Examples of mixture components inferred from simulated data sets. Green circles show the true mixture components, red points the simulated data points that serve as the input to the algorithms, and blue X's the inferred mixture components. (a) A uniform mixture of three independent components with no noise. Each data point is a mixture of all three components. Inferred mixture fractions for the three components, averaged over all points, are (0.295 0.367 0.339). (b) A tree-embedded mixture of three components with noise equal to signal. Each data point is a mixture of a root component (top, labeled 1) and one of two leaf components (bottom, labeled 2 and 3). The inset shows the phylogenetic tree in which the labeled components are embedded. Inferred mixture fractions averaged over points in the two branches of the simplex are (0.410 0.567 0.025) and (0.410 0.020 0.535) (c) A tree-embedded mixture of five components with 10% noise. Each data point contains a portion of the root component (bottom, labeled 1), a subset contain portions of one of two internal components (far left, labeled 2, and far right, labeled 4), and subsets of these contain portions of one of two leaf components (center left, labeled 3, and center right, labeled 5). The inset shows the phylogenetic tree in which the labeled components are embedded. Inferred mixture fractions averaged over points in the two branches of the simplex are (0.356 0.462 0.141 0.006 0.005) and (0.387 0.072 0.008 0.187 0.378).
Schwartz and Shackney BMC Bioinformatics 2010 11:42 doi:10.1186/1471-2105-11-42