Credible visualizations for planar projections

Abstract

Planar projections, i.e. projections from a high dimensional data space onto a two dimensional plane, are still in use to detect structures, such as clusters, in multivariate data. It can be shown that only the subclass of focusing projections such as CCA, NeRV and the ESOM are able to disentangle linear non separable data. However, even these projections are sometimes erroneous. U-matrix methods are able to visualize these errors for SOM based projections. This paper extends the U-matrix methods to other projections in form of a so called generalized U-matrix. Based on previous work, an algorithm for the construction of generalized U-matrix is introduced, that is more efficient and free of parameters which may be hard to determine. Results are presented on a difficult artificial data set and a real word multivariate data set from cancer research.