Multidimensional mapping

Streich, W.J., Dove, S. and Franke, R. (1980). On the Rotational Selection of Test Series. 1. Principal Component Method Combined with Multidimensional Mapping. JMed.Chem.,23,1452-1456. 

Bader, G.D., Heilbut, A., Andrews, B., Tyers, M., Ughes, T., and Boone, C. 2003. Functional genomics and proteomics Charting a multidimensional map of the yeast cell. Trends Cell Biol. 13,344-356. 

Fig. 2.4. Example of the choice of substituents by multidimensional mapping (from Wootton et at. 1975, copyright (1975) American Chemical Society).

Williamson, J.R. (1996). Gaussian ARTMAP A neural network for fast incremental learning of noisy multidimensional maps. Neural Networks, 9,881-897. 

The Kohonen network or self-organizing map (SOM) was developed by Teuvo Kohonen [11]. It can be used to classify a set of input vectors according to their similarity. The result of such a network is usually a two-dimensional map. Thus, the Kohonen network is a method for projecting objects from a multidimensional space into a two-dimensional space. This projection keeps the topology of the multidimensional space, i.e., points which are close to one another in the multidimensional space are neighbors in the two-dimensional space as well. An advantage of this method is that the results of such a mapping can easily be visualized. 

The case of multidimensional discrete-time mappings of the form... 

Wagner, K., Miliotis, T., Marko-Varga, G., Bischoff, R., Unger, K.K. (2002). An automated online multidimensional HPLC system for protein and peptide mapping with integrated sample preparation. Anal. Chem. 74, 809-820. 

---