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The PAGE climbing algorithm is a procedure a quantity of verlinkter documents, as for example the World Wide Web to evaluate on the basis its structure and/or to weights. A weight, which PAGE-climb, is assigned to each element due to the linking structure. The algorithm became of Larry PAGE (therefore it the name PAGE-climb) and Sergey Brin to the Stanford University develops and patented by this. It served Google, by Brin and PAGE created the enterprise, as basis for the evaluation on the part of.

The basic principle reads: The more left on a side, is the higher the weight of this side refers. The higher the weight of the referring sides is, the more largely is the effect. The PAGE climbing algorithm copies a user coincidentally surfenden by the net. The probability, with which this discovers a web page, correlated with PAGE-climb.

The PAGE climbing algorithm

Principle PAGE climbing algorithm is that each side weight (PAGE-climb) possesses, which is the larger, the refers more sides with a high own weight to this side. The weight PR_i of a side i computes itself thus from the weights PR_j of the sides J. linking on i linked j on altogether C_j different sides, then the weight is divided by R_j proportionately on these sides. The following recursive formula can be regarded as definition of the PAGE climbing algorithm:

P \! R_i = \ frac {1-d} {N} + D \, \ sum_ {j} {\ frac {P \! R_j} {C_j}}

N is the total number of the sides and D a break-even factor between 0 and 1, with which a small portion of the weight (1-d) is taken off from each side evenly and distributed on all sides. This is necessary, thus the weight not for sides "„flows off "“, which refer to no other side. Often above formula is indicated also without the Normierungsfaktor 1/N.

The equation knows both and self-vector problem of the matrix

M_ {\ mathrm {EV} \, ij} = \ frac {1-d} {N} + D \, T_ {ij} \,

T_ {ij} = \ begin {cases} 1/C_j, & \ mbox {if} j \ mbox {to side} i \ mbox {links side} \ \ 0, & \ mbox {otherwise} \ end {cases}

and (for <math>d < 1</math>) as solution of the linear set of equations

M_ {ij} \, P \! R_j = \ frac {1-d} {N}

with

M_ {ij} = \ delta_ {ij} - D \, T_ {ij}

is interpreted, whereby \ delta_ {ij} the Kronecker delta designates. The solution of the linear set of equations

P \! R_i = \ frac {1-d} {N} \ sum_j {M^ {- 1}} _ {ij}

can take place analytically or numerically. For <math>d < 1</math> the solution of the set of equations is clear. As a result of use of the Jacobi iteration for numerically solution above recursive equation arises. Other numeric procedures for the matrix inverting, like the minimal residue minimum or the Gauss Seidel method, converge however usually faster.

The algorithm used today by Google does not have probably any longer accurately this form, decreases/goes back however on this formula. Alternative algorithms are the procedure the stroke and Authorities of Jon small mountain, the Hilltop and the TrustRank algorithm.

Zufallssurfer model

If one standardizes PAGE-climbs on 1, then one can interpret the weight of a side as probability that a coincidental Surfer (see coincidence path) is on this side. A coincidental Surfer moves thereby as follows by the net: With probability D he selects coincidentally an outgoing left the current side; with probability 1-d he selects any new side. In order to avoid problems with sides without outgoing left, can be added with these left to all existing sides.

Toolbar and listing values

Information about PAGE-climb can from the Google Toolbar and the Google listing be inferred. Of Google into the Toolbar indicated PAGE-climb lies between 0 and 10, the value in the listing between 0 and 7. Both values form the material PAGE-climb on a logarithmic scale off.

Into the Google Toolbar indicated PAGE-climb in former times every 30 days one updated. In the meantime the interval between the updates rose, partly up to over 100 days.

Manipulation

Due to the economic meaning it came in the meantime to purposeful manipulations and falsifications. Thus this meaningful system became in practice from Suchmaschinenoptimierern by guest book, Blog and forum Spamming, to which operation of link farms and other dubious methods occurred. By forwarding on existing sides with high PAGE-climb, purposefully tries the announcement in the Google Toolbar to manipulate.

At the beginning of of 2005 implemented Google a new attribute, rel= " nofollow ", for references. This is to be proceeded an attempt against Spam. Left, which will provide with this attribute, for the PAGE climbing computation are not considered. By marking more outgoing left can be worked against so for example to the guest book, Blog and forum Spamming.

History

The PAGE climbing algorithm originally originates from the Soziometrie and can in the technical literature 1953 with Katz be proven for the first time. Already 1949 used Seelay the procedure for the explanation of coming off the status of an individual, however there is no standardisation in its description still on the number of outgoing edges and no absorption term. The latter was introduced 1965 by Charles H. stroke Bell.

Criticism

The disadvantages of PAGE-climb in the overview:

  • Financially strong one can acquire and become bake on the left of, positioned in search results more highly. This leads to the fact that instead of qualitatively high-quality contents often the financial possibilities decide on the order of the search results.
  • Web masters see often in PAGE-climb the only valuation criterion for the link exchange. Contents of the linked sides come into the background.
  • In most recent time methods become more important, which accomplish a qualitative measurement of web pages. For this knows PAGE-climb no contribution to supply.

See also

  • Left Popularity
  • Click Popularity
  • HITS algorithm
  • Sponsored left
  • Natural listing
  • Search machine optimization

Literature and sources

  • Sergey Brin, Lawrence PAGE: The Anatomy OF A Large Scale Hypertextual Web Search Engine. In: Computer network and ISDN of system 1998
  • Charles H. stroke Bell: At input outputs approach tons of clique identification. In: Sociometry, number 28, page 377-399, 1965
  • L. Katz: A new status index derived from sociometric analysis. In: Psychmetrika, number 18 (1), page 39-43, 1953

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