Distance-preserving projection method

When computing the index of the closest unit to the input vector, the Euclidean distance was used. This is not a restriction, as one may use any type of distance. If there is only a dissimilarity (i.e., pseudo-metric) available, we need to create a space where a distance can be defined that preserves as much as possible the original dissimilarities. The techniques used for that purpose are the MDS methods described in a previous section. Since different data analysis methods display different properties of the data set, the most useful approach is to use several methods together. A possible combination is to first reduce the amount of data either by clustering or by the SOM, and then to display the reference vectors with some distance-preserving projection method, to gain additional insight. 

Four pairs of structures with identical descriptors merge at a distance of zero. From the chemist s point of view clustering appears more satisfying than the linear projection method PCA (with only 47.6% of the total variance preserved by the first two PCA scores). A number of different clustering algorithms have been applied to the 20 standard amino acids by Willet (1987). 

---