Pangenome graph layout by Path-Guided Stochastic Gradient Descent

[Preprint]. 2023 Sep 23:2023.09.22.558964. [Version 1] doi: 10.1101/2023.09.22.558964

Algorithm 1: Pseudocode of PG-SGD in 1D.

\begin{matrix} PG - SGD (G) : \\ ∣ \begin{matrix} input : variation graph G = (V, E, P) \\ output : N - dimensional layout L with ∣ V ∣ nodes \\ X P \leftarrow PathIndex (G) ∕ ∕ for path position \\ lookup \\ L \leftarrow LayoutInitialization (V, N) \\ Z \leftarrow InitZip (G, X P) ∕ ∕ Zipfian distribution \\ for η i n a n n e a l i n g s c h e d u l e : \\ ∣ \begin{matrix} for each p l a n n e d t e r m u p d a t e : \\ ∣ \begin{matrix} s_{i} \leftarrow Unif (X P) ∕ ∕ uniform sampling of a \\ step from P \\ p \leftarrow Path (s_{i}, X P) ∕ ∕ path of s_{i} \\ if (c o o l i n g ‖ f l i p) then \\ ∣ \begin{matrix} s_{j} \leftarrow Unif (StepCount (p, X P)) ∕ ∕ uniform \\ sampling of a step from p \end{matrix} \\ else \\ ∣ \begin{matrix} s_{j} \leftarrow Zip (p) ∕ ∕ Zipfian sampling of a \\ step from p \end{matrix} \\ end \\ p_{i} \leftarrow StepPos (s_{i}) ∕ ∕ nuc . position \\ p_{j} \leftarrow StepPos (s_{j}) ∕ ∕ nuc . position \\ n d_{i j} \leftarrow ‖ p_{i} - p_{j} ‖ ∕ ∕ nuc . distance \\ l d_{i j} \leftarrow ‖ l_{i} - l_{j} ‖ ∕ ∕ layout distance \\ w_{i j} \leftarrow \frac{1.0}{n d_{i j}} ∕ ∕ term weight \\ μ \leftarrow w_{i j} η ∕ ∕ learning rate \\ if μ > 1 : \\ ∣ μ \leftarrow 1 \\ end \\ δ \leftarrow μ \cdot \frac{l d_{i j} - n d_{i j}}{2} ∕ ∕ the actual delta \\ if a b s (δ) < = 0 then \\ ∣ S T O P ∕ ∕ {we can}^{'} t optimize more \\ r \leftarrow δ - l d_{i j} ∕ ∕ size of the update \\ l_{i} \leftarrow l_{i} + r \cdot l d_{i j} ∕ ∕ update v_{i} coordinates \\ l_{j} \leftarrow l_{j} - r \cdot l d_{i j} ∕ ∕ update v_{j} coordinates \end{matrix} \\ end \end{matrix} \\ end \end{matrix} \\ end \end{matrix}