Sammons

Pontiff, D., and J. Sammons, Theory, Design and Operation of an Environmentally managed Pit System, First International Symposium on Oil and Gas Exploration Waste Management Practices, pp. 997-987, 1990. 

G. Barker, A. Gadner, andD. Sammon, J. Electrochem. Soc. 113 (1966) 1182. 

Figure 15.5 Sammon map with SVM classification of drugs based on their volume of distribution (a) and plasma half-life (b) [95].

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

SAMMON A M (1998) Protease inhibitors and carcinoma of the esophagus. Cancer. 83 405-8. 

Ekins, S., Balakin, K.V., Savchuk, N. and Ivanenkov, Y. (2006) Insights for human efher-a-go-go-related gene potassium channel inhibition using recursive partitioning and Kohonen and Sammon mapping techniques. Journal of Medicinal Chemistry, 49,... 

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... 

Sammon s NLM is one form of multidimensional scaling (MDS). There exist a number of other MDS methods with the common aim of mapping the similarities or dissimilarities of the data. The different methods use different distance measures and loss functions (see Cox and Cox 2001). 

For comparison the same fatty acid data have been visualized by Sammon s NLM with parameter p set to 1 which makes a local mapping preserving well the small distances between objects (Figure 3.25, left). The NLM result shows a compact cluster of the fresh reference samples (class 6), and somewhat separated the desert sample (5). The horizontal map coordinate separates fresh samples from the high mountain samples (4) and the other samples (glacier samples, 2 lake samples, 3 and iceman samples, 1). The clustering has been indicated by manually drawn ellipses it is very similar as obtained with the scores of the PCI and PC2. Furthermore, Figure 3.25... 

FIGURE 3.25 Sammon s NLM with p— 1 (left) and Kohonen map (right) of fatty acid concentration data from mummies and reference samples. 

FIGURE 3.29 Sammon s NLM (p = 1) using the original scaled data (left) and the ILR transformed data (right). 

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