Proximity measures

Once a proximity measure has been computed for all of the molecules, basically two paths exist for determining a lower-dimensional coordinate-based... 

The lower path is somewhat more complicated. The first step in the path involves either PCA (83) or principal-coordinate analysis (PCO) (83). This step can be followed by optimization of a function that minimizes the error between the proximity measure computed in the reduced-dimension and full coordinate systems if desired. Xie et al. (84) recently published an interesting paper along these lines. Kruscal stress (79) is a widely used function in this regard... 

An important question is whether the proximity measures are compatible with those of these references addresses the important issue of whether the proximity measure is compatible with embedding in a Euclidean space. For example, satisfying the distance axioms does not in itself guarantee that any distance matrix associated with a given set of molecules be compatible as the distance axioms are still satisfied in a non-Euclidean space. Gower has written extensively on this important issue, and his work should be consulted for details (89-91). Benigni (92), and Carbo (67) have also contributed interesting approaches in this area. 

The term proximity is used here to include similarity and dissimilarity coefficients in addition to distance measures. Individual proximity measures are not defined in this review full definitions can be found in standard texts and in the articles by Barnard, Downs, and Willett.We now define the terms centroid and square-error, because they will be used throughout this chapter. For a cluster of s compounds each represented by a vector, let x(r) be the rth vector. The vector of the cluster centroid, x(c), is then defined as... 

Further types of atomic features could also be considered, together with other proximity measures and weighting schemes. Among the eigenvalues obtained from each of these matrices, the highest and the lowest have been demonstrated to reflect relevant aspects of molecular structure, and are therefore useful for similarity searching. 

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The response time of an electrode describes the ion-selective electrode s sensitivity to ion activity changes. The response time is a sensitive parameter defined as the time taken by the experimental setup to reach a chosen percent of the final cell voltage following a given change in the activity of the primary ion. This definition is specific to a given experimental setup as the time response of the micropipette will vary with the type of micropipette used, the particular experimental conditions, the electronics, and the method used to cause the primary ion activity change. In terms of macro ion-selective electrode, common response times would be on the order of seconds (56, p. 70) while for ion-selective micropipettes, response times on the order of 10 ms have been reported (60). The response time of the electrode is of particular interest when close proximity measurements are made. 

Due to the high standard deviations reported above, a cluster analysis was carried out based on 5 variables representing the most important statements towards contracting contr 1-5). Euclidian Distance serves as proximity measure. The optimal number of clusters is first defined using Ward method. A four cluster solution is chosen based on scree test, dendrogram and plausibility considerations. In order to refine this solution in a second step, a K-means cluster analysis is conducted. 

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