Partitioning median

Godden JW, Xue L, Bajorath J. Classification of biologically active compounds by median partitioning. J Chem Inf Comput Sci 2002 42 1263-9. 

Einally, LDPE SPMDs with grass carp lipid were exposed for 21 d to 14C-2,2, 5,5 -TCB, 14c-3,3, 4,4 -TCB, i c-mirex and i c-fenvalerate, whereas SPMDs with triolein or lecithin were exposed to only " C-2,2, 5,5 -TCB. After 21 d, the largest mass fraction of these test chemicals ( " C-mirex was an exception) was in the triolein. The C-2,2, 5,5 -TCB log triolein-water partition coefficient was 6.01, whereas the " C-2,2, 5,5 -TCB partition coefficients for the grass carp lipid-water and lecithin-water systems were 30% and 35% lower, respectively. Comparison of these data to literature log AlowS of 2,2, 5,5 -TCB showed that the partition coefficients for the grass-carp lipid and the lecithin were not significantly different from median values reported for the log ATow of " C-2,2, 5,5 -TCB. However, the partition coefficient of 2,2, 5,5 -TCB in triolein and water in direct... 

Godden J. W., Furr J. R., and Bajorath, J. (2003) Recursive median partitioning for virtual screening of large databases../. Chem. Inf. Comput. Sci. 43, 182-188. 

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

Median partitioning is another statistical method distinct from RR The development of this methodology was driven by the need to select representative subsets from very large compound pools. Hierarchical clustering techniques... 

Once a basis set of descriptor medians is obtained, MP proceeds in a stepwise manner. In each of n subsequent steps, molecules with a value of the particular descriptor above (or equal to) the median are assigned 1 and molecules with value below the median are assigned 0. For n descriptors, a total of 2" unique partitions are created, each of which is characterized by a unique /z-digit partitioning code (for example, 10 descriptors produce 1024 partitions). Ultimately, each test molecule falls into a unique partition and is assigned its signature code... 

Fig. 1. Median partitioning and compound selection. In this schematic illustration, a two-dimensional chemical space is shown as an example. The axes represent the medians of two uncorrelated (and, therefore, orthogonal) descriptors and dots represent database compounds. In A, a compound database is divided in into equal subpopulations in two steps and each resulting partition is characterized by a unique binary code (shared by molecules occupying this partition). In B, diversity-based compound selection is illustrated. From the center of each partition, a compound is selected to obtain a representative subset. By contrast, C illustrates activity-based compound selection. Here, a known active molecule (gray dot) is added to the source database prior to MP and compounds that ultimately occur in the same partition as this bait molecule are selected as candidates for testing. Finally, D illustrates the effects of descriptor correlation. In this case, the two applied descriptors are significantly correlated and the dashed line represents a diagonal of correlation that affects the compound distribution. As can be seen, descriptor correlation leads to over- and underpopulated partitions.

Here A(cp) is the number of successfully co-partitioned known actives (subsets of which may occur in different partitions) and P(pop) the number of populated partitions. The total number of populated median partitions serves as a measure of the diversity spread among database compounds (just as in diversity analysis, as discussed above). 

Re-calculate medians, re-initialize descriptor selection, and re-partition... 

Classification of Active Compounds by Median and Cell-Based Partitioning ... 

Descriptor median values naturally depend on the composition and size of compound databases. Whenever source databases are changed, reduced, or extended in size, descriptor medians need to be re-calculated to ensure accurate MP analysis. Relatively small changes in median values can significantly alter partitioning results. 

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)...

STN7 Erdmann, M.D. and Holt, J.A. (1991). Medians for intact human chorionic gonadotropin during second trimester of pregnancy (14 thru 20 wks) using automated radial partition immunoassay. Clin. Chem. 37, 940, Abstr. 146. 

Using Brine Shrimp Nauplii as Food for Test Animals in Aquatic Toxicology Using Octanol-Water Partition Coefficient to Estimate Median Lethal Concentrations for Fish Due to Narcosis... 

To compare the two criteria we examined 32 data sets where each data set has between 150 and 600 objects, split into 20 true clusters on the average. We applied simulated annealing partitional clustering 5 times to each set with both B(p) and W(p). We then compared the best test results for W(p) and B(p) over the 32 data sets. Table 1 shows for each data set the best Jaccard score for each of the criteria. In addition, for W(p) it shows the best number of clusters parameter k in 18, 19, 20, 21, 22. Similarly, for B(p) the table shows the best median distance parameter v in the set 2.0, 2.5, 3.0, 3.5, 4.0 and the associated number of clusters in the final partitioning. At the bottom of the table is the minimum, maximum, and mean of each column. 

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