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I would not be so skeptical. Yes, there is lots of research on random walk based recommender/ranking systems, including those similar to PageRank. Yes, spectral methods and linear algebra are researched for such problems very well. And a sparse matrix is a natural data structure for this problem, so you'd find many implementations that exploit it. But if ...


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So I think that it is important to realize that pagerank utilizes the eigenvalues of the nodes to speed up computation. The thing is that turns out to be equivalent to a random walk. Based on what you mentioned in your question it sounds like you are describing a random walk in your 4 part procedure. The fact that you are solving it using linear algebra ...


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