Checking the projection display of multivariate data with colored graphs

Projection methods such as principal component analysis (PCA), nonlinear mapping (NLM), and the self-organizing map (SOM) are valuable algorithms for visualizing multidimensional data in a two-dimensional plane. Unfortunately, the reduction of the dimensionality involves distortions. In an attempt to graphically localize the distortions of the projected data, we suggest superposing colored graphs onto the 2D plots. The color of the edges of these graphs encodes the original high-dimensional distances between the connected points. The method is applied to a cluster analysis of 37 biologically active compounds and 471 molecules represented by a structural 3D descriptor.