Sammon nonlinear maps

Figure 13.6 Distributions of VGIC-specific ligand groups within the Sammon nonlinear map Calcuim channel antagonists (white circles, 1611 cmpds) potassium channel agonists and antagonists (gray circles, 1057 cmpds) sodium channel antagonists (black circles, 190cmpds) [137].

Sammon JE. A nonlinear mapping for data structure analysis. IEEE Trans Comput 1969 C-18 401-9. 

Nonlinear mapping (NLM) as described by Sammon (1969) and others (Sharaf et al. 1986) has been popular in chemometrics. Aim of NLM is a two-(eventually a one- or three-) dimensional scatter plot with a point for each of the n objects preserving optimally the relative distances in the high-dimensional variable space. Starting point is a distance matrix for the m-dimensional space applying the Euclidean distance or any other monotonic distance measure this matrix contains the distances of all pairs of objects, due. A two-dimensional representation requires two map coordinates for each object in total 2n numbers have to be determined. The starting map coordinates can be chosen randomly or can be, for instance, PC A scores. The distances in the map are denoted by d t. A mapping error ( stress, loss function) NLm can be defined as... 

An overall picture of similarity between [C4CiIm][PFg] and conventional solvents is given by the so-called nonlinear map, or Sammon map [20] in Figure 9.5. The closer the points representing solvents on the map, the more similar the solvents are. As is seen, the position of the IL on the map is between esters and aromatic hydrocarbons. 

Agrafiotis [60] has also developed a simulated annealing method for maximising diversity. The method employs a user-defined objective function and can therefore be tailored to encode different selection criteria. The results of subset selection can be visualized using Sammon s nonlinear mapping algorithm [61]. 

The most popular nonlinear display method was proposed by Sammon C401l and is called nonlinear mapping (NLH). The technique seeks to conserve interpoint distances. Let be... 

Another nonlinear mapping method, the Sammon s mapping, is closely related to the metric MDS. The only difference is that the errors in distance preservation are normalized with the distance in the original space. Thus, preservation of small distances is emphasized. The error function is defined as... 

PCA is not the only projection method that can be used. Various types of nonlinear projections have been employed, e.g., Sammon mapping and nonlinear PCA [80], and several software packages can be used to graphically visualize library distributions and aid compound selection [81]. 

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