Data topology visualization for the Self-Organizing Map

The Self-Organizing map (SOM), a powerful method for data mining and cluster extraction, is very useful for processing data of high dimensionality and complexity. Visualization methods present different aspects of the information learned by the SOM to gain insight and guide segmentation of the data. In this work, we propose a new visualization scheme that represents data topology superimposed on the SOM grid, and we show how it helps in the discovery of data structure. 1 Visualization of SOM knowledge The Self-Organizing Map (SOM) [1] is a widely and successfully used neural paradigm for clustering and data mining. Informative representation of the learned SOM’s knowledge greatly aids precise capture of the cluster boundaries. This is especially important for high-dimensional and large data sets with many meaningful clusters such as in remote sensing or medical imagery, which often also have interesting rare clusters to be discovered. An impressive suite of previous works include the U-matrix [2] and its variants, which are useful when relatively large SOM grid accomodates small data sets with a low number of clusters (e.g., [3], [4], [5]) but, because of averaging of prototype distances over neighbours or thresholding, they tend to miss finer structure in complicated data [6]. Unique approaches such as [7] and gravitational methods (e.g., Adaptive Coordinates [4]) visualize distances between receptive field centres in innovative ways that greatly help manual cluster extraction. Experiments with automated colour assignments aim at qualitative exploration of the approximate cluster structure [8], [9], [10]. We point the reader to [4], [11] for more review. Some earlier methods use the size of the receptive fields of the prototypes for visualization (e.g., [5], [9]), but none exploit the data topology. Visualization of the mapping of samples, adjacent in data space, to different SOM prototypes is useful when prototypes outnumber data samples [12]. When data samples are plenty, adjacent samples mapped to different prototypes are only the ones at the boundaries of the Voronoi polyhedra, causing the visualization to ignore a lot of helpful mapping information. We visualize the data topology on the SOM grid, showing topology violations and effectively aiding in detailed cluster capture including fine structure in large real data with many clusters of widely varying statistics. ∗This work was partially supported by grant NNG05GA94G from the Applied Information Systems Research Program, NASA, Science Mission Directorate. Figures are in colour, request colour copy by email: [email protected], [email protected] ESANN'2006 proceedings European Symposium on Artificial Neural Networks Bruges (Belgium), 26-28 April 2006, d-side publi., ISBN 2-930307-06-4.