Graph Based Representations of Density Distribution and Distances for Self-Organizing Maps

The self-organizing map (SOM) is a powerful method for manifold learning because of producing a 2-D spatially ordered quantization of a higher dimensional data space on a rigid lattice and adaptively determining optimal approximation of the (unknown) density distribution of the data. However, a postprocessing visualization scheme is often required to capture the data manifold. A recent visualization scheme CONNvis, which is shown effective for clustering, uses a topology representing graph that shows detailed local data distribution within receptive fields. This brief proposes that this graph representation can be adapted to show local distances. The proposed graphs of local density and local distances provide tools to analyze the correlation between these two information and to merge them in various ways to achieve an advanced visualization. The brief also gives comparisons for several synthetic data sets.