Partitioning algorithms

Key Words Biological activity chemical features chemical space cluster analysis compound databases dimension reduction molecular descriptors molecule classification partitioning algorithms partitioning in low-dimensional spaces principal component analysis visualization. 

Key Words Biological activity chemical descriptors chemical spaces classification methods compound databases decision trees diversity selection partitioning algorithms space transformation statistics statistical medians. 

In chemoinformatics research, partitioning algorithms are applied in diversity analysis of large compound libraries, subset selection, or the search for molecules with specific activity (1-4). Widely used partitioning methods include cell-based partitioning in low-dimensional chemical spaces (1,3) and decision tree methods, in particular, recursive partitioning (RP) (5-7). Partitioning in low-dimensional chemical spaces is based on various dimension reduction methods (4,8) and often permits simplified three-dimensional representation of... 

We test the component for planarity. If it is planar, we encode it using one of the methods in Section 7. If it is not planar, we encode it using the partitioning algorithm of Section 1+. We use the codes for components as labels in the decomposition tree, and encode the tree (and thus the entire graph) using the method of Section 5. 

D. McDaniel and M. Devine. A modified Benders partitioning algorithm for mixed integer programming. Management Sci., 24(3) 312, 1977. 

Partitioning. In contrast to clustering techniques, partitioning algorithms do not rely on pair-wise molecular and distance comparison and can therefore be applied to very large compound source databases. Rather than comparing molecular positions,... 

Figure 1.21. Application of a statistical partitioning algorithm (median partitioning, MP) and cell-based partitioning (based on PCA) to virtually screen compound databases. Known active compounds (or baits ) are shown in back and candidate molecules in gray (adapted from Stahura and Bajorath 2004)...

Dutt S (1993) New faster Kernighan-Lin type graph-partitioning algorithms. In Proceedings of the 1993 IEEE/ACM international conference on computer-aided design, Santa Clara, CA, pp 370-377... 

First, it is useful to indicate that performing any of the LES of Table 11.1 twice on the same machine with the same number of processors, the same initial conditions and the same partition algorithm leads to exactly the same solution, Nmax and Nmean being zero to machine accuracy. In that sense, the LES remains fully deterministic. However, this is true only if the order of operations at interfaces is not determined by the order of message arrival so that summations are always carried out in the same order. Otherwise, the randomness induced by the non deterministic order of message arrival is enough to induce diverging solutions. 

Squared-error is one of the most common of all clustering criteria. Provided that the clusters are fairly spherical and are of approximately the same size, squared-error performs extremely well. Thus, in the absence of any prior information, squared-error is often a suitable choice for exploring a new data set. This explains why squared-error is fundamental to many partitioning algorithms like ISODATA (Ball and Hall, 1965) and K-MEANS (see Hartigan, 1975). It provides a compact, accurate measure of clustering... 

Theorem 5 is the basis of the Rectangle Partition algorithm that reduces mask decomposition to two classical graph-theoretical problems computing the number of connected components in a graph (to compute a and w) and computing the size of maximal independent set in the bipartite graph. 

PHASE applys a novel, tree-based partitioning algorithm to exhaustively identify spatial arrangements of functional groups that are common and essential to the... 

Zhu, F. and Agrafiotis, D.K (2007) Recursive distance partitioning algorithm for common pharmacophore identification. Journal of Chemical Information and Modeling, 47,1619-1625. 

Fig. 9.1 The diamonds plot the values of Xi versus Xg obtained from the simulated time series. The rectangles are the result of a partitioning algorithm (see the text). (From [1].)...

The inputs of both the hierarchical and the partitioning algorithms are the overall dissimilarities obtained at the panel level. We will also outline strategies of analysis where the input data are the individual (i.e. subjects) dissimilarity matrices. In this strategy of analysis, the aim is to obtain what is usually referred to as a consensus partition. That is, a partition that agrees as much as possible with the partitions given by the subjects. 

A.6 Partitioning Algorithm for Preemptive Goal Programs A.6.1 Linear Goal Programs... 

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