Introduction to Information Retrieval Ch 1 Boolean Retrieval

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

Introduction to Information Retrieval In the Last Class § Ch 19 § Index size estimation § Near-duplicate detection using shingling § Ch 21 § Page. Rank § Hubs and Authorities 2

Introduction to Information Retrieval Next 2 Classes� § Ch 1 § 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 3

Introduction to 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). 4

Introduction to Information Retrieval 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. 5

Introduction to Information Retrieval 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 6

Introduction to Information Retrieval Unstructured (text) vs. structured (database) data in 1996 7

Introduction to Information Retrieval Unstructured (text) vs. structured (database) data in 2009 8

Introduction to Information Retrieval 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) 9

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

Introduction to Information Retrieval 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. 11

Introduction to Information Retrieval 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. 12

Introduction to 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 13

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

Introduction to Information Retrieval Sec. 1. 1 Can’t build the incidence matrix § Consider § 1 M documents § 500 K unique terms in all documents § 500 K x 1 M 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. 15

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

Sec. 1. 2 Introduction to Information Retrieval 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 Brutus 1 Caesar 1 Calpurnia Dictionary 2 2 2 31 Posting 4 11 31 45 173 174 4 5 6 16 57 132 54 101 Postings Sorted by doc. ID (more later on why). 17

Sec. 1. 2 Introduction to Information Retrieval Inverted index construction Documents to be indexed. Friends, Romans, countrymen. Tokenizer Token stream. Friends Romans Linguistic modules Modified tokens. Inverted index. friend roman Countrymen countryman Indexer friend 2 4 roman 1 2 countryman 13 16

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

Introduction to Information Retrieval Indexer steps: Sort § Sort by terms § And then doc. ID Core indexing step Sec. 1. 2

Introduction to Information Retrieval 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.

Sec. 1. 2 Introduction to Information Retrieval Where do we pay in storage? Lists of doc. IDs Terms and counts Pointers 22

Sec. 1. 3 Introduction to Information Retrieval Query processing: AND § Consider processing the query: Brutus AND Caesar § Locate Brutus in the Dictionary; § Retrieve its postings. § Locate Caesar in the Dictionary; § Retrieve its postings. § “Merge” the two postings: 2 4 8 16 1 2 3 5 32 8 64 13 128 21 Brutus 34 Caesar 23

Sec. 1. 3 Introduction to Information Retrieval The merge § Walk through the two postings simultaneously, in time linear in the total number of postings entries 2 8 2 4 8 16 1 2 3 5 32 8 128 64 13 21 Brutus 34 Caesar If the list lengths are x and y, the merge takes O(x+y) operations. Crucial: postings sorted by doc. ID. What is this? 24

Introduction to Information Retrieval Intersecting two postings lists (a “merge” algorithm) The time complexity of the “merge” algorithm: O(x+y) = O(N) 25

Introduction to Information Retrieval 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� 26

Introduction to Information Retrieval Sidetrack: Eg, Optimal Wedding § When a person has a chance to date K persons, the optimal wedding algorithm is: 1. Date upto (K/3)-th persons 1. Let the best person among K/3 as B using a criteria C 2. Start dating again from (K/3 + 1)-th person, p 3. If p is better than B using C 1. Stop and Marry p 4. Otherwise, keep dating till K-th person 27

Introduction to Information Retrieval Sidetrack: How good is an Algorithm? l Measure the rate of growth of an algorithm or problem based upon the size of the input l l l Compare algorithms to determine which is better for the situation Input N Describing the relationship as a function f(N) l f(N): the number of steps required by an algorithm 28

Introduction to Information Retrieval 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 29

Introduction to Information Retrieval Work required to finish Sidetrack: Growth of different f(N) N 2 N log N 1 Size of input N 30

Introduction to Information Retrieval Sidetrack: Informal Definition of Big-O l Q: How long does it take from State College to Washington DC if you drive? l About 3 hours l More than 60 minutes Lower Bound l Less than 10 days Upper Bound 31

Introduction to Information Retrieval 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 n 0 such that 0 f(n) cg(n) for all n n 0} “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 32

Introduction to Information Retrieval Work required to finish Sidetrack: Visual Illustration of Big-O Upper Bound cg(n) f(n) = O(g(n)) Our Algorithm n 0 Size of input 33

Introduction to Information Retrieval Sidetrack: Tight Upper-Bound We say Big O complexity of 3 n 2 + 2 = O(n 2) drop constants! because we can show that there is a n 0 and a c such that: 0 3 n 2 + 2 cn 2 for n n 0 e. g. , c = 4 and n 0 = 2 yields: 0 3 n 2 + 2 4 n 2 for n 2 You could say 3 n 2 + 2 = O(n 6) or 3 n 2 + 2 = O(n 700) But this is like answering: l How long does it take to drive to Washington DC? l Less than 11 years vs. Less than 5 hours 34

Introduction to Information Retrieval Sidetrack: Correct Interpretation of O() O(1) or “Order One” l Does not mean that it takes only one operation l Does mean that the work doesn’t change as N changes l Is notation for “constant work” O(N) or “Order N” l l l 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” 35

Introduction to Information Retrieval Sidetrack: Ex: Sequential Steps § If steps appear sequentially (one after another), then add their respective O(). loop. . . endloop N O(N + M) M 36

Introduction to Information Retrieval Sidetrack: Ex: Embedded Steps § If steps appear embedded (one inside another), then multiply their respective O(). loop. . . endloop M N O(N*M) 37

Introduction to Information Retrieval Sidetrack: Classes of Big O Functions § § § O(1): O(log n): O((log n)c), c>1: O(n): O(n logn) = O(log n!): O(n 2): O(n 3): O(nc), c>1: O(cn): O(n!) = O(nn): c. O(c^n) : l l l constant double logarithmic polylogarithmic linear quasilinear quadratic cubic polynomial exponential (or geometric) combinatorial double exponential

Introduction to Information Retrieval 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 39

Sec. 1. 3 Introduction to Information Retrieval 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 Caesar 1 Calpurnia 4 2 8 16 32 64 128 4 5 8 16 21 32 13 16 Query: Brutus AND Caesar AND Calpurnia 40

Sec. 1. 3 Introduction to Information Retrieval 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 Caesar 1 Calpurnia 4 2 8 16 32 64 128 4 5 8 16 21 32 13 16 Execute the query as (Calpurnia AND Brutus) AND Caesar. 41

Sec. 1. 3 Introduction to Information Retrieval Query optimization example Brutus 2 Caesar 1 Calpurnia 4 2 8 16 32 64 128 4 5 8 16 21 32 13 16 Execution order: (Brutus AND Caesar) AND Calpurnia Execution order: (Calpurnia AND Brutus) AND Caesar 42

Introduction to Information Retrieval 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. 43

Introduction to Information Retrieval More general optimization § If the query is: § friends AND romans AND (NOT countrymen) § how could we use the freq of countrymen? 44

Introduction to Information Retrieval Example: West. Law http: //www. westlaw. com/ Extended Boolean model w. ranking 45

Sec. 1. 4 Introduction to Information Retrieval Example: West. Law 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 46