Searching

1
Searching

• Binding of search statements
• Boolean queries
• Boolean queries in weighted systems
• Weighted Boolean queries in non-weighted systems
• Similarity measures
• Well-known measures
• Thresholds
• Ranking
• Relevance feedback

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Binding of Search Statements

• Search statements are generated by users to
  describe their information needs.
• Typically,a search statement uses Boolean logic
  or natural language.
• Three level of binding may be observed. At
  each level the query statement becomes more
  specific.
• 1.At the first level, the user attempts to
  specify the information
• needed, using his/her vocabulary and
  past experience.
• Example Find me information on the impact of
  oil spills in Alaska on the
  price of oil

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Binding of Search Statements(cont.)

• 2. At the next level,the system translates the
  query to its own internal language.
• This process is similar to that of processing
  (indexing) a new document. Example
  impact, oil (petroleum), spills (accidents),
  Alaska,price(cost,value)
• 3. At the final level, the system reconsiders
  the query based upon the specific database.
  For example, assigning weights to the terms
  based upon the document frequency of each term.
• Example impact(.308),oil(.606),petroleum(.65
  ),spills(.12),
  accidents(.23),Alaska(.45),price(.16),cost(.25),va
  lue(.10)

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Boolean Queries

• Boolean queries are natural in systems where
  weights are binary. A term either applies or
  does not apply to a query. Each term T is
  associated with the set of documents DT
• A AND B Retrieve all documents for which both
  A and B are relevant (
  )
• A OR B Retrieve all documents for which either
  A or B are relevant (
  )
• A NOT B Retrieve all documents for which A is
  relevant and B is not
  relevant ( )
• Consider two unnatural situations
• Boolean queries in systems that index documents
  with weighted terms.
• Weighted Boolean queries in systems that use
  non-weighted (binary) terms.

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Boolean Queries in weighted Systems

• Environment
• A weighted system, where the relevance of a term
  to a document is expressed with a weight.
• Boolean queries, involving AND and OR.
• Possible approach use threshold to convert all
  weights to binary representations.
• Possible approach
• Transform the query to disjunctive normalform
• Sets of conjunctions of the form T1 T2
  T3..
• Connected by a operators.
• Given a document D
• First, its relevance to each conjunct is computed
  as the minimum weight of any document term that
  appears in the conjunct.
• Then, the document relevance for the complete
  query is the maximum of the conjunct weights.

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Boolean Queries in Weighted Systems(cont.)

• Example Two documents indexed by 3 terms
• Doc1 Term1 / 0.2, Term2 / 0.5, term3 / 0.6
• Doc2 Term1 / 0.7, Term2 / 0.2, term3 / 0.1
• Query ( Term1 AND Term2 ) OR Term3
• Relevance of Doc1 to the query is 0.6
• Relevance of Doc2 to the query is 0.2

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Weighted Boolean Queries in Non-weighted Systems

• Environment
• A conventional system, where a term is either
  relevant or non-relevant to a document.
• Boolean queries, in which users associate a
  weight (importance) with each term.
• Possible approach
• OR
• A1 B1 includes all the documents in DA DB.
• A1 B0 includes all the documents in DA.
• As the weight of B changes from 0 to 1, Documents
  from DB - DA are added to DA.
• AND
• A1 B1 includes all the documents in DA
  DB.
• A1 B0 includes all the documents in DA.
• As the weight of B changes from 1to 0, Documents
  from DA - DB are added to DA DB.

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Weighted Boolean Queries in Non-weighted Systems
(cont.)

• NOT
• A1 B1 includes all the documents in DA -
  DB.
• A1 B0 includes all the documents in DA.
• As the weight of B changes from 1 to 0, Documents
  from DA DB are added to DA - DB.
• Algorithm
• determine the documents that satisfy the either
  of the extreme interpretations.
• Determine the centroid of the inner set.
• Calculate the similarity of the documents outside
  of the inner set and the centroid.
• Determine the number of document of documents to
  be added, by multiplying the actual weight B (a
  value between 0 and 1 ) by the number of
  documents outside of the inner set.
• Select the documents to be added as those most
  similar to the centroid.

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Similarity Measures

• Typical, similarity measures are used when both
  queries and documents are described by vectors
• A similarity measures gauges the similarity
  between two documents (for the purpose of search
  we do not consider here them similarity,but many
  of the consideration are identical)
• The measure increases as similarity grows(0
  reflects total dissimilarity)
• A variety of similarity measures has been
  proposed and experimented with.
• As queries are analogous to documents,the same
  similarity measures can be used to measure
• document-document similarity (used in document
  clustering)
• document-query similarity (used in searching)
• query-query similarity(?)

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Similarity MeasuresInner Product

• Consider again
• SIM(Di,Dj)
• Where the weights Wik are simple frequency counts
• The problem with this simple measure is that it
  is not normalized to account for variances in the
  length of documents
• This might be corrected by dividing each
  frequency count by the length of the document
• It may be also be corrected by dividing each
  frequency count by the maximum frequency count
  for the document
• Additional normalization is often performed to
  force all similarity values to the range between
  0 and 1

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Similarity MeasuresInner Product(cont.)

• This is a refinement of the previous measure
• (alternatively,the measure remains the inner
  product,but the representation are different)
• SIM(Q,D)
• where
• m is the number of documents in the collection
• n is the number of indexing terms
• Each document is a sequence of n weights D
  (d1,,dn)
• A query is also a sequence of n weights Q
  (q1,,qn)
• Each weight qk or dk IDFkTFk / MF
• IDFk The inverse document frequency for term Tk
  that is, a value that decreases as the
  frequency of the term in the collection
  increases
• for example,log2m/Dfki1,where DFk counts the
  number of documents in which term Tk appears)
• TFk/MF The frequency of term Tk in this
  document,divided by the maximal frequency of any
  term in this document
• There are other constants for fine-tuning the
  formulas performance

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Similarity MeasuresCosine

• A document or a query are treated as
  n-dimensional vectors
• SIM(Q,D)
• Formula measures the cosine of the angle between
  the two vectors
• As cosine approaches 1, the two vectors become
  coincident(document and query represent
  unrelated concepts)
• Problem Does not take into account the length of
  the vectors
• Consider
• Query (4,8,0)
• Doc1 (1,2,0)
• Doc2 (3,6,0)
• SIM(Query,Doc1) and SIM(Query,Doc2)are identical,
  even though Doc2 has significantly higher
  weights in the terms in common

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Similarity Measures Summary

• Four well-known measures of vector similarity
• Similarity Measure Evaluation for
  Binary Evaluation for Weighted
• sim(X, Y) Term
  Vectors Term Vectors
• Inner product
• Dice coefficient
• Cosine coefficient
• Jaccard coefficient

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Similarity Measures Summary(cont)

• Observations
• All four measures use the same inner product as
  nominator.
• The denominators of the last three maybe viewed
  as normalizations of the inner product.
• The definitions for binary term vectors are more
  intuitive.
• All measures are 1 when X Y and 0 when X and Y
  are disjoint

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Thresholds

• Use of similarity measures may return the entire
  database as a search result, because the
  similarity measure might yield close-to-zero
  values for most, if not all, of the documents.
• Similarity measures must be used with thresholds
  
• Threshold a value that the similarity measure
  must exceed
• It might also be a limit on the size of the
  answer.
• Example
• Terms
• American, geography, lake, Mexico, painter, oil,
  reserve, subject.
• Doc1 geography of Mexico suggests oil reserves
  are available.
• Doc1 ( 0, 1, 0, 1, 0, 1, 1, 0)
• Doc2 American geography has lakes available
  everywhere.
• Doc2 (1, 1, 1, 0, 0, 0, 0, 0)
• Doc3 painter suggest Mexico lakes as subjects.
• Doc3 (0, 0, 1, 1, 1, 0, 0, 1)
• Query oil reserves in Mexico
• Query (0, 0, 0, 1, 0, 1, 1, 0)

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Thresholds(cont.)

• Example(cont.)
• Using the inner product measures
• SIM(Query, Doc1) 3
• SIM(Query, Doc2) 0
• SIM(Query, Doc3) 1
• If a threshold of 2 is selected, then only Doc1
  is retrieved.
• Use of thresholds may decrease recall when
  documents are clustered, and search compares
  queries to centroids.
• There may be documents in a cluster that are not
  retrieved, even though they are similar enough to
  the query, because their cluster centroid is not
  close enough to the query.
• The risk increases as the deviation in the
  cluster increases (the documents are not
  clustered around the centroid the centroid -- bad
  cluster)

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Ranking

• Similarity measures provide a means for ranking
  the set of retrieved documents
• Ordering the documents from the most likely to
  satisfy the query to the least likely.
• Ranking reduces the user overhead.
• Because similarity measures are not accurate,
  precise ranking may be misleading documents may
  be grouped into sets, and the documents sets are
  ranked in order of relevance.

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Relevance Feedback

• An initial query might not provide an accurate
  description of the users needs
• Users lack of knowledge of the domain.
• Users vocabulary does not match authors
  vocabulary.
• After examining the result of his query, a user
  can often improve the description of his needs
• Querying is an iterative process.
• Further iterations are generated either manually,
  or automatically.
• Relevance feedback Knowledge of which returned
  documents are relevant and which are not, is used
  to generate the next query.
• Assumption the documents relevant to a query
  resemble each other(similar vectors).
• Hence, if a document is known to be relevant, the
  query can be improved by increasing its
  similarity to that document.
• Similarly, if a document is known to be
  non-relevant, the query can be improved by
  decreasing its similarity to that document.

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Relevance Feedback(cont.)

• Given a query (a vector) we
• add to it the average (centroid) of the relevant
  documents in the result, and
• subtract from it the average (centroid) of the
  non-relevant documents in the result.
• A vector algebra expression
• where
• Qi The present query.
• Qi1 The revised query.
• D A document in the result.
• R The relevant documents in the result(r
  cardinality or R)
• NR The non-relevant documents in the result(nr
  cardinality of NR)

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Relevance Feedback (cont.)

• A revised formula, giving more control over the
  various components
• where
• a,b, g Tuning constants for example, 1.0,
  0.5, 0.25
• Positive feedback factor. Uses the
  users judgments on relevant documents to
  increase the values of terms. Moves the query to
  retrieve documents similar to relevant documents
  retrieved (in the direction of more relevant
  documents).
• Negative feedback factor. Uses the
  users judgments on non-relevant documents to
  decrease the values of terms. Moves the query
  away from non-relevant documents.
• Positive feedback often weighted significantly
  more than negative feedback often, only positive
  feedback is used.

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Relevance Feedback(Cont.)

• Illustration Impact of relevance feedback.
  Illustration shows the effect of positive
  feedback only or negative feedback only
• Boxes filled present query hollow
  modified query.
• Oval set of documents retrieved by present
  query.
• Circles filled non-relevant documents
  hollow relevant.

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Relevance Feedback(Cont.)

• Example
• Assume query Q (3,0,0,2,0) retrieved three
  documents Doc1, Doc2, Doc3.
• Assume Doc1 and Doc2 are judged relevant and Doc3
  is judged non-relevant.
• Assume the constants used are 1.0, 0.5, 0.25.
• The revised query is
• Q (3, 0, 0, 2, 0)
• 0.5 ((21)/2, (43)/2, (00)/2, (00)/2,
  (20)/2)
• - 0.25 (0, 0, 4, 3, 2)
• (3.75, 1.75, -1, 1.25, 0) (3.75, 1.75,
  0, 1.25, 0)

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Relevance Feedback(Cont.)

• Example(cont.)
• Using the similarity formula
• we can compare the similarity of Q and Q to the
  three documents
• Compared to the original query, new query is more
  similar to Doc1 and Doc2(judged relevant), and
  less similar to Doc3(judged non-relevant).
• Notice how the new query added Term2, which was
  not in the original query.
• For example, a user may be searching for word
  processor to be used on a PC, and the revised
  query may introduce the term Mac.

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Relevance Feedback(Cont.)

• Problem Relevance feedback may not operate
  satisfactorily, if the identified relevant
  documents do not form a tight cluster.
• Possible solution Cluster the identified
  relevant documents, then split the original query
  into several, by constructing a new query for
  each cluster.
• Problem Some of the query terms might not be
  found in any of the retrieved documents. This
  will lead to reduction of their relative weight
  in the modified query(or even elimination).
  Undesirable, because these terms might still be
  found in future iterations.
• Possible solutions Ensure the original terms
  are kept or present all modified queries to the
  user for review.
• Fully automatic relevance feedbackThe rank
  values for the documents in the first answer are
  used as relevance feedback to automatically
  generate the second query(no human judgment).
• The highest ranking documents are assumed to be
  relevant(positive feedback only).