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

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.