Self organizing MAPS: understanding, measuring and reducing variability

Abstract

In classification self-organizing maps is used as a generalisation of the K-means method including a neighbourhood organization between clusters. The correspondence between this clusters organization and the input proximity is called the topology preservation. The aim of this paper is to measure, reduce and understand variability of SOM. Considering the property of topology preservation, a local approach of variability (at an individual level) is preferred to a global one. A complementary visualising tool, called Map of Distances between Classes (MDC), is presented to complete this local approach relating variability to the complexity of the data’s intrinsic structure. It basically allows the main information to be extracted from a very large matrix of distances between Self-Organizing Maps’ classes. In the presence of a complex structure, it enlarges the information set, linking the variability of acceptable representations to the data structure complexity. To reduce variability, a stochastic method based on a bootstrap process aims to increase the reliability of the induced neighbourhood structure. The resulting (robust) map, called R-Map, is more robust relative to the sensitivities of the outputs to the sampling method and to some of the learning options of the SOM’ algorithm (initialisation and order of data presentation). This 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 perceived as the map, among the group of solutions, and corresponds to the most common interpretation of the data set structure. When an R-map can be perceived as the representative of a given SOM network, the relevance of the chosen network depends on R-map’s ability to adjust the data structure. As an application, a criterion to validate the network size is proposed comparing its ability of adjustment with SOM outputs of a larger network.