IST 2140 Information Storage and Retrieval

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IST 2140Information Storage and Retrieval

• Week 3
• Information Retrieval Models

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Retrieval Tasks

• Ad hoc retrieval
• Static documents, new queries
• formerly called retrospective retrieval
• Filtering
• Static queries, new documents
• Based on user profile
• Formerly called SDI (selective dissemination of
  information) or current awareness

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Information Retrieval
Matching Process
Document Collection
Query
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Basic concepts

• Document is described by a set of representative
  keywords (index terms)
• Keywords may have binary weights or weights
  calculated from statistics of their frequency in
  text
• Retrieval is a matching process between
  document keywords and words in queries

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Information Retrieval Models

• A model is an embodiment of the theory in which
  we define a set of objects about which assertions
  can be made and restrict the ways in which
  classes of objects can interact
• A retrieval model specifies the representations
  used for documents and information needs, and how
  they are compared.
• (Turtle Croft, 1992)

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A formal characterization of Information
Retrieval Models

• An information retrieval model is a quadrupole
  D,Q,F,R(qi,dj) where
• D is a set of representations for the documents
  in the collection
• Q is a set of representations for the user
  information needs (queries)
• F is a framework for modelling document
  representations, queries, and their relationships
• R(qi,dj) is a ranking function which associates a
  real number with a query qi (qi ? Q) and document
  representation dj (dj ? D) (Baeza-Yates
  Ribeiro-Neto, 1999)

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Information Retrieval Models

• Three classic models
• Boolean Model
• Vector Space Model
• Probabilistic Model
• Additional models
• Extended Boolean
• Fuzzy matching
• Cluster-based retrieval
• Language models

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Implementation vs. Models

• An IR model is a formalization of the way of
  thinking about information retrieval
• Compare to implementation---how to operationalize
  the model in a given environment (e.g. file
  structures)

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Classic Retrieval Models

• Boolean
• Documents and queries are sets of index terms
• set theoretic
• Vector
• Documents and queries are documents in
  L-dimensional space
• algebraic
• Probabilistic
• Based on probability theory

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Boolean Model

• first online systems in 60s and 70s
• most widely used in commercial IR
• AND, OR, NOT operators
• usually supplemented with proximity operators
• requires an exact match
• based on inverted file

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Boolean Model

• Based on set theory and Boolean algebra
• Queries are specified as Boolean expressions
• Widely used in commercial IR systems (Dialog,
  Lexis/Nexis)
• Interpreted using Venn Diagrams

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Boolean Operators

• AND
• OR
• NOT

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Boolean AND

• Information AND Retrieval

Information
Retrieval
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Boolean OR

• Cats OR Felines

Felines
Cats
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Example

• Draw a Venn diagram for
• Care and feeding and (cats or dogs)
• What is the meaning of
• Information and retrieval and performance or
  evaluation

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Boolean-based Matching

• Exact match systems separate the documents
  containing a given term from those that do not.
• No similarity between document and query
  structure
• Proximity Judgment Gradations of the retrieved
  set

Queries
Terms
Mediterranean
scholarships
horticulture
agriculture
cathedrals
adventure
disasters
leprosy
recipes
bridge
tennis
Venus
flags
flags AND tennis
0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1
1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0
0 0 1 0
leprosy AND tennis
Venus OR (tennis AND flags)
Documents
(bridge OR flags) AND tennis
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Sample Boolean Query

• On DIALOG
• SELECT nutritional()value? and (junk()food? or
  fast()food? or pizza? or hamburger? or
  french()(fry or fries))
• (note use of positional operators)

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Boolean model

• Terms are present or absent
• Index term weights are binary 0,1
• Exact match system documents are predicted to be
  relevant or non-relevant

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Other Boolean features

• Order dependency of operators
• ( ), NOT, AND, OR (DIALOG)
• May differ on different systems
• Nesting of search terms
• Nutrition and (fast or junk) and food

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Other Boolean features

• Extensions to AND operator
• Positional operators
• adjacency A ADJ B, A(W)B
• Field limitations
• A/TI, B/TI,DE
• Extensions to OR operator
• Truncation
• A?, A?? ?
• Browsing indexes

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Pros and Cons

• simple formalism
• - hard to control (too many, too few documents
  retrieved)
• - requires formally constructed queries
• - performance issues??

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Extended Boolean model

• Add partial matching and term weighting
• E.g.
• take retrieval set and weight by binary terms
• Take retrieval set and calculate weights and
  ranks within the set

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Vector Model

• Non-binary weights
• Calculate degree of similarity between document
  and query
• Ranked output by sorting similarity values
• Also called vector space model

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Vector Space Model

• based on idea of n-dimensional document space
• query is also located in document space
• documents are ranked in order of their
  closeness to the query
• many possible matching functions

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Vector Space Model

• Documents and queries are points in L-dimensional
  space (where L is number of unique index terms in
  the data collection)

Q
D
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Document and Query Vectors

• Documents and Queries are vectors of terms
• Actual vectors have many terms (thousands)
• Vectors can use binary keyword weights or assume
  0-1 weights (term frequencies)
• Example terms dog,cat,house, sink,
  road, car
• Binary (1,1,0,0,0,0), (0,0,1,1,0,0)
• Weighted (0.01,0.01, 0.002, 0.0,0.0,0.0)
• Queries can be weighted also

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Vector Space Model with Term Weights

• assume document terms have different values for
  retrieval
• therefore assign weights to each term in each
  document
• example TFxIDF weighting
• proportional to frequency of term in document
• inversely proportional to frequency of term in
  collection

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A 2-D Document Space

• Consider a document collection with only two
  words cat, dog
• Three document vectors
• D1
• D2
• D3

D3
D2
D1
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A 3-D Document Space
Di 3 t1 4t2 2t3 Query0t1t2t3
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Term document matrix

• A document collection can be represented by a
  matrix in which rows are documents and columns
  are terms entries are 0 (if term is absent in a
  document) or a value for term weight
• Note that this is not effective for
  implementation other data structures are used
  (inverted file)

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Vector-based Matching Metrics

• Metric or Distance Measure documents close
  together in the vector space are likely to be
  highly similar

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Measuring similarity

• Need a means of computing similarity between
  documents and queries (or pairs or documents)
• Many proposed none ideal
• Allows
• Ranking
• Thresholding
• Query reformulation

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Some conventions

• N number of documents in collection
• L number of unique terms in collection
• Di the ith document in the collection
• Tj the jth term in the collection
• Q a query
• Wij the weight of term i in Document j
• WiQ the weight of term i in Query

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Inner product

• Many similarity functions are based on the inner
  product
• SIM(Di,Q) S(Dij,Qj)
• For binary vectors, reduces to number of terms in
  common in D and Q
• For weighted terms it is the sum of the products
  of the term weights in documents and query
• Favours longer documents

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Calculating Degree of Similarity

• Many candidate measures, e.g.
• Dice Coefficient
• Jaccard Coefficient
• Cosine Coefficient
• Based on contribution to similarity of
  co-occurring terms
• Generally normalized by length of document

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Dice Coefficient

• SIM (D,Q)
• 2 S (wiD wiQ)
• -------------------------
• S wiD2 S wiQ2
• Reduces to 2A/(BC) for binary documents
• Sum is taken over all i from 1?L (dimensionality
  of vector space)

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Jaccard Coefficient

• SIM (D,Q)
• S (wiD wiQ)
• -------------------------------------------------
  -
• S wiD2 S wiQ2 S (wiDwiQ)
• Reduces to A/(BC-A) for binary documents
• Sum is taken over all i from 1? L(dimensionality
  of vector space)

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Cosine Measure

• Very commonly used
• Measures cosine of angle between document-query
  (or document-document) vector

Di
)
Q
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Cosine coefficient

• SIM (Dj, Q)
• S (wi,Dj wi,q)
• ----------------------------
• SQRT(S wi,Dj2) SQRT( S wi,q2)
• Sum is taken over L(dimensionality of vector
  space)

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What Similarity Function to Use?

• Some studies comparing performance of measures
  (e.g. McGill, 67 measures)
• Significant differences in performance may
  perform differently with high or low frequency
  terms
• May be monotonic among similar measures
• No consensus over what types of measure best for
  what application
• Cosine measure is widely used

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Pros and Cons

• Term weights improve retrieval performance
• Partial matching means query need not be exact
• Ranking provides guidance to searcher
• Relevance feedback feasible
• - assumes orthogonality obviously false
• - high degree of empiricism
• - Less control by searcher?