Applications of Graphical Clustering Algorithms in Genome Wide Association Mapping

Identifying large sets of unrelated individuals and unrelated markers

“…FastIndep has been used for finding unlinked markers in data sets with very complex Linkage Disequilibrium patterns such as [ 17 ] where the extent of Linkage Disequilbrium in the ancestral populations varies so much that there is no easy way to use map information alone to select a set of independent markers. Retaining all the markers in [ 17 ] for analyzing population stratification along the lines of STRUCTURE [ 18 ] leads to poor convergence, however the use of a maximal independent set of markers selected along the lines of [ 8 ] leads to much better results because the algorithm in [ 8 ] ignores map information in selecting markers. As an added feature, the randomized nature of the algorithm permits the generation of multiple different sets of markers which can be successively used in the analysis of population stratification to ensure that the final results are independent of the choice of the set of markers; this procedure has been followed in [ 17 ].…”

“…The current implementation of FastIndep is closely related to the one described in [ 8 ] for the purpose of selecting a large subset of unlinked markers for analyzing population stratification and will be briefly described below. The key idea behind the algorithm is to start with a deterministic greedy heuristic (which typically finds a reasonably large maximal independent set), and then randomize the heuristic in order to explore solutions close to the one found by the deterministic algorithm.…”

“…The FastIndep algorithm was first introduced for selecting unlinked markers for analyzing population stratification and was first discussed in [ 8 ]. FastIndep differs from the Primus software of [ 6 ] in a number of respects most notably in that the FastIndep algorithm is a stochastic greedy heuristic regardless of the size of the problem.…”