Self-organizing geometric certainty maps: a compact and multifunctional approach to map building, place recognition and motion planning

In this paper we show how a self-organizing Kohonen neural network can use hyperellipsoid clustering (HEC) to build maps from actual sonar data. Since the HEC algorithm uses the Mahalanobis distance, the elongated shapes (typical of sonar data) can be learned. The Mahalanobis distance metric also gives a stochastic measurement of a data point´s association with a node. Hence, the HEC Kohonen can be used to build topographical maps and to recognize its own topographical cites for self-localization. The number of nodes can also be regulated in a self-organizing manner by using the Kolmogorov-Smirnov (KS) test for cluster compactness. The KS test determines whether a node should be divided (mitosis) or pruned completely. By incorporating principal component analysis, the HEC Kohonen can handle problems with several dimensions (3D, time-series, etc.). The HEC Kohonen is also multifunctional in that it accommodates compact geometric motion planning and self-referencing algorithms. It can also be used to solve a host of other pattern recognition problems