The flood algorithm—a multivariate, self-organizing-map-based, robust location and covariance estimator

Abstract

Self-organizing maps (SOMs) introduced by Kohonen (Biol. Cybern. 43(1):59---69, 1982) are well-known in the field of artificial neural networks. The way SOMs are performing is very intuitive, leading to great popularity and numerous applications (related to statistics: classification, clustering). The result of the unsupervised learning process performed by SOMs is a non-linear, low-dimensional projection of the high-dimensional input data, that preserves certain features of the underlying data, e.g.?the topology and probability distribution (Lee and Verleysen in Nonlinear Dimensionality Reduction, Springer, 2007; Kohonen in Self-organizing Maps, 3rd edn., Springer, 2001). With the U-matrix Ultsch (Information and Classification: Concepts, Methods and Applications, pp. 307---313, Springer, 1993) introduced a powerful visual representation of the SOM results. We propose an approach that utilizes the U-matrix to identify outlying data points. Then the revised subsample (i.e. the initial sample minus the outlying points) is used to give a robust estimation of location and scatter.