Non‐linear mapping for structure‐activity and structure‐property modelling

Abstract

SUMMARYFrom a review of the theoretical aspects of non-linear mapping and the different algorithms available in the literature, the methodological and practical problems linked to the use of this multivariate method in structure-activity and structure-property relationship studies are underlined. Useful tools for the graphical display of the outputs and the interpretation of the obtained clusters are presented. Statistical parameters estimating the quality of the graphical representation of each individual are also introduced. An example of application on a data matrix of 37 acaricides described by four physicochemical descriptors (T, F, R, M R ) is presented.

ART 2-A for Optimal Test Series Design in QSAR

“…A full analysis of the ART 2-A results and comparison with previously published results using different techniques was performed by inspecting the numerical outputs and using graphical display techniques such as nonlinear mapping. 41 Figure 3 illustrates for five different values of the vigilance parameter (F max ) the number of clusters formed versus the number of cycles required for convergence with ART 2-A. It is noteworthy that in all cases convergence was obtained after approximately 10 epochs.…”

A non-linear mapping-based generalized backpropagation network for unsupervised learning

“…The Euclidean counterparts of equations (13) and (14) can be found in Domine's review. 16 The Manhattan city block distance also contributes to a convenient initialization of the network parameters, to be discussed later.…”

“…The network parameters are adjusted in such a way as to minimize the selected criterion E subject to the non-linear constraints of the network dynamics (equations ( Equations (18) and (19) cannot be solved analytically. According to the analytical solutions of equations (16) and (17) …”

“…16 Many of these NLM approaches (iterative techniques) are subject to the drawback that, having mapped a finite set of samples to a display space, it is not a straightforward matter to map a new, unclassified sample in a consistent manner. Some parametric techniques based on basis function and distance transformation have been proposed to remedy this defect.…”

Supervised cluster classification using the originaln-dimensional space without transformation into lower dimension

“…The k-nearest-neighbor (KNN) technique [1] and soft independent modeling of class analogy (SIMCA) [2] are examples. The drawbacks of this class of methods [3], although still actively in use today, motivated many chemometricans to invent another class of methods to perform supervised cluster analysis [4][5][6][7][8]. This class has a common principal task of reducing the dimensionality of the original measurement space to three or two dimensions to allow human vision to recognize the patterns.…”