Modified by Dongwon Lee from slides by Ch 1 Boolean Retrieval Modified by Dongwon Lee from slides by Christopher Manning and Prabhakar Raghavan

In the Last Class Ch 19 Ch 21 Index size estimation Near-duplicate detection using shingling Ch 21 PageRank Hubs and Authorities

Next 2 Classes Ch 1 Ch 2 IR Basics Index: Incidence Matrix, Inverted Index Boolean vs. ranked retrieval models Ch 2 Processing terms of documents Improving inverted index Supporting keyword vs. phrase queries

Information Retrieval Information Retrieval (IR) is finding material (usually documents) of an unstructured nature (usually text) that satisfies an information need from within large collections (usually stored on computers).

IR vs. databases: Structured vs unstructured data Structured data tends to refer to information in “tables” Employee Manager Salary Smith Jones 50000 Chang Smith 60000 Ivy Smith 50000 Typically allows numerical range and exact match (for text) queries, e.g., Salary < 60000 AND Manager = Smith.

Unstructured data Typically refers to free text Allows Keyword queries including operators More sophisticated “concept” queries e.g., find all web pages dealing with drug abuse Classic model for searching text documents

Unstructured (text) vs. structured (database) data in 1996

Unstructured (text) vs. structured (database) data in 2009

Sec. 1.1 Unstructured data in 1680 Which plays of Shakespeare contain the words Brutus AND Caesar but NOT Calpurnia? One could grep all of Shakespeare’s plays for Brutus and Caesar, then strip out lines containing Calpurnia? Why is that not the answer? Slow (for large corpora) NOT Calpurnia is non-trivial Other operations (e.g., find the word Romans near countrymen) not feasible Ranked retrieval (best documents to return) Grep is line-oriented; IR is document oriented.

Term-document incidence Sec. 1.1 Term-document incidence 1 if play contains word, 0 otherwise Brutus AND Caesar BUT NOT Calpurnia

Incidence vectors So we have a 0/1 vector for each term. Sec. 1.1 Incidence vectors So we have a 0/1 vector for each term. To answer query: take the vectors for Brutus, Caesar and Calpurnia (complemented)  bitwise AND. 110100 AND 110111 AND 101111 = 100100.

Answers to query Antony and Cleopatra, Act III, Scene ii Sec. 1.1 Answers to query Antony and Cleopatra, Act III, Scene ii Agrippa [Aside to DOMITIUS ENOBARBUS]: Why, Enobarbus, When Antony found Julius Caesar dead, He cried almost to roaring; and he wept When at Philippi he found Brutus slain. Hamlet, Act III, Scene ii Lord Polonius: I did enact Julius Caesar I was killed i' the Capitol; Brutus killed me.

Basic assumptions of Information Retrieval Sec. 1.1 Basic assumptions of Information Retrieval Collection: Fixed set of documents Goal: Retrieve documents with information that is relevant to the user’s information need and helps the user complete a task

The classic search model TASK Get rid of mice in a politically correct way Misconception? Info Need Info about removing mice without killing them Mistranslation? Verbal form How do I trap mice alive? Misformulation? Query mouse trap SEARCH ENGINE Query Refinement Results Corpus

Can’t build the incidence matrix Sec. 1.1 Can’t build the incidence matrix Consider 1 M documents 500K unique terms in all documents 500K x 1M matrix has half-a-trillion 0’s and 1’s. But the matrix is extremely sparse What’s a better representation? We only record the 1 positions.

Sec. 1.2 Inverted index For each term t, we must store a list of all documents that contain t. Identify each by a docID, a document serial number Can we used fixed-size arrays for this? Brutus 1 2 4 11 31 45 173 174 Caesar 1 2 4 5 6 16 57 132 Calpurnia 2 31 54 101 What happens if the word Caesar is added to document 14?

Inverted index We need variable-size postings lists Sec. 1.2 Inverted index We need variable-size postings lists On disk, a continuous run of postings is normal and best In memory, can use linked lists or variable length arrays Some tradeoffs in size/ease of insertion Posting Brutus 1 2 4 11 31 45 173 174 Dictionary Caesar 1 2 4 5 6 16 57 132 Linked lists generally preferred to arrays Dynamic space allocation Insertion of terms into documents easy Space overhead of pointers Calpurnia 2 31 54 101 Postings Sorted by docID (more later on why).

Inverted index construction Sec. 1.2 Inverted index construction Documents to be indexed. Friends, Romans, countrymen. Tokenizer Token stream. Friends Romans Countrymen More on these later. Linguistic modules Modified tokens. friend roman countryman Indexer Inverted index. friend roman countryman 2 4 13 16 1

Indexer steps: Token sequence Sec. 1.2 Indexer steps: Token sequence Sequence of (Modified token, Document ID) pairs. Doc 1 Doc 2 I did enact Julius Caesar I was killed i' the Capitol; Brutus killed me. So let it be with Caesar. The noble Brutus hath told you Caesar was ambitious

Indexer steps: Sort Sort by terms Core indexing step And then docID Sec. 1.2 Indexer steps: Sort Sort by terms And then docID Core indexing step

Indexer steps: Dictionary & Postings Sec. 1.2 Indexer steps: Dictionary & Postings Multiple term entries in a single document are merged. Split into Dictionary and Postings Doc. frequency information is added.

Where do we pay in storage? Sec. 1.2 Where do we pay in storage? Lists of docIDs Terms and counts Pointers

Query processing: AND Consider processing the query: Brutus AND Caesar Sec. 1.3 Query processing: AND Consider processing the query: Brutus AND Caesar Locate Brutus in the Dictionary; Retrieve its postings. Locate Caesar in the Dictionary; “Merge” the two postings: 2 4 8 16 32 64 128 Brutus 1 2 3 5 8 13 21 34 Caesar

Sec. 1.3 The merge Walk through the two postings simultaneously, in time linear in the total number of postings entries 34 128 2 4 8 16 32 64 1 3 5 13 21 2 4 8 16 32 64 128 Brutus Caesar 2 8 1 2 3 5 8 13 21 34 If the list lengths are x and y, the merge takes O(x+y) operations. Crucial: postings sorted by docID. What is this?

Intersecting two postings lists (a “merge” algorithm) The time complexity of the “merge” algorithm: O(x+y) = O(N)

Sidetrack: What is Algorithm? Algorithm: a sequence of finite instructions for doing some task unambiguous and simple to follow Eg, Euclid’s algorithm to determine the greatest common divisor (gcd) of two integers greater than 1 Divide the larger number (A) by the smaller number (B) to get the remainder A’ Divide the larger number (B) by the smaller number (A’) to get the remainder B’ … Divide the larger number (A’) by the smaller number (B’) to get the remainder A’’ … Repeat until you get 0 or 1: Then, gcd is the last divider

Sidetrack: Eg, Optimal Wedding When a person has a chance to date K persons, the optimal wedding algorithm is: Date upto (K/3)-th persons Let the best person among K/3 as B using a criteria C Start dating again from (K/3 + 1)-th person, p If p is better than B using C Stop and Marry p Otherwise, keep dating till K-th person

Sidetrack: How good is an Algorithm? Measure the rate of growth of an algorithm or problem based upon the size of the input Compare algorithms to determine which is better for the situation Input N Describing the relationship as a function f(N) f(N): the number of steps required by an algorithm

Sidetrack: Why Input Size N? What are other factors that affect computation time? Speed of the CPU Size of memory Choice of programming languages Size of the input … Since an algorithm can be implemented in different machines, by different programming languages, and run on different platforms, we are interested in comparing algorithms using factors that are not affected by implementations

Sidetrack: Growth of different f(N) Work required to finish log N 1 Size of input N

Sidetrack: Informal Definition of Big-O Q: How long does it take from State College to Washington DC if you drive? About 3 hours More than 60 minutes Less than 10 days Lower Bound Upper Bound

Sidetrack: Formal Definition of Big-O For a given function g(n), O(g(n)) is defined to be the set of functions O(g(n)) = {f(n) : there exist positive constants c and n0 such that 0  f(n)  cg(n) for all n  n0} “f(n) = O(g(n))” means that f(n) is no worse than the function g(n) when n is large. That is, asymptotic upper bound

Sidetrack: Visual Illustration of Big-O cg(n) Upper Bound f(n) f(n) = O(g(n)) Work required to finish Our Algorithm n0 Size of input

Sidetrack: Tight Upper-Bound We say Big O complexity of 3n2 + 2 = O(n2)  drop constants! because we can show that there is a n0 and a c such that: 0  3n2 + 2  cn2 for n  n0 e.g., c = 4 and n0 = 2 yields: 0  3n2 + 2  4n2 for n  2 You could say 3n2 + 2 = O(n6) or 3n2 + 2 = O(n700) But this is like answering: How long does it take to drive to Washington DC? Less than 11 years vs. Less than 5 hours

Sidetrack: Correct Interpretation of O() Does not mean that it takes only one operation Does mean that the work doesn’t change as N changes Is notation for “constant work” Does not mean that it takes N operations Does mean that the work changes in a way that is proportional to N Is a notation for “work grows at a linear rate” O(1) or “Order One” O(N) or “Order N”

Sidetrack: Ex: Sequential Steps If steps appear sequentially (one after another), then add their respective O(). loop . . . endloop N O(N + M) M

Sidetrack: Ex: Embedded Steps If steps appear embedded (one inside another), then multiply their respective O(). loop . . . endloop M N O(N*M)

Sidetrack: Classes of Big O Functions constant double logarithmic logarithmic polylogarithmic linear quasilinear quadratic cubic polynomial exponential (or geometric) combinatorial double exponential O(1): O(log log n): O(log n): O((log n)c), c>1: O(n): O(n logn) = O(log n!): O(n2): O(n3): O(nc), c>1: O(cn): O(n!) = O(nn): cO(c^n) :

Boolean queries: Exact match Sec. 1.3 Boolean queries: Exact match The Boolean retrieval model is being able to ask a query that is a Boolean expression: Boolean Queries are queries using AND, OR and NOT to join query terms Views each document as a set of words Is precise: document matches condition or not. Perhaps the simplest model to build an IR system on Primary commercial retrieval tool for 3 decades. Many search systems still use are Boolean: Email, library catalog, Mac OS X Spotlight

Query optimization What is the best order for query processing? Sec. 1.3 Query optimization What is the best order for query processing? Consider a query that is an AND of n terms. For each of the n terms, get its postings, then AND them together. Brutus 2 4 8 16 32 64 128 Caesar 1 2 4 5 8 16 21 32 Calpurnia 13 16 Query: Brutus AND Caesar AND Calpurnia 40

Query optimization example Sec. 1.3 Query optimization example Process in order of increasing freq: start with smallest set, then keep cutting further. This is why we kept document freq. in dictionary Brutus 2 4 8 16 32 64 128 Caesar 1 2 4 5 8 16 21 32 Calpurnia 13 16 Execute the query as (Calpurnia AND Brutus) AND Caesar.

Query optimization example Sec. 1.3 Query optimization example Brutus 2 4 8 16 32 64 128 Caesar 1 2 4 5 8 16 21 32 Calpurnia 13 16 Execution order: (Brutus AND Caesar) AND Calpurnia Execution order: (Calpurnia AND Brutus) AND Caesar

More general optimization Sec. 1.3 More general optimization e.g., (madding OR crowd) AND (ignoble OR strife) Get doc. freq.’s for all terms. Estimate the size of each OR by the sum of its doc. freq.’s (conservative). Process in increasing order of OR sizes.

More general optimization If the query is: friends AND romans AND (NOT countrymen) how could we use the freq of countrymen?

Example: WestLaw http://www.westlaw.com/ Extended Boolean model w. ranking

Example: WestLaw http://www.westlaw.com/ Sec. 1.4 Example: WestLaw http://www.westlaw.com/ Largest commercial (paying subscribers) legal search service (started 1975; ranking added 1992) Tens of terabytes of data; 700,000 users Majority of users still use boolean queries Example query: What is the statute of limitations in cases involving the federal tort claims act? LIMIT! /3 STATUTE ACTION /S FEDERAL /2 TORT /3 CLAIM /3 = within 3 words, /S = in same sentence