Modeling

1
Modeling

• Modern Information Retrieval
• by R. Baeza-Yates and B. Ribeiro-Neto
• Addison-Wesley, 1999.
• (Chapter 2)

2
Introduction

• Ranking algorithms
• The central problem regarding IR systems is the
  issue of predicting which documents are relevant
  and which are not.
• Taxonomy of IR Models
• Boolean set theoretic
• Vector algebraic
• Probabilistic

3
Retrieval

• Ad hoc
• the documents in the collection remain relatively
  static while new queries are submitted to the
  system
• Filtering (Routing)
• the queries remain relatively static while new
  documents come into the system
• construction of user profile

4
Basic Concepts

• In the classic models
• each document is described by a set of
  representative keywords called index terms
• index terms are mainly nouns
• distinct index terms have varying relevance
• index term weights are usually assumed to be
  mutually independent

5
Boolean Model

• Binary decision criterion
• Data retrieval model
• A query is a Boolean expression which can be
  represented as a disjunction of conjunctive
  vectors
• Advantage
• clean formalism, simplicity
• Disadvantage
• exact matching may lead to retrieval of too few
  or too many documents

6
Vector Model (1/4)

• Index terms are assigned non-binary weights
• Term weights are used to compute the degree of
  similarity between documents and the user query
• Then, retrieved documents are sorted in
  decreasing order.
• Definition For the vector model, the weight wi,j
  is associated with term ki and document dj

7
Vector Model (2/4)

• Degree of similarity

8
Vector Model (3/4)

• Salton
• IR vs. clustering
• intra-clustering similarity tf factor (term
  frequency)
• inter-cluster dissimilarity idf factor (inverse
  document frequency)
• Definition
• normalized frequency
• inverse document fequency
• term-weighting schemes
• query-term weights

9
Vector Model (4/4)

• Advantages
• its term-weighting scheme improves retrieval
  performance
• its partial matching strategy allows retrieval of
  documents that approximate the query conditions
• its cosine ranking formula sorts the documents
  according to their degree of similarity to the
  query
• Disadvantage
• The assumption of mutual independence between
  index terms

10
Probabilistic Model (1/7)

• Introduced by Roberston and Sparck Jones, 1976
• Also called binary independence retrieval (BIR)
  model
• Idea Given a user query q, and the ideal answer
  set of the relevant documents, the problem is to
  specify the properties for this set.
• i.e.the probabilistic model tries to estimate the
  probability that the user will find the document
  dj relevant with ratio
• P(dj relevant to q)/P(dj nonrelevant to q)

11
Probabilistic Model (2/7)

• Definition
• All index term weights are all binary i.e., wi,j
  ? 0,1
• Let R be the set of documents know to be relevant
  to query q
• Let be the complement of R
• Let be the probability that the
  document dj is relevant to the query q
• Let be the probability that the
  document dj is nonelevant to query q

12
Probabilistic Model (3/7)

• The similarity sim(dj,q) of the document dj to
  the query q is defined as the ratio
• Using Bayes rule,
• P(R) stands for the probability that a document
  randomly selected from the entire collection is
  relevant
• stands for the probability of
  randomly selecting the document dj from the set R
  of relevant documents

13
Probabilistic Model (4/7)

• Assuming independence of index terms and given
  q(d1, d2, , dt),

14
Probabilistic Model (5/7)

• Pr(ki R) stands for the probability that the
  index term ki is present in a document randomly
  selected from the set R
• stands for the probability that the
  index term ki is not present in a document
  randomly selected from the set R
• let Pr(ki R)pi
• di is either 0 or 1
• 0 di is absent from q
• 1 di is present in q

15
Probabilistic Model (6/7)
16
Probabilistic Model (7/7)

• The retrieval value of each ki present in a
  document (i.e., di1) is term relevance weight
• pj 0.5, qj dfj / N

17
Estimation of Term Relevance