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The damping factor is subtracted from 1 (and in some variations of the algorithm, the result is divided by the number of documents (N) in the collection) and this term is then added to the product of the damping factor and the sum of the incoming PageRank scores. That is,
Fig.1. Google matrix of Wikipedia articles network, written in the bases of PageRank index; fragment of top 200 X 200 matrix elements is shown, total size N=3282257 (from [1]) A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links between pages.
Comparison of damping factors for a solid state amplifier (Luxman L-509u) and a tube amplifier (Rogue Atlas) In typical solid state and tube amplifiers, the damping factor varies as a function of frequency. In solid state amplifiers, the damping factor usually has a maximum value at low frequencies, and it reduces progressively at higher ...
Numeric examples of PageRank values in a small graph with a damping factor of 0.85. The exact solution is: = ... Page Rank; Usage on bn.wikipedia.org
In "Damping Factor", after the two formulas, it states, "The difference between them is that the PageRank values in the first formula sum to one, while in the second ...
The (non-negative) damping factor is adjusted at each iteration. If reduction of S {\displaystyle S} is rapid, a smaller value can be used, bringing the algorithm closer to the Gauss–Newton algorithm , whereas if an iteration gives insufficient reduction in the residual, λ {\displaystyle \lambda } can be increased ...
The logarithmic decrement can be obtained e.g. as ln(x 1 /x 3).Logarithmic decrement, , is used to find the damping ratio of an underdamped system in the time domain.. The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5; it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped.
Unlike PageRank, the edges are typically undirected and can be weighted to reflect a degree of similarity. Once the graph is constructed, it is used to form a stochastic matrix, combined with a damping factor (as in the "random surfer model"), and the ranking over vertices is obtained by finding the eigenvector corresponding to eigenvalue 1 (i ...