Self-Organizing Map with Generating and Moving Neurons in Visible Space

Abstract

Kohonen's Self-Organizing feature Map (SOM) is used to obtain topology-preserving mapping from high-dimensional feature space to visible space of two or fewer dimensions. The SOM algorithm uses a fixed structure of neurons in visible space and learns a dataset by updating reference points in feature space. The mapping result depends on mapping parameters fixed, which are the number and visible positions of neurons, and parameters of learning, which are the learning rate, total iteration, and the setting of neighboring radii. To obtain a satisfactory result, the user usually must try many combinations of parameters. It is wasteful, however, to set up every possible combination of parameters and to repeatedly run the algorithm from the beginning because the computation cost for learning is large, especially for a large-scale dataset. These problems arise due to the fixing of two types of mapping parameters, i.e., the number and visible positions of neurons. The high computation cost is mainly in the calculation of distances from each sample to all reference points. At the beginning of learning, reference points should be adjusted globally to preserve the topology well because they are initially set far from optimal positions in feature space, e.g. randomly. Such many reference points subdivides feature space into unnecessarily fine Voronoi regions. To avoid this computational waste, it is natural to start learning with a small number of neurons and increase the number of neurons during learning. We propose a new SOM method that varies the number and visible positions of neurons, and thus is applicable also to visible torus and sphere spaces. We apply our proposal to spherical visible space. We use central Voronoi tessellation to move visible positions for two reasons: to tessellate visible space evenly for easy visualization and to level the number of neighboring neurons and better preserve topology. We demonstrate the effect of generating neurons to reduce computation cost and of moving visible positions in visualization and topology preservation.