EECS 395495 Lecture 6: Document Ranking and Link Analysis

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EECS 395/495 Lecture 6Document Ranking and Link
Analysis

• Doug Downey

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How Does Web Search Work?

• Inverted Indices
• Web Crawlers
• Ranking Algorithms
• Basics of Machine Learning and Text
  Classification
• Document Ranking
• Link Analysis

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Document Ranking

• Static Features
• Which Web pages are good?
• Dynamic Features
• Which pages are most relevant to the query?

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Static Ranking (1)

• Known Reputable Sites
• Wikipedia, .edu domains, etc.
• Spam detection
• Link Analysis
• More later
• (Real) Popularity
• Page features
• Length of page, length of URL
• Anchor Text features
• How much text in links to page, how varied,

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Static Ranking (2)

• Beyond PageRank Machine Learning for Static
  RankingRichardson et al., 2005

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Dynamic Ranking

• Vector-space model
• Term frequency (tf) vectors
• The bag of words representation
• Idea score(q, d) q . d(i.e. dot product of
  frequency vectors)

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Normalization

• Problem with naïve vector space model
• Unimportant terms dominate
• Solution Normalize frequencies by
• Overall frequency in the document collection?
• Number of distinct docs mentioning term?
• Christopher D. Manning, Prabhakar Raghavan and
  Hinrich Schütze, Introduction to Information
  Retrieval, Cambridge University Press. 2008

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TF-IDF Weighting

• tf term frequency
• idf inverse document frequency
• log (N / df)N total of documents
• Score by tfidf (also denoted tf-idf)
• Christopher D. Manning, Prabhakar Raghavan and
  Hinrich Schütze, Introduction to Information
  Retrieval, Cambridge University Press. 2008

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On the Web Other Weighting Factors

• Title
• Anchor Text
• Font/Color
• Position on page
• Implicit Feedback(More on this later from
  Justin, Arun, and Brent)

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Putting it all together

• Googles 400 lines of code (?)
• Microsoft Live Search
• Static dynamic features computed for several
  query/document sets
• Neural network trained on human-annotated result
  ratings(more on this later from Gang, Samir, and
  Hongyu)

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Problem synonyms

• Query for doctors
• Also want documents containing physicians
• Query for user interface design
• Also want documents containing human-computer
  interaction

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Latent Semantic Analysis (LSA)

• Idea
• Represent documents/words in terms of semantics
• E.g.
• If two words tend to occur in similar documents,
  the words are similar
• If two documents tend to include similar words,
  the documents are similar

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LSA Linear Algebra Formulation (1)

• X term-frequency matrix (t x d)

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LSA Linear Algebra Formulation (2)

• Write X (t x d) as X W S PT
• Where
• W (t x r) and P (d x r) are orthonormal matrices
• S (r x r) is a diagonal matrix, entries sorted in
  decreasing order
• .where r min(t, r)

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LSA Linear Algebra Formulation (3)

• X W S PT
• Xk Wk Sk PkT (all but first k entries of S gt
  0)
• Key Xk is the best rank-k approx. to X(in mean
  squared error)

X
Xk
Wk
W
Sk
S
PkT
PT
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Rank-k approximation

• Xk Wk Sk PkT
• Put another way
• Represent each term as k-vector of numbers
• Represent each document as another k-vector
• Vectors represent semantics in the sense that
• Entry in Xk is dot product of term doc
  vectors(with dims weighted by Sk)
• No other length k vectorization approximates X
  better

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Example

• From

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Xk
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To Review

• Represent each term as k-vector of numbers
• human 0.22, -0.11
• Represent each document as another k-vector
• d1 0.2, 0.61
• Entry in Xk for human appearing in p1 is dot
  product of vectors, weighted by entries of Sk
  Sk (1,1)0.220.2 Sk (2,2) -0.110.61 -0.02
• So using k 1, what does the word vector
  signify?The document vector?

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LSA vs. Stemming

• Stemming often confabulates meanings, e.g. flower
  becomes flow as compared to LSA
• flower-flow have cos -.01,
• dish-dishes cos .68.
• More examples of cos in latent space capturing
  word meaning
• Flower petals .93, gymnosperms 0.47
• Flow flows .84, opens 0.46
• Dish sauce 0.70, bowl 0.63
• Dishes kitchen 0.75, cup 0.57
• Thomas K Landauer and Susan Dumais (2008),
  Scholarpedia, 3(11)4356 http//www.scholarpedia.o
  rg/article/Latent_semantic_analysis

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LSA for IR

• Score cos(query k-vector, document k-vector)

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LSA Limitations

• Ignores polysemy
• Chicago represented by only one fixed vector
• Ignores word order
• Starts from term vectors
• Scalability
• advances have made training on far larger
  corpora possible for example a 500 million word
  corpus in 2007, took less than a day on a
  modest-sized cluster.Landauer Dumais, 2008
• Increasingly fancy probabilistic models have been
  posited to solve the first two problems (and
  potentially exacerbate the third)

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How Does Web Search Work?

• Inverted Indices
• Web Crawlers
• Ranking Algorithms
• Basics of Machine Learning and Text
  Classification
• Document Ranking
• Link Analysis