Understanding and reducing variability of SOM neighbourhood structure

The self-organizing map (SOM) is a nonlinear unsupervised method for vector quantization. In the context of classification and data analysis, the SOM technique highlights the neighbourhood structure between clusters. The correspondence between this clustering and the input proximity is called the topology preservation. We present here a stochastic method based on bootstrapping in order to increase the reliability of the induced neighbourhood structure. Considering the property of topology preservation, a local approach of variability (at an individual level) is preferred to a global one. The resulting (robust) map, called R-map, is more stable relatively to the choice of the sampling method and to the learning options of the SOM algorithm (initialization and order of data presentation). The method consists of selecting one map from a group of several solutions resulting from the same self-organizing map algorithm, but obtained with various inputs. The R-map can be thought of as the map, among the group of solutions, corresponding to the most common interpretation of the data set structure. The R-map is then the representative of a given SOM network, and the R-map ability to adjust the data structure indicates the relevance of the chosen network.