Transition model & Ranking model

take simple transition data as an example :

• From A to {B, C, D}
• From B to {A, D}
• From C to {A}
• From D to {B, C}

It able to build web to web traffic flow, you can think it is web preference (voting), the most vote it can make + the most vote it got --> high PageRank

I assume at the beginning all page (URL) got the same PageRankresult, and use webpage's relation, to convert real PageRank.

In the real product, we should combine more factors to decide PageRank. Here, I only use web relationship to provide one factor.

PageRank1 = Transition x PageRank0

From math :

• Using transition fact (from A to B ... etc), to generate transition matrix
• Using default PageRankdefine to generate PageRankmatrix
• PageRank1 = Transition x PageRank0 (converge to find stable value)

Via MapReduce :

• handle big matrix calculation by distributed system
• make transition matrix cell * pagerank matrix cell

MapReduce Process :

• Use web relation to generate Mapper out, with another page rank mapper output <web, pr_val>, reducer will get 2 type of inputs (from 2 different mapper<page, b=1/3, c=1/3, d=1/3, 1/4>), need to parse first then make multiplication. reducer output format <page, transition cell * PageRank cell>
• Use another MapReduce, to sum up each cell (the same key)