Non-negative matrix factorization.

<p>Non-negative matrix factorization.</p

Learning models of protein evolution with NNMF.

<p>A schematic overview of the procedure.</p

NNMF basis matrices.

<p>The set of NNMF basis matrices obtained for ranks ranging from 1 to 5. Amino acids are ordered according to their Stanfel classification <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028898#pone.0028898-Stanfel1" target="_blank">[25]</a>. Rates are indicated in grayscale, with pure white being a rate of zero and pure black being the maximum rate in the matrix.</p

scores for all models.

<p>Each table entry is the number of datasets with in that range. For any dataset, the best model has . A model with has essentially no support.</p

NNMF basis matrices correlate with amino acid properties.

<p>The correlations between amino acid properties and the basis matrices. The horizontal black line (at −0.16867) indicates the threshold for significant negative correlation (, one tailed, ).</p

Interpretation of the matrix factorization in Figure 1.

<p>Interpretation of the matrix factorization in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028898#pone-0028898-g001" target="_blank">Figure 1</a>.</p

for all models with gamma rate variation (4 categories).

<p>Each table entry is the number of datasets with in that range. For any dataset, the best model has . A model with has essentially no support.</p

Distribution of the optimal number of basis matrices.

<p>The number of basis matrices that minimized the AICc across 50 test alignments.</p

Selecting the larger Pandit alignments.

<p>Each blue dot represents an alignment in the Pandit database. The green region covers the alignments used in the training set, and the thin red region covers those in the test set.</p

Convergence of NNMF.

<p>The sum of squared error decreases as more basis matrices are included.</p