Vector comparison, pairwise

Vector comparison The DM must compare a set of p-dimensional vectors and specify the best, the worst, or the order of preference. (Note that this can be done by a series of pairwise comparisons.)... 

The problem lies in the model. The Euclidean distance calculation is inappropriate for use with correlated variables because it is based only on pairwise comparisons, without regard to the elongation of data point swarms along particular axes. In effect, Euclidean distance imposes a spherical constraint on the data set (18). When correlation has been removed from the data, (by derivation of standardized characteristic vectors) Euclidean distance and average-linkage cluster analysis return the three groups. 

Martin et al. [2] have developed a diversity measure that uses a combination of log P, topological indices, pairwise similarities calculated from Daylight fingerprints, and atom layer properties based on receptor recognition descriptors. Principal-components analysis and multidimensional scaling are used to produce a vector that is input to D-optimal design. Hassan et al. [34] use molar refractivity and calculated log P. Cummins et al. [30] use free energy of solvation in database comparisons. 

Once the pairwise comparisons are completed, the local priority vector is computed as the unique solution to ... 

The AHP divides a complex decision problem into a hierarchical system of decision elements. A pairwise comparison matrix of these elements is constructed, and then the normalized principal eigenvector is calculated for the priority vector, which provides a measure of the relative importance (weight) of each element. Consider the example in Nydick and Hill (1992), where four suppliers are evaluated based on the factors of quality, price, service, and delivery. 

Binary pairwise comparison The DM must compare a pair of two-dimensional vectors at each interaction. 

---