in a lower dimensional space, is discussed as well. These properties have been confirmed by our experimental results on a variety of data sets.

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Series Advances in Intelligent and Soft Computing
Astudillo, C.A. (César A.), & Oommen, J. (2009). A novel self organizing map which utilizes imposed tree-based topologies. Advances in Intelligent and Soft Computing.