Add Support for User-Defined Reset Probability in Personalized PageRank Algorithm

[gzone0111]

Is your feature request related to a problem? Please describe.
Currently, the Personalized PageRank algorithm in Neo4j GDS only supports an equal reset probability for each source node. This limitation restricts the flexibility needed for applications where different importance or influence should be assigned to source nodes based on specific criteria or user-defined metrics.

Describe the solution you would like
I would like to request an enhancement to the Personalized PageRank algorithm to allow for user-defined reset probabilities for each source node. This would enable users to customize the influence of each source node in the random walk, thereby providing more tailored results based on their specific use cases.

[AlfredClemedtson]

Hi @gzone0111 and thank you for your feature request!

If you’re talking about the likeliness of the random walk restarting, then I don’t think it is possible since we don’t know the origin of a random walk due to its Markov nature.

However, you could obtain something similar by biasing some nodes so that random walks are more likely to be teleported to them, i.e. some biased version of personalized PageRank.

Do you think this would be useful for your case?

[gzone0111]

Hi @AlfredClemedtson ,

Thank you for your response regarding my feature request.

What I'm trying to achieve is to use a list of similarity scores for specific source nodes (a subset of all nodes in the database) ranging from [0, 1]. I want to personalize the PageRank by biasing the teleport probability for the random walk. As mentioned, the PageRank in GDS does not support reset probabilities. I know that one workaround is to first perform a random walk with restart, however, as noted in gds.graph.sample.rwr, it currently only supports uniform restart probabilities, which does not meet my requirements. Additionally, since I'm dealing with billions of nodes, every time I receive a change to the reset probabilities, I would need to redo the random walk, which is inefficient in my case.

If a biased version of Personalized PageRank can achieve this, could you please explain how to implement it? I need to run multiple PageRank calculations with different source node reset probabilities, and running graph projections can be time-consuming.

The ideal solution would allow for a biased PageRank that operates on a single projected graph.

Thank you!