2002.10.29 - SLIDE 1IS 202 – FALL 2002 Prof. Ray Larson & Prof. Marc Davis UC Berkeley SIMS Tuesday and Thursday 10:30 am - 12:00 pm Fall 2002

2002.10.29 - SLIDE 1IS 202 – FALL 2002

Prof. Ray Larson & Prof. Marc Davis

UC Berkeley SIMS

Tuesday and Thursday 10:30 am - 12:00 pm

Fall 2002http://www.sims.berkeley.edu/academics/courses/is202/f02/

SIMS 202:

Information Organization

and Retrieval

Lecture 17: Statistical Properties of Text

2002.10.29 - SLIDE 2IS 202 – FALL 2002

Lecture Overview

• Review– Central Concepts in IR– Boolean Logic

• Content Analysis

• Statistical Properties of Text– Zipf distribution– Statistical dependence

• Indexing and Inverted Files

Credit for some of the slides in this lecture goes to Marti Hearst

2002.10.29 - SLIDE 3IS 202 – FALL 2002

Central Concepts in IR

• Documents

• Queries

• Collections

• Evaluation

• Relevance

2002.10.29 - SLIDE 4IS 202 – FALL 2002

Relevance (introduction)

• In what ways can a document be relevant to a query?– Answer precise question precisely

– Who is buried in grant’s tomb? Grant

– Partially answer question– Where is Danville? Near Walnut Creek

– Suggest a source for more information– What is lymphodema? Look in this Medical Dictionary…

– Give background information– Remind the user of other knowledge– Others ...

2002.10.29 - SLIDE 5IS 202 – FALL 2002

Relevance

• “Intuitively, we understand quite well what relevance means. It is a primitive ‘y’ know’ concept, as is information for which we hardly need a definition. … if and when any productive contact [in communication] is desired, consciously or not, we involve and use this intuitive notion or relevance.”

» Saracevic, 1975 p. 324

2002.10.29 - SLIDE 6IS 202 – FALL 2002

Janes’ View

Topicality

Pertinence

Relevance

Utility

Satisfaction

2002.10.29 - SLIDE 7IS 202 – FALL 2002

Boolean Queries

• Cat

• Cat OR Dog

• Cat AND Dog

• (Cat AND Dog)

• (Cat AND Dog) OR Collar

• (Cat AND Dog) OR (Collar AND Leash)

• (Cat OR Dog) AND (Collar OR Leash)

2002.10.29 - SLIDE 8IS 202 – FALL 2002

Boolean Logic

A B

BABA

BABA

BAC

BAC

AC

AC

:Law sDeMorgan'

2002.10.29 - SLIDE 9IS 202 – FALL 2002

Boolean Logic

t33

t11 t22

D11D22

D33

D44D55

D66

D88D77

D99

D1010

D1111

m1

m2

m3m5

m4

m7m8

m6

m2 = t1 t2 t3

m1 = t1 t2 t3

m4 = t1 t2 t3

m3 = t1 t2 t3

m6 = t1 t2 t3

m5 = t1 t2 t3

m8 = t1 t2 t3

m7 = t1 t2 t3

2002.10.29 - SLIDE 10IS 202 – FALL 2002

Boolean Systems

• Most of the commercial database search systems that pre-date the WWW are based on Boolean search– Dialog, Lexis-Nexis, etc.

• Most Online Library Catalogs are Boolean systems– E.g. MELVYL

• Database systems use Boolean logic for searching

• Many of the search engines sold for intranet search of web sites are Boolean

2002.10.29 - SLIDE 11IS 202 – FALL 2002

Content Analysis

• Automated Transformation of raw text into a form that represents some aspect(s) of its meaning

• Including, but not limited to:– Automated Thesaurus Generation– Phrase Detection– Categorization– Clustering– Summarization

2002.10.29 - SLIDE 12IS 202 – FALL 2002

Techniques for Content Analysis

• Statistical– Single Document– Full Collection

• Linguistic– Syntactic– Semantic– Pragmatic

• Knowledge-Based (Artificial Intelligence)

• Hybrid (Combinations)

2002.10.29 - SLIDE 13IS 202 – FALL 2002

Text Processing

• Standard Steps:– Recognize document structure

• titles, sections, paragraphs, etc.

– Break into tokens• usually space and punctuation delineated• special issues with Asian languages

– Stemming/morphological analysis– Store in inverted index (to be discussed later)

2002.10.29 - SLIDE 14IS 202 – FALL 2002

Content Analysis Areas

How isthe text processed?

Informationneed

Index

Pre-process

Parse

Collections

Rank

Query

text input

How isthe queryconstructed?

2002.10.29 - SLIDE 15

Document Processing Steps

From “Modern IR” textbook

2002.10.29 - SLIDE 16IS 202 – FALL 2002

Stemming and Morphological Analysis

• Goal: “normalize” similar words• Morphology (“form” of words)

– Inflectional Morphology• E.g,. inflect verb endings and noun number• Never change grammatical class

– dog, dogs– tengo, tienes, tiene, tenemos, tienen

– Derivational Morphology • Derive one word from another, • Often change grammatical class

– build, building; health, healthy

2002.10.29 - SLIDE 17IS 202 – FALL 2002

Automated Methods

• Powerful multilingual tools exist for morphological analysis– PCKimmo, Xerox Lexical technology– Require a grammar and dictionary– Use “two-level” automata

• Stemmers:– Very dumb rules work well (for English)– Porter Stemmer: Iteratively remove suffixes– Improvement: pass results through a lexicon

2002.10.29 - SLIDE 18IS 202 – FALL 2002

Errors Generated by Porter Stemmer

Too Aggressive Too Timid organization/ organ european/ europe

policy/ police cylinder/ cylindrical

execute/ executive create/ creation

arm/ army search/ searcher

From Krovetz ‘93

2002.10.29 - SLIDE 19IS 202 – FALL 2002

Statistical Properties of Text

• Token occurrences in text are not uniformly distributed

• They are also not normally distributed

• They do exhibit a Zipf distribution

2002.10.29 - SLIDE 20IS 202 – FALL 2002

Plotting Word Frequency by Rank

• Main idea:– Count how many times tokens occur in the

text• Sum over all of the texts in the collection

• Now order these tokens according to how often they occur (highest to lowest)

• This is called the rank

2002.10.29 - SLIDE 21IS 202 – FALL 2002

A Typical Collection

8164 the4771 of4005 to2834 a2827 and2802 in1592 The1370 for1326 is1324 s1194 that 973 by

969 on 915 FT 883 Mr 860 was 855 be 849 Pounds 798 TEXT 798 PUB 798 PROFILE 798 PAGE 798 HEADLINE 798 DOCNO

1 ABC 1 ABFT 1 ABOUT 1 ACFT 1 ACI 1 ACQUI 1 ACQUISITIONS 1 ACSIS 1 ADFT 1 ADVISERS 1 AE

Government documents, 157734 tokens, 32259 unique

2002.10.29 - SLIDE 22IS 202 – FALL 2002

A Small Collection (Stems)Rank Freq Term1 37 system2 32 knowledg3 24 base4 20 problem5 18 abstract6 15 model7 15 languag8 15 implem9 13 reason10 13 inform11 11 expert12 11 analysi13 10 rule14 10 program15 10 oper16 10 evalu17 10 comput18 10 case19 9 gener20 9 form

150 2 enhanc151 2 energi152 2 emphasi153 2 detect154 2 desir155 2 date156 2 critic157 2 content158 2 consider159 2 concern160 2 compon161 2 compar162 2 commerci163 2 clause164 2 aspect165 2 area166 2 aim167 2 affect

2002.10.29 - SLIDE 23IS 202 – FALL 2002

The Corresponding Zipf Curve

Rank Freq1 37 system2 32 knowledg3 24 base4 20 problem5 18 abstract6 15 model7 15 languag8 15 implem9 13 reason10 13 inform11 11 expert12 11 analysi13 10 rule14 10 program15 10 oper16 10 evalu17 10 comput18 10 case19 9 gener20 9 form

2002.10.29 - SLIDE 24IS 202 – FALL 2002

Zoom in on the Knee of the Curve

43 6 approach44 5 work45 5 variabl46 5 theori47 5 specif48 5 softwar49 5 requir50 5 potenti51 5 method52 5 mean53 5 inher54 5 data55 5 commit56 5 applic57 4 tool58 4 technolog59 4 techniqu

2002.10.29 - SLIDE 25IS 202 – FALL 2002

Zipf Distribution

• The Important Points:– a few elements occur very frequently– a medium number of elements have medium

frequency– many elements occur very infrequently

2002.10.29 - SLIDE 26IS 202 – FALL 2002

• The product of the frequency of words (f) and their rank (r) is approximately constant– Rank = order of words’ frequency of occurrence

• Another way to state this is with an approximately correct rule of thumb:– Say the most common term occurs C times– The second most common occurs C/2 times– The third most common occurs C/3 times

Zipf Distribution

10/

/1

NC

rCf

2002.10.29 - SLIDE 27

Zipf Distribution

Linear Scale Logarithmic Scale

2002.10.29 - SLIDE 28IS 202 – FALL 2002

What has a Zipf Distribution?

• Words in a text collection– Virtually any use of natural language

• Library book checkout patterns

• Incoming Web Page Requests (Nielsen)

• Outgoing Web Page Requests (Cunha & Crovella)

• Document Size on Web (Cunha & Crovella)

2002.10.29 - SLIDE 29IS 202 – FALL 2002

Related Distributions/”Laws”

• Bradford’s Law of Scattering

• Lotka’s Law of Productivity

• De Solla Price’s Urn Model for “Cumulative Advantage Processes”

½ = 50% 2/3 = 66% ¾ = 75%Pick Pick

Replace +1 Replace +1

2002.10.29 - SLIDE 30IS 202 – FALL 2002

Very frequent word stemsWORD FREQu 63245ha 65470california 67251m 67903

1998 68662system 69345t 70014about 70923servic 71822work 71958home 72131other 72726research 74264

1997 75323can 76762next 77973your 78489all 79993public 81427us 82551c 83250www 87029wa 92384program 95260

not 100204http 100696d 101034html 103698student 104635univers 105183inform 106463will 109700new 115937have 119428page 128702messag 141542from 147440you 162499edu 167298be 185162publib 189334librari 189347i 190635lib 223851that 227311s 234467berkelei 245406re 272123web 280966archiv 305834

From the Cha-Cha Web Index for the Berkeley.EDU domain

2002.10.29 - SLIDE 31IS 202 – FALL 2002

Frequent words on the WWW• 65002930 the• 62789720 a• 60857930 to• 57248022 of• 54078359 and• 52928506 in• 50686940 s• 49986064 for• 45999001 on• 42205245 this• 41203451 is• 39779377 by• 35439894 with• 35284151 or• 34446866 at• 33528897 all• 31583607 are

• 30998255 from• 30755410 e• 30080013 you• 29669506 be• 29417504 that• 28542378 not• 28162417 an• 28110383 as• 28076530 home• 27650474 it• 27572533 i• 24548796 have• 24420453 if• 24376758 new• 24171603 t• 23951805 your• 23875218 page

• 22292805 about• 22265579 com• 22107392 information• 21647927 will• 21368265 can• 21367950 more• 21102223 has• 20621335 no• 19898015 other• 19689603 one• 19613061 c• 19394862 d• 19279458 m• 19199145 was• 19075253 copyright• 18636563 us

(see http://elib.cs.berkeley.edu/docfreq/docfreq.html)

2002.10.29 - SLIDE 32IS 202 – FALL 2002

Words that occur few times WORD FREQagendaaugust 1anelectronic 1centerjanuary 1packardequipment 1systemjuly 1systemscs186 1todaymcb 1workshopsfinding 1workshopsthe 1lollini 10+ 1

0 100summary 1

35816 135823 1

01d 135830 135837 1

02-156-10 135844 135851 1

02aframst 1311 1313 1

03agenvchm 1401 1408 1

408 1422 1424 1429 1

04agrcecon 104cklist 105-128-10 1

501 1506 1

05amstud 106anhist 107-149 107-800-80 107anthro 108apst 1

From the Cha-Cha Web Index for the Berkeley.EDU domain

2002.10.29 - SLIDE 33IS 202 – FALL 2002

Consequences of Zipf

• There are always a few very frequent tokens that are not good discriminators.– Called “stop words” in IR– Usually correspond to linguistic notion of “closed-

class” words• English examples: to, from, on, and, the, ...• Grammatical classes that don’t take on new members.

• There are always a large number of tokens that occur once (and can have unexpected consequences with some IR algorithms)

• Medium frequency words most descriptive

2002.10.29 - SLIDE 34IS 202 – FALL 2002

Word Frequency vs. Resolving Power

The most frequent words are not the most descriptive.

(from van Rijsbergen 79)

2002.10.29 - SLIDE 35IS 202 – FALL 2002

• How likely is a red car to drive by given we’ve seen a black one?

• How likely is the word “ambulence” to appear, given that we’ve seen “car accident”?

• Color of cars driving by are independent (although more frequent colors are more likely)

• Words in text are not independent (although again more frequent words are more likely)

Statistical Independence vs. Dependence

2002.10.29 - SLIDE 36IS 202 – FALL 2002

Statistical Independence

• Two events x and y are statistically independent if the product of the probabilities of their happening individually equals the probability of their happening together

),()()( yxPyPxP

2002.10.29 - SLIDE 37IS 202 – FALL 2002

Statistical Independence and Dependence

• What are examples of things that are statistically independent?

• What are examples of things that are statistically dependent?

2002.10.29 - SLIDE 38IS 202 – FALL 2002

Lexical Associations

• Subjects write first word that comes to mind– doctor/nurse; black/white (Palermo & Jenkins 64)

• Text Corpora can yield similar associations• One measure: Mutual Information (Church and

Hanks 89)

• If word occurrences were independent, the numerator and denominator would be equal (if measured across a large collection)

)(),(

),(log),( 2 yPxP

yxPyxI

2002.10.29 - SLIDE 39IS 202 – FALL 2002

Statistical Independence

• Compute for a window of words

collectionin wordsofnumber

in occur -co and timesofnumber ),(

position at starting ndow within wiwords

5)(say windowoflength ||

),(1

),(

:follows as ),( eapproximat llWe'

/)()(

t.independen if ),()()(

||

1

N

wyxyxw

iw

ww

yxwN

yxP

yxP

NxfxP

yxPyPxP

i

wN

ii

w1 w11w21

a b c d e f g h i j k l m n o p

2002.10.29 - SLIDE 40IS 202 – FALL 2002

Interesting Associations with “Doctor”

I(x,y) f(x,y) f(x) x f(y) y11.3 12 111 Honorary 621 Doctor

11.3 8 1105 Doctors 44 Dentists

10.7 30 1105 Doctors 241 Nurses

9.4 8 1105 Doctors 154 Treating

9.0 6 275 Examined 621 Doctor

8.9 11 1105 Doctors 317 Treat

8.7 25 621 Doctor 1407 Bills

AP Corpus, N=15 million, Church & Hanks 89

2002.10.29 - SLIDE 41IS 202 – FALL 2002

I(x,y) f(x,y) f(x) x f(y) y0.96 6 621 doctor 73785 with

0.95 41 284690 a 1105 doctors

0.93 12 84716 is 1105 doctors

These associations were likely to happen because the non-doctor words shown here are very common

and therefore likely to co-occur with any noun.

Un-Interesting Associations with “Doctor”

AP Corpus, N=15 million, Church & Hanks 89

2002.10.29 - SLIDE 42IS 202 – FALL 2002

Document Vectors

• Documents are represented as “bags of words”

• Represented as vectors when used computationally– A vector is like an array of floating point– Has direction and magnitude– Each vector holds a place for every term in

the collection– Therefore, most vectors are sparse

2002.10.29 - SLIDE 43IS 202 – FALL 2002

Document Vectors

ID nova galaxy heat h'wood film role diet furA 10 5 3B 5 10C 10 8 7D 9 10 5E 10 10F 9 10G 5 7 9H 6 10 2 8I 7 5 1 3

“Nova” occurs 10 times in text A“Galaxy” occurs 5 times in text A“Heat” occurs 3 times in text A(Blank means 0 occurrences.)

2002.10.29 - SLIDE 44IS 202 – FALL 2002

Document Vectors

ID nova galaxy heat h'wood film role diet furA 10 5 3B 5 10C 10 8 7D 9 10 5E 10 10F 9 10G 5 7 9H 6 10 2 8I 7 5 1 3

“Hollywood” occurs 7 times in text I“Film” occurs 5 times in text I“Diet” occurs 1 time in text I“Fur” occurs 3 times in text I

2002.10.29 - SLIDE 45IS 202 – FALL 2002

Document Vectors

ID nova galaxy heat h'wood film role diet furA 10 5 3B 5 10C 10 8 7D 9 10 5E 10 10F 9 10G 5 7 9H 6 10 2 8I 7 5 1 3

2002.10.29 - SLIDE 46IS 202 – FALL 2002

We Can Plot the Vectors

Star

Diet

Doc about astronomyDoc about movie stars

Doc about mammal behavior

2002.10.29 - SLIDE 47

Documents in 3D Space

2002.10.29 - SLIDE 48IS 202 – FALL 2002

Content Analysis Summary

• Content Analysis: transforming raw text into more computationally useful forms

• Words in text collections exhibit interesting statistical properties– Word frequencies have a Zipf distribution– Word co-occurrences exhibit dependencies

• Text documents are transformed to vectors– Pre-processing includes tokenization, stemming,

collocations/phrases– Documents occupy multi-dimensional space

2002.10.29 - SLIDE 49IS 202 – FALL 2002

Inverted Index

• This is the primary data structure for text indexes

• Main Idea:– Invert documents into a big index

• Basic steps:– Make a “dictionary” of all the tokens in the

collection– For each token, list all the docs it occurs in.– Do a few things to reduce redundancy in the data

structure

2002.10.29 - SLIDE 50IS 202 – FALL 2002

Informationneed

Index

Pre-process

Parse

Collections

Rank

Query

text inputHow isthe indexconstructed?

2002.10.29 - SLIDE 51IS 202 – FALL 2002

Inverted Indexes

• We have seen “Vector files” conceptually– An Inverted File is a vector file “inverted” so

that rows become columns and columns become rows

docs t1 t2 t3D1 1 0 1D2 1 0 0D3 0 1 1D4 1 0 0D5 1 1 1D6 1 1 0D7 0 1 0D8 0 1 0D9 0 0 1

D10 0 1 1

Terms D1 D2 D3 D4 D5 D6 D7 …

t1 1 1 0 1 1 1 0t2 0 0 1 0 1 1 1t3 1 0 1 0 1 0 0

2002.10.29 - SLIDE 52IS 202 – FALL 2002

How Inverted Files Are Created

• Documents are parsed to extract tokens. These are saved with the Document ID.

Now is the timefor all good men

to come to the aidof their country

Doc 1

It was a dark andstormy night in

the country manor. The time was past midnight

Doc 2

Term Doc #now 1is 1the 1time 1for 1all 1good 1men 1to 1come 1to 1the 1aid 1of 1their 1country 1it 2was 2a 2dark 2and 2stormy 2night 2in 2the 2country 2manor 2the 2time 2was 2past 2midnight 2

2002.10.29 - SLIDE 53IS 202 – FALL 2002

How Inverted Files are Created

• After all documents have been parsed the inverted file is sorted alphabetically.

Term Doc #a 2aid 1all 1and 2come 1country 1country 2dark 2for 1good 1in 2is 1it 2manor 2men 1midnight 2night 2now 1of 1past 2stormy 2the 1the 1the 2the 2their 1time 1time 2to 1to 1was 2was 2

Term Doc #now 1is 1the 1time 1for 1all 1good 1men 1to 1come 1to 1the 1aid 1of 1their 1country 1it 2was 2a 2dark 2and 2stormy 2night 2in 2the 2country 2manor 2the 2time 2was 2past 2midnight 2

2002.10.29 - SLIDE 54IS 202 – FALL 2002

How Inverted Files are Created

• Multiple term entries for a single document are merged.

• Within-document term frequency information is compiled.

Term Doc # Freqa 2 1aid 1 1all 1 1and 2 1come 1 1country 1 1country 2 1dark 2 1for 1 1good 1 1in 2 1is 1 1it 2 1manor 2 1men 1 1midnight 2 1night 2 1now 1 1of 1 1past 2 1stormy 2 1the 1 2the 2 2their 1 1time 1 1time 2 1to 1 2was 2 2

Term Doc #a 2aid 1all 1and 2come 1country 1country 2dark 2for 1good 1in 2is 1it 2manor 2men 1midnight 2night 2now 1of 1past 2stormy 2the 1the 1the 2the 2their 1time 1time 2to 1to 1was 2was 2

2002.10.29 - SLIDE 55IS 202 – FALL 2002

How Inverted Files are Created

• Then the file can be split into – A Dictionary file – and – A Postings file

2002.10.29 - SLIDE 56IS 202 – FALL 2002

How Inverted Files are Created

Dictionary PostingsTerm Doc # Freqa 2 1aid 1 1all 1 1and 2 1come 1 1country 1 1country 2 1dark 2 1for 1 1good 1 1in 2 1is 1 1it 2 1manor 2 1men 1 1midnight 2 1night 2 1now 1 1of 1 1past 2 1stormy 2 1the 1 2the 2 2their 1 1time 1 1time 2 1to 1 2was 2 2

Doc # Freq2 11 11 12 11 11 12 12 11 11 12 11 12 12 11 12 12 11 11 12 12 11 22 21 11 12 11 22 2

Term N docs Tot Freqa 1 1aid 1 1all 1 1and 1 1come 1 1country 2 2dark 1 1for 1 1good 1 1in 1 1is 1 1it 1 1manor 1 1men 1 1midnight 1 1night 1 1now 1 1of 1 1past 1 1stormy 1 1the 2 4their 1 1time 2 2to 1 2was 1 2

2002.10.29 - SLIDE 57IS 202 – FALL 2002

Inverted indexes

• Permit fast search for individual terms• For each term, you get a list consisting of:

– document ID – frequency of term in doc (optional) – position of term in doc (optional)

• These lists can be used to solve Boolean queries:

• country -> d1, d2• manor -> d2• country AND manor -> d2

• Also used for statistical ranking algorithms

2002.10.29 - SLIDE 58IS 202 – FALL 2002

How Inverted Files are Used

Dictionary PostingsDoc # Freq

2 11 11 12 11 11 12 12 11 11 12 11 12 12 11 12 12 11 11 12 12 11 22 21 11 12 11 22 2

Term N docs Tot Freqa 1 1aid 1 1all 1 1and 1 1come 1 1country 2 2dark 1 1for 1 1good 1 1in 1 1is 1 1it 1 1manor 1 1men 1 1midnight 1 1night 1 1now 1 1of 1 1past 1 1stormy 1 1the 2 4their 1 1time 2 2to 1 2was 1 2

Query on

“time” AND “dark”

2 docs with “time” in dictionary ->

IDs 1 and 2 from posting file

1 doc with “dark” in dictionary ->

ID 2 from posting file

Therefore, only doc 2 satisfied the query.

2002.10.29 - SLIDE 59IS 202 – FALL 2002

Next Time

• More on Vector Representation

• The Vector Model of IR

• Term weighting

• Statistical ranking methods