CS246
Basic Information Retrieval
Today’s Topic Basic Information Retrieval (IR)
Bag of words assumption Boolean Model
Inverted index Vector-space model
Document-term matrix TF-IDF vector and cosine similarity
Phrase queries Spell correction
Information-Retrieval System Information source: Existing text documents Keyword-based/natural-language query The system returns best-matching documents
given the query Challenge
Both queries and data are “fuzzy” Unstructured text and “natural language” query
What documents are good matches for a query? Computers do not “understand” the documents or the
queries Developing a computerizable “model” is essential to
implement this approach
Bag of Words: Major Simplification Consider each document as a “bag of words”
“bag” vs “set” Ignore word ordering, but keep word count
Consider queries as bag of words as well Great oversimplification, but works adequately
in many cases “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 Return all documents that contain the words
in the query Simplest model for information retrieval
No notion of “ranking” A document is either a match or non-match
Q: How to find and return matching documents? Basic algorithm? Useful data structure?
Inverted Index Allows quick lookup of document ids with a
particular word
Q: How can we use this to answer “UCLA Physics”?
lexicon/dictionary DIC 3 8 10 13 16 20
Stanford
UCLA
MIT
…
1 2 3 9 16 18
PL(Stanford)
PL(UCLA)
Postings list
4 5 8 10 13 19 20 22 PL(MIT)
Inverted Index Allows quick lookup of document ids with a
particular word
lexicon/dictionary DIC 3 8 10 13 16 20
Stanford
UCLA
MIT
…
1 2 3 9 16 18
PL(Stanford)
PL(UCLA)
Postings list
4 5 8 10 13 19 20 22 PL(MIT)
Size of Inverted Index (1) 100M docs, 10KB/doc,
1000 unique words/doc, 10B/word, 4B/docid
Q: Document collection size?
Q: Inverted index size?
Heap’s Law: Vocabulary size = k nb with 30 < k < 100 and 0.4 < b < 1 k = 50 and b = 0.5 are good rule of thumb
Size of Inverted Index (2) Q: Between dictionary and postings lists,
which one is larger?
Q: Lengths of postings lists?
Zipf’s law: collection term frequency 1/frequency rank
Q: How do we construct an inverted index?
Inverted Index ConstructionC: set of all documents (corpus)DIC: dictionary of inverted indexPL(w): postings list of word w
1: For each document d C:2: Extract all words in content(d) into W3: For each w W:4: If w DIC, then add w to DIC5: Append id(d) to PL(w)
Q: What if the index is larger than main memory?
Inverted-Index Construction For large text corpus
Block-sorted based construction Partition and merge
Evaluation: Precision and Recall Q: Are all matching documents what users
want?
Basic idea: a model is good if it returns document if and only if it is “relevant”.
R: set of “relevant” documentD: set of documents returned by a model
||
||Precision
D
RD
||
||Recall
R
RD
Vector-Space Model Main problem of Boolean model
Too many matching documents when the corpus is large
Any way to “rank” documents? Matrix interpretation of Boolean model
Document – Term matrix Boolean 0 or 1 value for each entry
Basic idea Assign real-valued weight to the matrix entries
depending on the importance of the term “the” vs “UCLA”
Q: How should we assign the weights?
TF-IDF Vector A term t is important for document d
If t appears many times in d or If t is a “rare” term
TF: term frequency # occurrence of t in d
IDF: inverse document frequency # documents containing t
TF-IDF weighting TF X Log(N/IDF)
Q: How to use it to compute query-document relevance?
Cosine Similarity Represent both query and document as a TF-
IDF vector Take the inner product of the two normalized
vectors to compute their similarity
Note: |Q| does not matter for document ranking. Division by |D| penalizes longer document.
DQ
DQ
Cosine Similarity: Example idf(UCLA)=10, idf(good)=0.1,
idf(university) = idf(car) = idf(racing) = 1
Q = (UCLA, university), D = (car, racing)
Q = (UCLA, university), D = (UCLA, good)
Q = (UCLA, university), D = (university, good)
Finding High Cosine-Similarity Documents Q: Under vector-space model, does
precision/recall make sense?
Q: How to find the documents with highest cosine similarity from corpus?
Q: Any way to avoid complete scan of corpus?
Inverted Index for TF-IDF Q · di = 0 if di has no query words Consider only the documents with query
words Inverted Index: Word Document
18
Word IDF
Stanford
UCLA
MIT
…
1/3530
1/9860
1/937
docid TF
D1
D14
D376
2
308
(TF may be normalized by document size)
Postinglist
Lexicon
Phrase Queries “Havard University Boston” exactly as a
phrase Q: How can we support this query?
Two approaches Biword index Positional index
Q: Pros and cons of each approach?
Rule of thumb: x2 – x4 size increase for positional index compared to docid only
Spell correction 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. Probabilistic approach: Find c with the highest
probability P(c|w). Q: How to estimate it?
Bayes’ rule: P(c|w) = P(w|c)P(c)/P(w) 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 Boolean model Vector-space model
TF-IDF weight, cosine similarity Inverted index
Boolean model TF-IDF model Phrase queries
Spell correction