Graph Spectral Coefficient Initialization

[joneswong]

Hi, I noticed that the coefficient of the K-th order term is initialized in a way that is different from others. In one of my experiments, the learned coefficient of the K-th order term thus is much larger than others (alpha=0.1). Could you tell me why this is needed? Thanks!

GPRGNN/src/GNN_models.py

Line 36 in dc24683

TEMP[-1] = (1-alpha)**K

[elichienxD]

Hi @joneswong ,

This follows the original PPR formulation when truncated at step K. This makes the coefficient sum equal to 1. Note that in APPNA they also use this rule. More specifically:

$$ \sum_{k=0}^{K-1} \alpha (1-\alpha)^k + (1-\alpha)^K = \alpha\frac{1-(1-\alpha)^K}{1-(1-\alpha)} + (1-\alpha)^K = 1$$

Let me know if you have further questions.

Best,
Eli

[joneswong]

Thanks for your explanation! I just found that this works better than that multiplies $\alpha$ to the last term as previous terms.