Self Organizing Maps Whose Topologies Can Be Learned With Adaptive Binary Search Trees Using Conditional Rotations
This work addresses the need for more flexible and adaptive SOMs in machine learning, particularly for data clustering and visualization, but it is incremental as it builds on existing tree-based SOM variants.
The paper tackles the problem of enhancing Self-Organizing Maps (SOMs) by making their underlying tree topologies adaptive using Conditional Rotations (CONROT) to decrease Weighted Path Length, introducing Neural Promotion where neurons gain prominence based on significance. The result is the TTOCONROT algorithm, which converges to represent stochastic data distributions and optimize neighborhood properties, as confirmed by experiments on various datasets.
Numerous variants of Self-Organizing Maps (SOMs) have been proposed in the literature, including those which also possess an underlying structure, and in some cases, this structure itself can be defined by the user Although the concepts of growing the SOM and updating it have been studied, the whole issue of using a self-organizing Adaptive Data Structure (ADS) to further enhance the properties of the underlying SOM, has been unexplored. In an earlier work, we impose an arbitrary, user-defined, tree-like topology onto the codebooks, which consequently enforced a neighborhood phenomenon and the so-called tree-based Bubble of Activity. In this paper, we consider how the underlying tree itself can be rendered dynamic and adaptively transformed. To do this, we present methods by which a SOM with an underlying Binary Search Tree (BST) structure can be adaptively re-structured using Conditional Rotations (CONROT). These rotations on the nodes of the tree are local, can be done in constant time, and performed so as to decrease the Weighted Path Length (WPL) of the entire tree. In doing this, we introduce the pioneering concept referred to as Neural Promotion, where neurons gain prominence in the Neural Network (NN) as their significance increases. We are not aware of any research which deals with the issue of Neural Promotion. The advantages of such a scheme is that the user need not be aware of any of the topological peculiarities of the stochastic data distribution. Rather, the algorithm, referred to as the TTOSOM with Conditional Rotations (TTOCONROT), 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. These properties have been confirmed by our experimental results on a variety of data sets.