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We present a strategy by which a Self-Organizing Map (SOM) with an underlying Binary Search Tree (BST) structure can be adaptively re-structured using conditional rotations. These rotations on the nodes of the tree are local and are performed in constant time , guaranteeing a decrease in the Weighted Path Length (WPL) of the entire tree. As a result, the algorithm, referred to as the Tree-based Topology-Oriented SOM with Conditional Rotations (TTO-CONROT), converges in such a manner that the neurons are ultimately placed in the input space so as to represent its stochastic distribution, and additionally, the neighborhood properties of the neurons suit the best BST that represents the data.

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.