1 research outputs found
Self Organizing Maps Whose Topologies Can Be Learned With Adaptive Binary Search Trees Using Conditional Rotations
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