Overview%20of%20Web%20Ranking%20Algorithms:%20HITS%20and%20PageRank

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Overview of Web Ranking Algorithms HITS and
PageRank

• April 6, 2006
• Presented by Bill Eberle

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Overview

• Problem
• Web as a Graph
• HITS
• PageRank
• Comparison

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Problem

• Specific queries (scarcity problem).
• Broad-topic queries (abundance problem).
• Goal to find the smallest set of authoritative
  sources.

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Web as a Graph

• Web pages as nodes of a graph.
• Links as directed edges.

my page
www.uta.edu
my page
www.uta.edu
www.uta.edu
www.google.com
www.google.com
www.google.com
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Link Structure of the Web

• Forward links (out-edges).
• Backward links (in-edges).
• Approximation of importance/quality a page may
  be of high quality if it is referred to by many
  other pages, and by pages of high quality.

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HITS

• HITS (Hyperlinked-Induced Topic Search)
• Authoritative Sources in a Hyperlinked
  Environment, Jon Kleinberg, Cornell University.
  1998.

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Authorities and Hubs

• Authority is a page which has relevant
  information about the topic.
• Hub is a page which has collection of links to
  pages about that topic.

a1
a2
h
a3
a4
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Authorities and Hubs (cont.)

• Good hubs are the ones that point to good
  authorities.
• Good authorities are the ones that are pointed to
  by
• good hubs.

h1
a1
a2
h2
a3
h3
a4
h4
a5
h5
a6
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Finding Authorities and Hubs

• First, construct a focused sub-graph of the www.
• Second, compute Hubs and Authorities from the
  sub-graph.

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Construction of Sub-graph
Rootset Pages
Expanded set Pages
Search Engine
Crawler
Topic
Forward link pages
Rootset
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Root Set and Base Set

• Use query term to collect a root set of pages
  from text-based search engine (AltaVista).

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Root Set and Base Set (cont.)

• Expand root set into base set by including (up to
  a designated size cut-off)
• All pages linked to by pages in root set
• All pages that link to a page in root set

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Hubs Authorities Calculation

• Iterative algorithm on Base Set authority
  weights a(p), and hub weights h(p).
• Set authority weights a(p) 1, and hub weights
  h(p) 1 for all p.
• Repeat following two operations(and then
  re-normalize a and h to have unit norm)

v1
v1
h(v1)
a(v1)
p
v2
p
v2
h(v2)
a(v2)
v3
h(v3)
v3
a(v3)
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Example
0.45, 0.45
0.45, 0.45
Hub 0.45, Authority 0.45
0.45, 0.45
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Example (cont.)
0.45, 0.9
1.35, 0.9
Hub 0.9, Authority 0.45
0.45, 0.9
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Algorithmic Outcome

• Applying iterative multiplication (power
  iteration) will lead to calculating eigenvector
  of any non-degenerate initial vector.
• Hubs and authorities as outcome of process.
• Principal eigenvector contains highest hub and
  authorities.

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Results

• Although HITS is only link-based (it completely
  disregards page content) results are quite good
  in many tested queries.
• When the authors tested the query search
  engines
• The algorithm returned Yahoo!, Excite, Magellan,
  Lycos, AltaVista
• However, none of these pages described themselves
  as a search engine (at the time of the
  experiment)

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Issues

• From narrow topic, HITS tends to end in more
  general one.
• Specific of hub pages - many links can cause
  algorithm drift. They can point to authorities in
  different topics.
• Pages from single domain / website can dominate
  result, if they point to one page - not
  necessarily a good authority.

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Possible Enhancements

• Use weighted sums for link calculation.
• Take advantage of anchor text - text
  surrounding link itself.
• Break hubs into smaller pieces. Analyze each
  piece separately, instead of whole hub page as
  one.
• Disregard or minimize influence of links inside
  one domain.
• IBM expanded HITS into Clever not seen as viable
  real-time search engine.

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PageRank

• The PageRank Citation Ranking Bringing Order to
  the Web, Lawrence Page and Sergey Brin, Stanford
  University. 1998.

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Basic Idea

• Back-links coming from important pages convey
  more importance to a page. For example, if a web
  page has a link off the yahoo home page, it may
  be just one link but it is a very important one.
• A page has high rank if the sum of the ranks of
  its back-links is high. This covers both the case
  when a page has many back-links and when a page
  has a few highly ranked back-links.

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Definition

• My pages rank is equal to the sum of all the
  pages pointing to me.

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Simplified PageRank Example

• Rank(u) Rank of page u , where c is a
  normalization constant (c lt 1 to cover for pages
  with no outgoing links).

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Expanded Definition

• R(u) page rank of page u
• c factor used for normalization (lt1)
• Bu set of pages pointing to u
• Nv outbound links of v
• R(v) page rank of site v that points to u
• E(u) distribution of web pages that a random
  surfer periodically jumps (set to 0.15)

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Problem 1 - Rank Sink

• Page cycles pointed by some incoming link.
• Loop will accumulate rank but never distribute it.

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Problem 2 - Dangling Links

• In general, many Web pages do not have either
  back links or forward links.
• Dangling links do not affect the ranking of any
  other page directly, so they are removed until
  all the PageRanks are calculated.

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Random Surfer Model

• PageRank corresponds to the probability
  distribution of a random walk on the web graphs.

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Solution Escape Term

• Escape term E(u) can be thought of as the random
  surfer gets bored periodically and jumps to a
  different page not staying in the loop forever.
• We term this E to be a vector over all the web
  pages that accounts for each pages escape
  probability (user defined parameter).

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PageRank Computation

- initialize vector
over web pages Loop
- new ranks sum of normalized backlink
ranks
- compute normalizing
factor
- add escape
term
- control
parameter While
- stop when converged
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Matrices

• A is designated to be a matrix, u and v
  correspond to the columns of this matrix.
• Given that A is a matrix, and R be a vector over
  all the Web pages, the dominant eigenvector is
  the one associated with the maximal eigenvalue.

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Example
AT
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Example (cont.)
R c A R M R c eigenvalue R eigenvector of
A
A
A x ? x A - ?I x 0
R
Normalized
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Implementation

• 1. URL -gt id
• 2. Store each hyperlink in a database.
• 3. Sort link structure by Parent id.
• 4. Remove dangling links.
• 5. Calculate the PR giving each page an initial
  value.
• 6. Iterate until convergence.
• 7. Add the dangling links.

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Example
Which of these three has the highest page rank?
Page A
Page B
Page C
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Example (cont.)
Page A
Page B
Page C
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Re-write the system of equations as a Matrix-
Vector product.
Example (cont.)
The PageRank vector is simply an eigenvector
(scalarvector matrixvector) of the
coefficient matrix.
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Example (cont.)
PageRank 0.4
PageRank 0.2
Page A
Page B
Page C
PageRank 0.4
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Example (cont.)
with d 0.5 Pr(A) PR(B)
PR(C)
0 1 2 3 . . . . 11 12
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Convergence

• PageRank computation is O(log(V)).

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Other Applications

• Help user decide if a site is trustworthy.
• Estimate web traffic.
• Spam detection and prevention.
• Predict citation counts.

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Issues

• Users are not random walkers.
• Starting point distribution (actual usage data as
  starting vector).
• Bias towards main pages.
• Linkage spam.
• No query specific rank.

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PageRank vs. HITS

• HITS
• (CLEVER)
• performed on the set of retrieved web pages for
  each query
• computes authorities and hubs
• easy to compute, but real-time execution is hard

• PageRank
• (Google)
• computed for all web pages stored in the database
  prior to the query
• computes authorities only
• Trivial and fast to compute

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References

• Authoritative Sources in a Hyperlinked
  Environment, Jon Kleinberg, Cornell University.
  1998.
• The PageRank Citation Ranking Bringing Order to
  the Web, Lawrence Page and Sergey Brin, Stanford
  University. 1998.