Nearest-neighbor selection

Plate 5. A snapshot of David GrifFeath s Stepping Stone CA. The rule is defined as follows. First, choose a number between 0 and 1 to set the update probability p for all sites. For each site i, generate a random number 0 < pi < 1 at each time step. If Pi > p, change the color of the site to that of one of its (four nearest) neighbors selected at random. In effect, the Stepping Stone rule has each site randomly eat one of its neighbors. See http //psoup.math.wisc.edu/. 

In the CVM, the free energy of a given alloy is approximated in terms of probabihties for a selected set of finite clusters. The largest cluster explicitly considered in the free energy functional specifies the level of the approximation. The common practice for an fcc-based system is the tetrahedron approximation [26] in which nearest neighbor tetrahedron cluster is taken as the largest cluster. Hence, within the tetrahedron approximation, the free energy expression, F,is symbolically expressed as... 

Dissimilarity-based compound selection (DECS) methods involve selecting a subset of compounds directly based on pairwise dissimilarities [37]. The first compound is selected, either at random or as the one that is most dissimilar to all others in the database, and is placed in the subset. The subset is then built up stepwise by selecting one compound at a time until it is of the required size. In each iteration, the next compound to be selected is the one that is most dissimilar to those already in the subset, with the dissimilarity normally being computed by the MaxMin approach [38]. Here, each database compound is compared with each compound in the subset and its nearest neighbor is identified the database compound that is selected is the one that has the maximum dissimilarity to its nearest neighbor in the subset. 

When applied to QSAR studies, the activity of molecule u is calculated simply as the average activity of the K nearest neighbors of molecule u. An optimal K value is selected by the optimization through the classification of a test set of samples or by the leave-one-out cross-validation. Many variations of the kNN method have been proposed in the past, and new and fast algorithms have continued to appear in recent years. The automated variable selection kNN QSAR technique optimizes the selection of descriptors to obtain the best models [20]. 

Zheng W, Tropsha A. Novel variable selection quantitative structure-property relationship approach based on the k-nearest-neighbor principle. J Chem Inf Comput Sci 2000 40(l) 185-94. 

A similarity-related approach is k-nearest neighbor (KNN) analysis, based on the premise that similar compounds have similar properties. Compounds are distributed in multidimensional space according to their values of a number of selected properties the toxicity of a compound of interest is then taken as the mean of the toxicides of a number (k) of nearest neighbors. Cronin et al. [65] used KNN to model the toxicity of 91 heterogeneous organic chemicals to the alga Chlorella vulgaris, but found it no better than MLR. 

Figure 6. Digital x-ray imaging of zeolite ZSM-5 (Si/Al 49,5) thin section a) bright-field STEM image, b) A1 x-ray image smoothed by averaging each pixel with its 8 nearest neighbors. The darker shading within the particle indicates higher A1 content. The circular field is due to the image of the selected area diffraction aperture.

The dielectric constant and refractive index parameters and different functions of them that describe the reactive field of solvent [45] are insufficient to characterize the solute-solvent interactions. For this reason, some empirical scales of solvent polarity based on either kinetic or spectroscopic measurements have been introduced [46,47]. The solvatochromic classification of solvents is based on spectroscopic measurements. The solvatochromic parameters refer to the properties of a molecule when its nearest neighbors are identical with itself, and they are average values for a number of select solutes and somewhat independent of solute identity. 

Another approach to explain tubule formation was taken by Lubensky and Prost as part of a general theoretical study of the relationship between orientational order and vesicle shape.173 These authors note that a membrane in an Lp/ phase has orientational order within the membrane which is lacking in the La phase. The clearest source of orientational order is the tilt of the molecules with respect to the local membrane normal The molecules select a particular tilt direction, and hence the local elastic properties of the membrane become anisotropic. A membrane might also have other types of orientational order. For example, if it is in a hexatic phase, it has order in the orientations of the intermolecular bonds (not chemical bonds but lines indicating the directions from one molecule to its nearest neighbors in the membrane). 

A parameter representing the number of nearest neighbors , K ( N), is selected. 

The distance methods operate differently. The classification of a test set member is based on the class assignment of the samples in the training set nearest to the unknowns. The type of distance used can differ but is usually the Euclidian distance, and the number of nearest neighbors is selected in advance. Usually the 3 to 5 nearest neighbors are selected and the possibility that the unknown may not be represented in the training sets is allowed. 

---