title: Pagerank vs SVD
body: <p><a href="http://en.wikipedia.org/wiki/PageRank" rel="noreferrer">Pagerank</a> works on the nodegraph of a series of pages and the directed edges formed by their respective inward and outward links. Thus the rank of a particular page is broadly a locally-induced effect in the nodegraph.</p>
  
  <p><a href="http://en.wikipedia.org/wiki/Singular_value_decomposition" rel="noreferrer">SVD</a>, on the other hand, works on a whole matrix of values, and has no directionality - a link between site A and site B would only register as a 1 on the correct matrix element. It is a global system, so ranking is a global effect.</p>
  
  <p>Given the extreme sparseness of web-derived matrices, I would expect SVD to be a bad performer here, as it requires a complete dataset, and has significant memory requirements.</p>
  
  <p>Is that true? Does Pagerank outdo SVD largely because it is a nodegraph-based algorithm? How can Pagerank infer semantic relevance from a page beyond the number of times a word is mentioned? Or would that be a second step, performed after Pagerank has ranked the pages?</p>