2003.10.30 - SLIDE 1IS 202 – FALL 2003 Prof. Ray Larson & Prof. Marc Davis UC Berkeley SIMS Tuesday and Thursday 10:30 am - 12:00 pm Fall 2003

2003.10.30 - SLIDE 1IS 202 – FALL 2003

Prof. Ray Larson & Prof. Marc Davis

UC Berkeley SIMS

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

Fall 2003http://www.sims.berkeley.edu/academics/courses/is202/f03/

SIMS 202:

Information Organization

and Retrieval

Lecture 18: Statistical Properties of Texts and Vector Representation

2003.10.30 - SLIDE 2IS 202 – FALL 2003

Lecture Overview

• Review– Boolean Searching– Content Analysis

• Statistical Properties of Text– Zipf Distribution– Statistical Dependence

• Indexing and Inverted Files• Vector Representation• Term Weights• Vector Matching

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

2003.10.30 - SLIDE 3IS 202 – FALL 2003

Lecture Overview





2003.10.30 - SLIDE 4IS 202 – FALL 2003

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)

2003.10.30 - SLIDE 5IS 202 – FALL 2003

Boolean Logic

A B

BABA

BABA

BAC

BAC

AC

AC

:Law sDeMorgan'

2003.10.30 - SLIDE 6IS 202 – FALL 2003

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

2003.10.30 - SLIDE 7IS 202 – FALL 2003

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

2003.10.30 - SLIDE 8IS 202 – FALL 2003

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

2003.10.30 - SLIDE 9IS 202 – FALL 2003

Techniques for Content Analysis

• Statistical– Single Document– Full Collection

• Linguistic– Syntactic– Semantic– Pragmatic

• Knowledge-Based (Artificial Intelligence)

• Hybrid (Combinations)

2003.10.30 - SLIDE 10IS 202 – FALL 2003

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)

2003.10.30 - SLIDE 11IS 202 – FALL 2003

Techniques for Content Analysis

• Statistical– Single Document– Full Collection

• Linguistic– Syntactic– Semantic– Pragmatic

• Knowledge-Based (Artificial Intelligence)

• Hybrid (Combinations)

2003.10.30 - SLIDE 12

Document Processing Steps

From “Modern IR” Textbook

2003.10.30 - SLIDE 13IS 202 – FALL 2003

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

2003.10.30 - SLIDE 14IS 202 – FALL 2003

Lecture Overview





2003.10.30 - SLIDE 15IS 202 – FALL 2003

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

2003.10.30 - SLIDE 16IS 202 – FALL 2003

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

2003.10.30 - SLIDE 17IS 202 – FALL 2003

Zipf Distribution

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

frequency– Many elements occur very infrequently

2003.10.30 - SLIDE 18

Zipf Distribution

Linear Scale Logarithmic Scale

2003.10.30 - SLIDE 19IS 202 – FALL 2003

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

2003.10.30 - SLIDE 20IS 202 – FALL 2003

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)

2003.10.30 - SLIDE 21IS 202 – FALL 2003

Word Frequency vs. Resolving Power

The most frequent words are not the most descriptive

(from van Rijsbergen 79)

2003.10.30 - SLIDE 22IS 202 – FALL 2003

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

2003.10.30 - SLIDE 23IS 202 – FALL 2003

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

2003.10.30 - SLIDE 24IS 202 – FALL 2003

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

2003.10.30 - SLIDE 25IS 202 – FALL 2003

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

2003.10.30 - SLIDE 26IS 202 – FALL 2003

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

2003.10.30 - SLIDE 27IS 202 – FALL 2003

Lecture Overview





2003.10.30 - SLIDE 28IS 202 – FALL 2003

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

2003.10.30 - SLIDE 29IS 202 – FALL 2003

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

2003.10.30 - SLIDE 30IS 202 – FALL 2003

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

2003.10.30 - SLIDE 31IS 202 – FALL 2003

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

2003.10.30 - SLIDE 32IS 202 – FALL 2003

Lecture Overview





2003.10.30 - SLIDE 33IS 202 – FALL 2003

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

2003.10.30 - SLIDE 34IS 202 – FALL 2003

Vector Space Model

• Documents are represented as vectors in term space– Terms are usually stems– Documents represented by binary or weighted vectors

of terms

• Queries represented the same as documents• Query and Document weights are based on

length and direction of their vector• A vector distance measure between the query

and documents is used to rank retrieved documents

2003.10.30 - SLIDE 35IS 202 – FALL 2003

Vector Representation

• Documents and Queries are represented as vectors

• Position 1 corresponds to term 1, position 2 to term 2, position t to term t

• The weight of the term is stored in each position

absent is terma if 0

,...,,

,...,,

21

21

w

wwwQ

wwwD

qtqq

dddi itii

2003.10.30 - SLIDE 36IS 202 – FALL 2003

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.)

2003.10.30 - SLIDE 37IS 202 – FALL 2003

Document Vectors


“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

2003.10.30 - SLIDE 38IS 202 – FALL 2003

Document Vectors


2003.10.30 - SLIDE 39IS 202 – FALL 2003

We Can Plot the Vectors

Star

Diet

Doc about astronomyDoc about movie stars

Doc about mammal behavior

2003.10.30 - SLIDE 40IS 202 – FALL 2003

Documents in 3D Space

Primary assumption of the Vector Space Model: Documents that are “close together” in space are similar in meaning

2003.10.30 - SLIDE 41IS 202 – FALL 2003

Vector Space Documents and Queries

docs t1 t2 t3 RSV=Q.DiD1 1 0 1 4D2 1 0 0 1D3 0 1 1 5D4 1 0 0 1D5 1 1 1 6D6 1 1 0 3D7 0 1 0 2D8 0 1 0 2D9 0 0 1 3

D10 0 1 1 5D11 0 0 1 4

Q 1 2 3q1 q2 q3

D1

D2

D3

D4

D5

D6

D7

D8

D9

D10

D11

t2

t3

t1

Boolean term combinationsQ is a query – also represented as a vector

2003.10.30 - SLIDE 42IS 202 – FALL 2003

Documents in Vector Space

t1

t2

t3

D1

D2

D10

D3

D9

D4

D7

D8

D5

D11

D6

2003.10.30 - SLIDE 43IS 202 – FALL 2003

Lecture Overview





2003.10.30 - SLIDE 44IS 202 – FALL 2003

Assigning Weights to Terms

• Binary Weights

• Raw term frequency

• tf*idf– Recall the Zipf distribution– Want to weight terms highly if they are

• Frequent in relevant documents … BUT• Infrequent in the collection as a whole

• Automatically derived thesaurus terms

2003.10.30 - SLIDE 45IS 202 – FALL 2003

Binary Weights

• Only the presence (1) or absence (0) of a term is included in the vector


D10 0 1 1D11 1 0 1

2003.10.30 - SLIDE 46IS 202 – FALL 2003

Raw Term Weights

• The frequency of occurrence for the term in each document is included in the vector


D10 0 3 5D11 4 0 1

2003.10.30 - SLIDE 47IS 202 – FALL 2003

Assigning Weights

• tf*idf measure:– Term frequency (tf)– Inverse document frequency (idf)

• A way to deal with some of the problems of the Zipf distribution

• Goal: Assign a tf*idf weight to each term in each document

2003.10.30 - SLIDE 48IS 202 – FALL 2003

tf*idf

)/log(* kikik nNtfw

log

Tcontain that in documents ofnumber the

collection in the documents ofnumber total

in T termoffrequency document inverse

document in T termoffrequency

document in term

nNidf

Cn

CN

Cidf

Dtf

DkT

kk

kk

kk

ikik

ik

2003.10.30 - SLIDE 49IS 202 – FALL 2003

Inverse Document Frequency

• IDF provides high values for rare words and low values for common words

41

10000log

698.220

10000log

301.05000

10000log

010000

10000log

For a collectionof 10000 documents(N = 10000)

2003.10.30 - SLIDE 50IS 202 – FALL 2003

Lecture Overview





2003.10.30 - SLIDE 51IS 202 – FALL 2003

Similarity Measures

|)||,min(|

||

||||

||

||||

||||

||2

||

21

21

DQ

DQ

DQ

DQ

DQDQ

DQ

DQ

DQ

Simple matching (coordination level match)

Dice’s Coefficient

Jaccard’s Coefficient

Cosine Coefficient

Overlap Coefficient

2003.10.30 - SLIDE 52IS 202 – FALL 2003

tf*idf Normalization

• Normalize the term weights (so longer vectors are not unfairly given more weight)– Normalize usually means force all values to

fall within a certain range, usually between 0 and 1, inclusive

t

k kik

kikik

nNtf

nNtfw

1

22 )]/[log()(

)/log(

2003.10.30 - SLIDE 53IS 202 – FALL 2003

Vector Space Similarity

• Now, the similarity of two documents is:

• This is also called the cosine, or normalized inner product – The normalization was done when weighting

the terms

),( 1

t

kjkikji wwDDsim

2003.10.30 - SLIDE 54IS 202 – FALL 2003

Vector Space Similarity Measure

• Combine tf and idf into a similarity measure

)()(

),(

:combined

are comparison similarity theandion normalizat otherwise

),( :normalized are weights termif

absent is terma if 0 ...,,

,...,,

1

2

1

2

1

1

,21

21

t

jd

t

jqj

t

jdqj

i

t

jdqji

qtqq

dddi

ij

ij

ij

itii

ww

ww

DQsim

wwDQsim

wwwwQ

wwwD

2003.10.30 - SLIDE 55IS 202 – FALL 2003

Computing Similarity Scores

98.0cos

74.0cos

)8.0 ,4.0(

)7.0 ,2.0(

)3.0 ,8.0(

2

1

2

1

Q

D

D

2

1 1D

Q2D

1.0

0.8

0.6

0.8

0.4

0.60.4 1.00.2

0.2

2003.10.30 - SLIDE 56IS 202 – FALL 2003

What’s Cosine Anyway?

“One of the basic trigonometric functions encountered in trigonometry. Let theta be an angle measured counterclockwise from the x-axis along the arc of the unit circle. Then cos(theta) is the horizontal coordinate of the arcendpoint. As a result of this definition, the cosine function is periodic with period 2pi.”

From http://mathworld.wolfram.com/Cosine.html

2003.10.30 - SLIDE 57IS 202 – FALL 2003

Cosine vs. Degrees

Cosine

Degrees

2003.10.30 - SLIDE 58IS 202 – FALL 2003

Computing a Similarity Score

98.0 42.0

64.0

])7.0()2.0[(*])8.0()4.0[(

)7.0*8.0()2.0*4.0(),(

yield? comparison similarity their doesWhat

)7.0,2.0(document Also,

)8.0,4.0(or query vect have Say we

22222

2

DQsim

D

Q

2003.10.30 - SLIDE 59IS 202 – FALL 2003

Vector Space Matching

1.0

0.8

0.6

0.4

0.2

0.80.60.40.20 1.0

D2

D1

Q

1

2

Term B

Term A

Di=(di1,wdi1;di2, wdi2;…;dit, wdit)Q =(qi1,wqi1;qi2, wqi2;…;qit, wqit)

t

j

t

j dq

t

j dq

i

ijj

ijj

ww

wwDQsim

1 1

22

1

)()(),(

Q = (0.4,0.8)D1=(0.8,0.3)D2=(0.2,0.7)

98.042.0

64.0

])7.0()2.0[(])8.0()4.0[(

)7.08.0()2.04.0()2,(

2222

DQsim

74.058.0

56.),( 1 DQsim

2003.10.30 - SLIDE 60IS 202 – FALL 2003

Weighting Schemes

• We have seen something of– Binary– Raw term weights– TF*IDF

• There are many other possibilities– IDF alone– Normalized term frequency

2003.10.30 - SLIDE 61IS 202 – FALL 2003

Document Space Has High Dimensionality

• What happens beyond 2 or 3 dimensions?

• Similarity still has to do with how many tokens are shared in common

• More terms -> harder to understand which subsets of words are shared among similar documents

• One approach to handling high dimensionality: Clustering

2003.10.30 - SLIDE 62IS 202 – FALL 2003

Vector Space Visualization

2003.10.30 - SLIDE 63IS 202 – FALL 2003

Text Clustering

• Finds overall similarities among groups of documents

• Finds overall similarities among groups of tokens

• Picks out some themes, ignores others

2003.10.30 - SLIDE 64IS 202 – FALL 2003

Text Clustering

Clustering is“The art of finding groups in data.” -- Kaufmann and Rousseau

Term 1

Term 2

2003.10.30 - SLIDE 65IS 202 – FALL 2003

Scatter/Gather

• Cutting, Pedersen, Tukey & Karger 92, 93, Hearst & Pedersen 95

• Cluster sets of documents into general “themes”, like a table of contents

• Display the contents of the clusters by showing topical terms and typical titles

• User chooses subsets of the clusters and re-clusters the documents within

• Resulting new groups have different “themes”

2003.10.30 - SLIDE 66IS 202 – FALL 2003

S/G Example: Query on “star”

Encyclopedia text14 sports

8 symbols 47 film, tv 68 film, tv (p) 7 music97 astrophysics 67 astronomy(p) 12 stellar phenomena10 flora/fauna 49 galaxies, stars

29 constellations 7 miscelleneous

Clustering and re-clustering is entirely automated

2003.10.30 - SLIDE 70IS 202 – FALL 2003

Clustering Result Sets

• Advantages:– See some main themes

• Disadvantage:– Many ways documents could group together

are hidden

• Thinking point: What is the relationship to classification systems and facets?

2003.10.30 - SLIDE 71IS 202 – FALL 2003

Dan Perkel on Cooper

• Are the problems that Cooper lays out the most pressing ones that web users face today? If not, what are some more pressing problems? Who are Cooper’s users?

• Regardless of answer to previous question, how adequate are his solutions? Where are strengths and weaknesses?

2003.10.30 - SLIDE 72IS 202 – FALL 2003

Simon King on Hearst

• Prof. Hearst mentions "an algorithm called TextTiling that automatically splits long documents into multi-paragraph subtopical units." Sounds nice, but what if the termsets/concepts you're searching on just happen to appear on opposite sides of one of the boundaries that TextTiling created? In plans for future work she mentions using an inverse distance measure rather than a fixed proximity constraint. This is good unless your search terms appear at the end of one section of a document and the beginning of the next (they're not separated by many words, but may not be related within the document.) Is one of these approaches clearly better than the other?

2003.10.30 - SLIDE 73IS 202 – FALL 2003

Simon King on Hearst

• Is there any reason that the optimal query size for Hearst's queries seems to be two or three concepts? Is this due to the way we write and think -- can't discuss more than a couple ideas at a time? Or is there some other reason?

2003.10.30 - SLIDE 74IS 202 – FALL 2003

Sean Savage on MIR 7

• Considering these trends:– the proliferation of networked, mobile devices used at

the front end in everyday information retrieval scenarios, and

– the increase in cheap processing power and memory on the back end;

• And considering these facts:– mobile devices possess very limited input and output

capabilities compared to those of desktop machines; and

– most usage scenarios beyond the desktop involve significant constraints on the amount of time and attention that users can devote to these devices.

2003.10.30 - SLIDE 75IS 202 – FALL 2003


• Should we now focus most of our development resources in the realm of large-scale text transformations on improving the quality of search results (i.e., striving to improve precision and recall by pre-processing text, and by using categorization hierarchies at the front end to guide users in focusing queries), as opposed to directing those resources towards even more effective compression techniques to reduce query response times?

2003.10.30 - SLIDE 76IS 202 – FALL 2003


• Given the trends and facts above, should those in the IR community who work on text compression now focus on compressing small batches of text to be transmitted more efficiently across wireless networks, rather than on compressing the gigantic collections residing in databases, which this chapter seems to chiefly address?

2003.10.30 - SLIDE 77IS 202 – FALL 2003

Next Time

• Avi Rappoport of Searchtools.com on “Implementing Web Site Search Engines”– For discussion, please prepare by looking at

some web sites with search capabilities (but NOT Ebay, Amazon, Google, Yahoo, or AllTheWeb) and find one that you like and one that you don’t

• Ray will be away from Tuesday-Friday next week, Marc will be in town, but at a conference all next week

2003.10.30 - SLIDE 1IS 202 – FALL 2003 Prof. Ray Larson & Prof. Marc Davis UC Berkeley SIMS Tuesday and Thursday 10:30 am - 12:00 pm Fall 2003

Documents

boolean slide

leash slide

vector representation

marti hearst slide

boolean logic ab slide

modern ir textbook slide

pm fall

boolean systems