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Table 2.1 – Relationship to Langville and Meyer's PageRank notation. A Rosetta stone to translate my notation for readers familiar with Langville and Meyer’s popular book Google’s PageRank and Beyond. Their symbol a E G H L + S Our symbol d evT MT P ̄ T A x PT Discussion Our initiation to PageRank was through Kamvar’s papers in which d is the dangling node vector. We always make the matrix E explicit to emphasize its rank-1 structure. Here the G stands for the Google matrix. We use the application neutral M for the PageRank modified matrix. Langville and Meyer use the symbol H to suggest the hyperlink matrix without any sort of correction. We use P ̄ to suggest “P−” and that P ̄ needs an eventual correction to a stochastic matrix. Using A follows common notation in graph theory where A is the adjacency matrix; L hints at the link matrix. To keep consistent with solving linear systems (Ax = b) and eigenvalue problems (Ax = λx), we use x to denote the unknown PageRank variables in the problem. The symbol S suggests stochastic, whereas we use P to denote a standard Markov chain transition matrix. 2.4 ⋅ algorithms 23 must cope with matrices derived from such graphs. In this case, classic iter- ative algorithms for linear systems and eigenvectors actually perform well, partly because they use only one or two working vectors. In order to take advantage of additional structure in the strongly personalized PageRank prob- lem, we derive all the algorithms for a sub-stochastic matrix P ̄ and a graph. In terms of figure 2.2, this structure is why algorithms lie before the theory. To discuss specializations of these algorithms on the PageRank problem properly, we need one surprising preliminary discussion.PDF Image | Instagram Cheat Sheet
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