Mapping, non-linear

Forina M, Armanino C (1982) Eigenvector projection and simplified non-linear mapping of fatty acid content of Italian olive oils. Ann Chim [Rome] 72 127... 

Domine, D., Devillers, J., Chastrette, M., and Karcher, W. (1993). Non-linear mapping for structure-activity and structure-property modeling. J. Chemometrics 7, 227-242. 

Sammon, J.W. Jr., A non-linear mapping for data structure analysis, IEEE Trans. Comp., C-18,401-409,1969. 

The fourth method is a statistical method that uses multiple voice parameters and a non linear mapping to derive a quality measure via a training procedure on a training set... 

Foct, F 2 > AE, and Log P) were used in the cluster analysis. The results are shown in Fig. 3. This is a non-linear map of the descriptors in their four-dimensional space projected into two-dimensions. Nine different clusters can be identified. However, one cluster plus one member of a nearby cluster (the enclosed area within the map) contains all active compounds except for the 3-hydroxy nitroso-piperidine. That is, highly carcinogenic compounds cluster together while the "non-carcinogenic" cyclic nitrosamines are scattered about in the four-dimensional descriptor space. 

Principal component analysis (PCA) Cluster analysis Non-linear mapping Kohonen mapping... 

Large data tables may hide information which is not easily detected by simple inspection of the various columns. Principal component analysis and some closely related techniques such as factor analysis (FA), correspondence factor analysis (CFA) and non-linear mapping (NLM), reduce a data matrix to new supervariables retaining a maximum of information or variance from the original data matrix. These new variables are called latent variables or principal components, and are orthogonal vectors composed of linear combinations of the original variables. This concept is shown schematically in Fig. 22.15. 

Thus PCA may be used to filter out the most relevant information in a data set. Applications of variations of PCA, such as correspondence factorial analysis and non-linear mapping may have small advantages with particular data sets, but require expert support. 

Like PCA, non-linear mapping (NLM), or multidimensional scaling, is a method for visualizing relationships between objects, which in the medicinal chemistry context often are compounds, but could equally be a number of measured activities. It is an iterative minimization procedure which attempts to preserve interpoint distances in multidimensional space in a 2D or 3D representation. Unlike PCA however, the axes are not orthogonal and are not clearly interpretable with respect to the original variables. Nonlinear mapping has been used to cluster aromatic and aliphatic substituents. ... 

Fig. 22.17 Comparison of (a) principal components analysis, (b) non-linear mapping, (c) Ward s cluster analysis and (d) Kohonen mapping to display similarity of 15 substituents characterized by five para substituent constants (tt, F, R, MR and /.).

Another paper C296U deals with the recognition of seven metal ions (Cd, Ni, Co, Pb, Sb, Tl / Cu ). However, classifiers computed from synthetic polarograms did not work satisfactor ly on actual measured curves. A non linear mapping of the data showed that no compact clusters exist especially the patterns for Co, Cu, and Ni lie far outside of the clusters- Therefore, it is not surprising that the best classification result (79 % correct) was obtained by the KNN-method. 

An early application of a pattern recognition method to the prediction of olfactory qualities from physicochemical data was reported by Schiffman C2623. A set of 39 odorants was represented by 25 parameters (including Raman spectral information). Non-linear mapping revealed correlations of the chemical structure and smell. 

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