U*-Matrix: a tool to visualize clusters in high dimensional data

Abstract

Emergent self organizing feature maps (ESOM) may be regarded as self organized, topology preserving projections of high dimensional data onto a two dimensional map. On top of this ordered floor space an U-Matrix gives insights into the local distance structures of the data set. Using the ESOM/U-Matrix methods for clustering has the advantage of a nonlinear disentanglement of complex cluster structures. Distances inside a cluster are, however, depicted in the same manner as distances between different clusters on an U-Matrix. This may prevent the detection of clusters in some data sets. This is demonstrated on a data set from tumor research. An enhancement of the U-Matrix by taking density information into account is proposed. This leads to a new visualization tool, called U*-Matrix. The U*-Matrix of the tumor data shows structures compatible with a clustering of the data by other algorithms. The combination of distance and density information is expected to be very useful for data mining and knowledge discovery.