6533b81ffe1ef96bd1276fcb

RESEARCH PRODUCT

Tree Structured Self-Organizing Maps

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Publisher Summary This chapter provides an overview of the tree structured self-organizing maps (TS-SOM). It was originally intended as a fast implementation of the self-organizing map (SOM). The chapter explains that TS-SOM is a constructive smoother for a class of dimension reduction problems. There is a well known relation between self-organizing maps and principal curves. Unfortunately in most presentations it is derived by simple reasoning, avoiding the mathematical statement of the problem, which is essential to understand how efficient SOM implementations can be constructed. In this chapter, SOM is derived as a numerical solution of a generic model in a continuous domain, which differs from the ad hoc way of constructing neural networks. It is then shown that many variations of the SOM are just different numerical implementations, including generative models, which leads to the derivation of the TS-SOM algorithm.