Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The PageRank algorithm is used today within b information retrieval to provide a content-neutral ranking metric over b pages. It employs por method iterations to solve for the steady-state vector of a DTMC. The defining one-step probability transition matrix of this DTMC is derived from the hyperlink structure of the b and a model of b surfing behaviour which accounts for user bookmarks and memorised URLs.#R##N##R##N#  look to provide a more accessible, more broadly applicable explanation than has been given in the literature of how to make PageRank calculation more tractable through removal of the dangling-page matrix. This allows b pages without outgoing links to be removed before  employ por method iterations. It also allows decomposition of the problem according to irreducible subcomponents of the original transition matrix. Our explanation also covers a PageRank extension to accommodate TrustRank. In setting out our alternative explanation,  introduce and apply a general linear algebraic theorem which allows us to map homogeneous singular linear systems of index one to inhomogeneous non-singular linear systems with a shared solution vector. As an aside,  show in this paper that irreducibility is not required for PageRank to be ll-defined.
['Douglas Vincent de Jager', 'Jeremy T. Bradley']
I am writing a research paper on a idea PageRank: Splitting Homogeneous Singular Linear Systems of Index One
[{"from": "human", "value": "I am writing a research paper on a idea PageRank: Splitting Homogeneous Singular Linear Systems of Index One"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The PageRank algorithm is used today within b information retrieval to provide a content-neutral ranking metric over b pages. It employs por method iterations to solve for the steady-state vector of a DTMC. The defining one-step probability transition matrix of this DTMC is derived from the hyperlink structure of the b and a model of b surfing behaviour which accounts for user bookmarks and memorised URLs.#R##N##R##N#  look to provide a more accessible, more broadly applicable explanation than has been given in the literature of how to make PageRank calculation more tractable through removal of the dangling-page matrix. This allows b pages without outgoing links to be removed before  employ por method iterations. It also allows decomposition of the problem according to irreducible subcomponents of the original transition matrix. Our explanation also covers a PageRank extension to accommodate TrustRank. In setting out our alternative explanation,  introduce and apply a general linear algebraic theorem which allows us to map homogeneous singular linear systems of index one to inhomogeneous non-singular linear systems with a shared solution vector. As an aside,  show in this paper that irreducibility is not required for PageRank to be ll-defined."}]