Growing a hypercubical output space in a self-organizing feature map

Abstract

Neural maps project data from an input space onto a neuron position in a (often lower dimensional) output space grid in a neighborhood preserving way, with neighboring neurons in the output space responding to neighboring data points in the input space. A map-learning algorithm can achieve an optimal neighborhood preservation only, if the output space topology roughly matches the effective structure of the data in the input space. We here present a growth algorithm, called the GSOM or growing self-organizing map, which enhances a widespread map self-organization process, Kohonen's self-organizing feature map (SOFM), by an adaptation of the output space grid during learning. The GSOM restricts the output space structure to the shape of a general hypercubical shape, with the overall dimensionality of the grid and its extensions along the different directions being subject of the adaptation. This constraint meets the demands of many larger information processing systems, of which the neural map can be a part. We apply our GSOM-algorithm to three examples, two of which involve real world data. Using recently developed methods for measuring the degree of neighborhood preservation in neural maps, we find the GSOM-algorithm to produce maps which preserve neighborhoods in a nearly optimal fashion.

An Efficient Initialization Scheme for SOM Algorithm Based on Reference Point and Filters

“…Several research papers [1], [3], [14], [19], [21] have attempted to shorten the processing time of SOM. Kohonen originally identified three speedup approaches, namely, Shortcut Winner Search, Increasing the Number of Units in SOM, and Smoothing [8].…”

Cluster Analysis of Cortical Pyramidal Neurons Using SOM

“…Yet, this topographic mapping can not be achieved for any data-lattice-configuration. Growing variants of SOM (GSOM) try to adapt the edge length ratio as well as the dimensionality of the lattice to result a topographic map [12].…”

Extensions and Modifications of the Kohonen-SOM and Applications in Remote Sensing Image Analysis

“…5 The ¿rst approach to inÀuence the magni¿cation of a learning vector quantizer, proposed in [12] is called the mechanism of conscience. For this purpose a bias term is added in the winner rule (1):…”

“…The corresponding learning scheme can easily be implemented into the standard learning rule. A growing SOM (GSOM) approach was developed to generate a guaranteed topology preserving mapping in a simple hypercube structure of the lattice [5]. Both the GSOM and magni¿cation control approaches were shown to be powerful instruments for visualization and classi¿cation of remote sensing spectral data.…”