CS246
Basic Information Retrieval
Today’s Topic
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Basic Information Retrieval (IR)
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Bag of words assumption
Boolean Model
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Vector-space model
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Inverted index
Document-term matrix
TF-IDF vector and cosine similarity
Phrase queries
Spell correction
Information-Retrieval System
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Information source: Existing text documents
Keyword-based/natural-language query
The system returns best-matching documents given the
query
Challenge
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Both queries and data are “fuzzy”
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Unstructured text and “natural language” query
What documents are good matches for a query?
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Computers do not “understand” the documents or the queries
Developing a computerizable “model” is essential to implement this
approach
Bag of Words: Major Simplification
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Consider each document as a “bag of words”
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Consider queries as bag of words as well
Great oversimplification, but works adequately in many
cases
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“bag” vs “set”
Ignore word ordering, but keep word count
“John loves only Jane” vs “Only John loves Jane”
The limitation still shows up on current search engines
Still how do we match documents and queries?
Boolean Model
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Return all documents that contain the words in the query
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No notion of “ranking”
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Simplest model for information retrieval
A document is either a match or non-match
Q: How to find and return matching documents?
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Basic algorithm?
Useful data structure?
Inverted Index
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Allows quick lookup of document ids with a
particular word
Postings list
lexicon/dictionary DIC
3
8
10 13 16 20
PL(Stanford)
1
2
3
9
PL(UCLA)
4
5
8
10 13 19 20 22
Stanford
UCLA
MIT
…
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16 18
PL(MIT)
Q: How can we use this to answer “UCLA Physics”?
Inverted Index

Allows quick lookup of document ids with a
particular word
Postings list
lexicon/dictionary DIC
3
8
10 13 16 20
PL(Stanford)
1
2
3
9
PL(UCLA)
4
5
8
10 13 19 20 22
Stanford
UCLA
MIT
…
16 18
PL(MIT)
Size of Inverted Index (1)
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100M docs, 10KB/doc,
1000 unique words/doc, 10B/word, 4B/docid
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Q: Document collection size?
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Q: Inverted index size?
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Heap’s Law:Vocabulary size = k nb with 30 < k < 100 and 0.4 <
b<1
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k = 50 and b = 0.5 are good rule of thumb
Size of Inverted Index (2)
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Q: Between dictionary and postings lists, which one is
larger?
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Q: Lengths of postings lists?
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Zipf’s law: collection term frequency  1/frequency rank
Q: How do we construct an inverted index?
Inverted Index Construction
C: set of all documents (corpus)
DIC: dictionary of inverted index
PL(w): postings list of word w
1: For each document d  C:
2:
Extract all words in content(d) into W
3:
For each w  W:
4:
If w  DIC, then add w to DIC
5:
Append id(d) to PL(w)
Q: What if the index is larger than main memory?
Inverted-Index Construction
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For large text corpus
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Block-sorted based construction
Partition and merge
Evaluation: Precision and Recall
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Q: Are all matching documents what users want?
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Basic idea: a model is good if it returns document if and
only if it is “relevant”.
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R: set of “relevant” document
D: set of documents returned by a model
| DR|
Precision 
|D|
| DR|
Recall 
|R|
Vector-Space Model
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Main problem of Boolean model
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Matrix interpretation of Boolean model
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Too many matching documents when the corpus is large
Any way to “rank” documents?
Document – Term matrix
Boolean 0 or 1 value for each entry
Basic idea
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Assign real-valued weight to the matrix entries depending on
the importance of the term
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“the” vs “UCLA”
Q: How should we assign the weights?
TF-IDF Vector
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A term t is important for document d
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TF: term frequency
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# documents containing t
TF-IDF weighting
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# occurrence of t in d
IDF: inverse document frequency
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If t appears many times in d or
If t is a “rare” term
TF X Log(N/IDF)
Q: How to use it to compute query-document relevance?
Cosine Similarity
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Represent both query and document as a TF-IDF vector
Take the inner product of the two normalized vectors to
compute their similarity
QD
QD
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Note: |Q| does not matter for document ranking.
Division by |D| penalizes longer document.
Cosine Similarity: Example
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idf(UCLA)=10, idf(good)=0.1,
idf(university) = idf(car) = idf(racing) = 1
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Q = (UCLA, university), D = (car, racing)
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Q = (UCLA, university), D = (UCLA, good)
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Q = (UCLA, university), D = (university, good)
Finding High Cosine-Similarity Documents
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Q: Under vector-space model, does precision/recall make
sense?
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Q: How to find the documents with highest cosine
similarity from corpus?
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Q: Any way to avoid complete scan of corpus?
Inverted Index for TF-IDF
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Q · di = 0 if di has no query words
Consider only the documents with query words
Inverted Index: Word  Document
Word
Lexicon
IDF
docid
TF
Stanford
1/3530
D1
2
UCLA
1/9860
D14
30
MIT
1/937
D376
8
…
Posting
list
(TF may be normalized
18
by document size)
Phrase Queries
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“Havard University Boston” exactly as a phrase
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Q: How can we support this query?
Two approaches
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Biword index
Positional index
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Q: Pros and cons of each approach?
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Rule of thumb: x2 – x4 size increase for positional index
compared to docid only
Spell correction
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Q: What is the user’s intention for the query “Britnie
Spears”? How can we find the correct spelling?
Given a user-typed word w, find its correct spelling c.
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Bayes’ rule: P(c|w) = P(w|c)P(c)/P(w)
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Probabilistic approach: Find c with the highest probability
P(c|w).
Q: How to estimate it?
Q: What are these probabilities and how can we estimate
them?
Rule of thumb: 75% misspells are within edit distance 1.
98% are within edit distance 2.
Summary
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Boolean model
Vector-space model
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Inverted index
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TF-IDF weight, cosine similarity
Boolean model
TF-IDF model
Phrase queries
Spell correction