Figure S3. Convergence of bNMF algorithm tested with simulated data sets.

Two factor matrices W and H with dimensions 100 × 5 and 5 × n (n = 10, 100, and 1,000) were generated by sampling their elements from gamma priors $\text{Pr}\left(w\right)\sim w^{a_w-1}{e}^{-a_{w}w/b_w}$ and $\text{Pr}\left(h\right)\sim h^{a_h-1}{e}^{-a_{h}h/b_h},$ such that $\text{E}\left(w\right)=b_w,$ $\text{E}\left(h\right)=b_h,$ and $a_w$, $a_h$ control variances. The hyperparameters were set as $a_w=a_h=0.1$ and $b_w=b_h=1$. (A, B) With increasing sample sizes, log evidence becomes increasingly narrower, peaked at rank 5. (C, D) Distribution of optimal rank over 200 realizations of matrices under n = 10 and 100 (n = 1,000 is similar to (D)). (E, F) Distributions of converged hyperparameters.