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Latent Semantic Analysis

a tutorial at CogSci'2005

Benoît Lemaire

Laboratoire Leibniz-IMAG (CNRS UMR 5522)University of Grenoble

FranceBenoit.Lemaire@imag.fr

Outline

Intuitive introductionrepresenting the meaning of words from the analysis of huge corpora

LSA techniqueTestsCognitive modelsLimitsCompeting models

Intuitive introductionIntroductionLSA techniqueTestsCognitive modelsLimitsCompeting models

Corpus

planeairport

flybee pilot

truckcar

wingsbird

traintravel

restauranteat

applebanana

vegetablesapples

fruittree

gardenflower

flowersgrow

bouquetpetals

flyingflew

nectarhoney

From words to textsIntroductionLSA techniqueTestsCognitive modelsLimitsCompeting models

planeairport

flybee pilot

truckcar

wingsbird

traintravel

restauranteat

applebanana

vegetablesapples

fruittree

gardenflower

flowersgrow

bouquetpetals

flyingflew

nectarhoney

The pilot parks the plane

planeairport

flybee pilot

truckcar

wingsbird

traintravel

restauranteat

applebanana

vegetablesapples

fruittree

gardenflower

flowersgrow

bouquetpetals

flyingflew

nectarhoney

planeairport

flybee pilot

truckcar

wingsbird

traintravel

restauranteat

applebanana

vegetablesapples

fruittree

gardenflower

flowersgrow

bouquetpetals

flyingflew

nectarhoney

planeairport

flybee pilot

truckcar

wingsbird

traintravel

restauranteat

applebanana

vegetablesapples

fruittree

gardenflower

flowersgrow

bouquetpetals

flyingflew

nectarhoney

Usages of LSA

airport

flybee

wingsbird

travelpark

restauranteat

applebanana

vegetablesapples

fruittree

gardenflower

flowers

bouquetpetals

flyingflew

nectarhoney

Corpus

IntroductionLSA techniqueTestsCognitive modelsLimitsCompeting models

LSA as a tool

Compare textsControl experiment material

airport

flybee

wingsbird

travelpark

restauranteat

applebanana

vegetablesapples

garden

flowersbouquet

petals

flyingflew

nectarhoney

Corpus

LSA as a cognitive modelof semantic memory

Build lots of cognitive modelsText comprehensionInterface navigation...

Corpus

airport

flybee

wingsbird

travelpark

restauranteat

applebanana

vegetablesapples

fruittree

gardenflower

flowers

bouquetpetals

flyingflew

nectarhoney

LSA as a cognitive model of word acquisition

airport

flybee

wingsbird

travelpark

restauranteat

applebanana

vegetablesapples

fruittree

gardenflower

flowers

bouquetpetals

flyingflew

nectarhoney

Corpus

Humans also construct the meaning of words from written materialDoes LSA account for this process?

Outline

Intuitive introductionLSA techniqueTestsCognitive modelsLimitsCompeting models

Semantic information is drawn from raw texts

Take a huge corpusSplit it into paragraphsDetermine the statistical context in which each word occurs

A first approach based on co-occurrence

Define the meaning of a word from the co-occurring wordsTwo words are similar if they occur in the same paragraphs

plane= (1,0,0,1,0,0,0,0,2,1,0,1,1,0,0,0,0,0,1,1)

airport=(1,1,0,0,0,0,0,0,1,1,0,2,1,0,0,0,0,0,0,1)

Does not work well (French, Perfetti)

A better approach

Two words are similar if they occur in the same paragraphs

A better approach

Two words are similar if they occur in the same paragraphs

Two words are similar if they occur in similar paragraphs

A better approach

Two words are similar if they occur in the same paragraph

Two paragraphs are similar if they

contain common words

A better approach

contain similar words

Two words are similar if they occur in the same paragraph

A mutual recursion

Mathematicians know how to solve such circular systemsSuppose P paragraphs, W wordsBuild M, a P x W matrix

M[i,j] = nb of occurrence of word i in paragraph j

Each word is a P-dimension vectorReduce the matrix to its best 300 dimensions

Example (Landauer & Dumais 1997)

Human 1 0 0 1 0 0 0 0 0

interface 1 0 1 0 0 0 0 0 0

computer 1 1 0 0 0 0 0 0 0

user 0 1 1 0 1 0 0 0 0

system 0 1 1 2 0 0 0 0 0

response 0 1 0 0 1 0 0 0 0

time 0 1 0 0 1 0 0 0 0

EPS 0 0 1 1 0 0 0 0 0

survey 0 1 0 0 0 0 0 0 1

trees 0 0 0 0 0 1 1 1 0

graph 0 0 0 0 0 0 1 1 1

minors 0 0 0 0 0 0 0 1 1

§1: Human machine interface for ABC computer applications§2: A survey of user opinion of computer system response time§3: The EPS user interface management system§4: System and human system engineering testing of EPS§5: Relation of user perceived response time to error measurement§6: The generation of random, binary, ordered trees§7: The intersection graph of paths in trees§8: Graph minors IV: Widths of trees and well-quasi-ordering§9: Graph minors: A survey

Matrix reduction

= x x0

0Mwords

paragraphs

Matrix reduction

= x x0

0Mwords

paragraphs

= x xM'

paragraphs

Example (Landauer & Dumais 1997)

Human 1 0 0 1 0 0 0 0 0 .16 .40 .38 .47 .18 -.05 -.12 -.16 -.09

interface 1 0 1 0 0 0 0 0 0 .14 .37 .33 .40 .16 -.03 -.07 -.10 -.04

computer 1 1 0 0 0 0 0 0 0 .15 .51 .36 .41 .24 .02 .06 .09 .12

user 0 1 1 0 1 0 0 0 0 .26 .84 .61 .70 .39 .03 .08 .12 .19

system 0 1 1 2 0 0 0 0 0 .45 1.23 1.05 1.27 .56 -.07 -.15 -.21 -.05

response 0 1 0 0 1 0 0 0 0 .16 .58 .38 .42 .28 .06 .13 .19 .22

time 0 1 0 0 1 0 0 0 0 .16 .58 .38 .42 .28 .06 .13 .19 .22

EPS 0 0 1 1 0 0 0 0 0 .22 .55 .51 .63 .24 -.07 -.14 -.20 -.11

survey 0 1 0 0 0 0 0 0 1 .10 .53 .23 .21 .27 .14 .31 .44 .42

trees 0 0 0 0 0 1 1 1 0 -.06 .23 -.14 -.27 .14 .24 .55 .77 .66

graph 0 0 0 0 0 0 1 1 1 -.06 .34 -.15 -.30 .20 .31 .69 .98 .85

minors 0 0 0 0 0 0 0 1 1 -.04 .25 -.10 -.21 .15 .22 .50 .71 .62

r(human,user)= -.38 r(human,user)=.94

§1: Human machine interface for ABC computer applications§2: A survey of user opinion of computer system response time§3: The EPS user interface management system§4: System and human system engineering testing of EPS§5: Relation of user perceived response time to error measurement§6: The generation of random, binary, ordered trees§7: The intersection graph of paths in trees§8: Graph minors IV: Widths of trees and well-quasi-ordering§9: Graph minors: A survey

Meaning as vectors

The meaning of a each word is represented as a vector

computer

disk workbike

disk = (2,4,6,-1,0,3,-4,8,-5,8,12.....9,0,1,-9,4,1) computer = (1,4,5,-1,0,2,-2,5,-6,8,11.....8,0,0,-5,7,1)

Illustrative purpose only: does not work in 2 dimensions!

Comparison with symbolic approaches

bikeride

bicycle

bike bicycleSYNONYM

wheelsride

FUNCTION HAS

Human-propelledvehicle

vehicle

guidon

Representation is absoluteGood for drawing inferencesNot so good for comparisonsHard to compound nodes

bike bicycleSYNONYM

wheelsride

FUNCTION HAS

Human-propelled

vehicle

guidon

Representation is relativeGood for semantic comparisonsEasy to compound words

bikeride

bicycle

funguidon

Semantic comparison

Semantic distance = cosine between vectorsA value between –1 and 1Other measures:

Euclidian distanceHellinger distance...

Outline

Word comparisons

A semantic space built from a 4.6 million word encyclopedia (lsa.colorado.edu)

Closest words to bicycle:pedals: .84handlebars .79bicycles .79pedaling .75bike .75

fly – insect: .26fly -plane: .48insect – plane: .02

Existing semantic spaces

Englishencyclopedia, literature, psychology textbooks, scientific textbooks (available at lsa.colorado.edu)

Frenchnewspaper, literature, children tales, children production (some of them are available at lsa.colorado.edu)

What is the right number of dimensions?

Too few dimensions would not capture the latent semantic structureToo much dimensions would describe idiosyncrasic structuresAn open issue300 dimensions seems a good value for the whole language (Dumais found a maximum of performance at 90 dim. for a specific domain)

From words to texts

Sum up word vectors to get text vectors

disk= (2, 4, 6,-1, 0, 3,-4, 8,.....9, 0,-9, 4, 1)

computer=(1 4, 5,-1, 0, 2,-2, 5,.....8, 0,-5, 7, 1)

kid= (1, 0, 0,-9, 4, 5,-1, 2,.....0, 2, 3, 4, 5)

broken= (5,-3, 8, 6, 5,-2, 2, 0,.....6, 1, 7, 1, 2)

S = The computer disk was broken by the kid

S= (9, 5,19,-5, 9, 8,-5, 15....23, 3,-4,16, 9)

Text comparisons

A semantic space built from a 4.6 million word encyclopedia (lsa.colorado.edu)

The cat was lost in a forest / My little feline disappeared in the trees: .66The radius of spheres / a circle's diameter: .55 (Landauer)

The radius of spheres / the music of spheres: .01(Landauer)

No syntax processing

Paragraphs are bags of wordsSemantic is determined from the lexical level

Lexical level

Syntax level

Semantic level

No syntax processing

We learned that this is about birds, nests and a building processThe analysis unit is the paragraph

Birds build nests

Nests build birds

Outline

Models based on LSA

Semantic representationVocabulary acquisitionText comprehensionFree text assessment

Semantic representation

Comparison of wordsTOEFL testVocabulary test for children

Comparison of sentencesMeasure of coherence

Comparison of texts

Comparison of words

Synonymy part of the TOEFL test (Landauer & Dumais, 97)

80 items: 1 word/4 alternative wordsGuess which one is the closestExample: levied

imposed

believed

requested

correlated

LSA was trained on a 4.6 million word corpusLSA score : 64.4%Foreign applicants to US colleges: 64.5%

Vocabulary test:LSA vs children

(Denhière & Lemaire, 2004)

115 items

4 definitions : correct, close, distant, unrelated

Subjects were in grade 2 to 4

Example (translated from French):

slope rising road tilted surface which goes up or down small piece of ground face of a rock or a mountain

A children's semantic space

Stories and tales for children: ~ 1,600,000 wordsChildren productions: ~ 800,000 wordsTextbooks: ~ 400,000 wordsEncyclopedia: ~ 400,000 wordsDictionary: ~ 50,000 words

TOTAL : 3,2 million words

Vocabulary test: results

Correct Close Far Unrelated0

Children data

2nd grade

3rd grade

4th grade

Vocabulary test: resultsIntroductionLSA techniqueTestsCognitive modelsLimitsCompeting models

Children+Model data

2nd grade

3rd grade

4th grade

99 most frequent wordsIntroductionLSA techniqueTestsCognitive modelsLimitsCompeting models

Children+Model data

2nd grade

3rd grade

4th grade

115 words

99 words

Vocabulary test: word lemmatization

Children+Model data

2nd grade

3rd grade

4th grade

115 words

99 words

Vocabulary test: verb lemmatization

Children+Model data

2nd grade

3rd grade

4th grade

115 words

99 words

verb lemm.

Comparison of sentences

● Use LSA to measure the coherence of a text

● Compute the semantic similarities between adjacent sentences

coherence (T) = Σ cosine(sentence i, sentence i+1)

Foltz et al. (1998) experiment

McNamara et al. (1996) data4 versions of text about the heart

Low local coherence, low macro coherence (lm)Low local coherence, high macro coherence (lM)High local coherence, low macro coherence (Lm)High local coherence, high macro coherence (LM)

Corpus: 21 texts, 100 dimensions

Foltz et al. (1998) experiment

Results :Coherence(lm) = 0.177Coherence(lM) = 0.205Coherence(Lm) = 0.210Coherence(LM) = 0.242

comprehension

coherence

.14 .18 .22

LSA r2=0.853word overlap

r2=0.098

Can LSA assess text recall ?

Measure M1 : cosine between source text and texts recalled

Measure M2 : number of propositions recalled

Text Recall Nb subjects Correlation M1/M2Poule Immediate n = 48 (8,3 years old) 0.49Dragon Immediate n = 48 (8,3 years old) 0.64Dragon Delayed n = 48 (8,3 years old) 0.7Araignée Immediate n = 57 (16-20 years old) 0.81Clown Immediate n = 57 (16-20 years old) 0.65Géant Immediate n = 130 (16-20 years old) 0.6Ourson Immediate n = 44 (16-20 years old) 0.48Clown Summary n = 44 (16-20 years old) 0.86

Comparison of textsFoltz et al. (1996)

● Compare texts and their summaries● Britt et al. (1994) data

● 24 participants read 21 texts ● Participants write an essay

● Corpus: 21 texts + 8 encyclopedia texts + 2 book excerpts

● Assessing the essays:● Score 1 = average similarity between each sentence and

the closest text sentence● Score 2 = same but compare with the main 10 text

sentences

Comparison of textsFoltz et al. (1996)

Judge1 Judge2 Judge3 Judge4 Score1 Score2

Judge1 .575** .768** .381 .418* .589*

Judge2 .582** .412* .552** .626**

Judge3 .367 .317 .384+

Judge4 .117 .240

** p<.01 * p<.05 + p<.06

Models based on LSA

A model of learning

LSA learns the meaning of words from textsDoes it mimic the human rate of learning?Landauer & Dumais (1997) experiment:

Most of the lexicon is acquired from textChildren data:

3500 words read / day50 new words encountered / day10 words learned / dayControlled experiments lead to 2.5 words learned / day

Direct and indirect effects

How do children acquire the remaining 7.5 words/day?The poverty of stimulus problem

how do children acquire as much knowledge on the basis of little information?

Hypothesis: a word is learned…From texts containing it (direct effect)From texts not containing it (indirect effect)

LSA simulation

TOEFL test score is function of:T: total number of paragraphsS: number of paragraphs containing the stem word

score=0.128 (log 0.076 T) (log 31.910 S)

Correlation with observed score= .98After “reading” 25,000 paragraphs, what is the effect of the 25,001th?

When the stem word belongs to it?When the stem word does not belong to it?

Example

Suppose a word that appeared twice in the 25,000 paragraphsScore = 0.128 (log 0.076*25000)(log 31.91*2) = .75809

Direct effect: the word belongs to the 25,001th paragraphScore = 0.128 (log 0.076*25001)(log 31.91*3) = .83202

Indirect effect: the word does not belong to the 25,001th paragraphScore = 0.128 (log 0.076*25001)(log 31.91*2) = .75810

LSA simulation

Effects are cumulated over all word-frequency bandDirect effect:

.0007 words gained per word encountered

.0007 * 3500 = 2.5 words acquired / day

Indirect effect:.15 words gained per paragraph encountered.15 * 50 = 7.5 words acquired / day

The meaning of a word would be acquiredfor 25% by reading text containing itfor 75% by reading texts not containing it

Direct and indirect effects(Lemaire et al., to appear)

20002721345441874909563063527073780685289249998210797117051261213520-0,1

acheter (to buy)/magasin (store)

Number of paragraphs

Cosine acheter/magasin

Total gain: .58

Gain due to the occurrence of acheter: -.10

Gain due to the occurrence of magasin: -.19

Gain due to the co-occurrence: .73

Gain due to 2nd order co-occurrences: .11

Gain due to 3rd and more co-occurrences: .03

Same measures on 28 words

Total gain: .13

Gain due to the occurrence of W1: -.16

Gain due to the occurrence of W2: -.19

Gain due to the co-occurrence: .34

Gain due to 2nd order co-occurrences: .05

Gain due to 3rd and more co-occurrences: .09

Models based on LSA

Text comprehension

Cognitive models can be simulated on computers, using LSA as a model of semantic memory:

the construction-integration model (Kintsch, 1998)A predication algorithmMetaphor comprehension

A Computational model of text comprehension (Lemaire et al, to

appear)

Next sentence

Selectassociates

SEMANTICMEMORY

(LSA)WORKINGMEMORY

EPISODICMEMORY

Retrievepreviouselements

Integration

Example (translated from French)

A woodcutter was walking in the forest

Select associates:walk: stroll, meet, pickwoodcutter: ax, forest, cottage

forest: glade, oak, wood

walk/woodcutter/forest

forest

woodcutterstroll

pick ax

cottage

forest

woodcutterstroll

pickax

cottage

forest

woodcutterstroll

pick ax

cottage

forest

woodcutterstroll

pick ax

cottage

The construction-integration model

Before LSA, the construction step was performed by handLink weights were set approximatelyAll nodes being vectors, the weight of a link is the cosine of the corresponding nodes A question remains: what is the vector of P(A1,…An) ?

The predication algorithm (Kintsch, 2001)

The centroid rule: P(A) P+A

…does not work wellThe meaning of the predicate depends on the meaning of the argumentsThe horse ran / The color ranshark(lawyer) ≠ shark + lawyer

A better rule: P(A) P+A+M1+…+Mn

Mi are vectors that are close to both P and A

Example 1:construction step (Kintsch, 2001)

The horse ran ran(horse)

stopped

hopped

horse.21

Example 1:integration step

stopped

hopped

horse.46

The horse ran horse+ran+stopped

Example 2:construction step

The color ran ran(color)

stopped

hopped

color.06

Example2:integration step

stopped

hopped

color.00

The color ran color+ran+down

Predication algorithm: test(Kintsch, 2001)

.11.01.01dissolve

.29.75.33gallop

color ranhorse ranranLandmarks

Inferences (Kintsch, 2001)

.70.73Predication

.54.66Centroid

The elk was deadThe hunter was deadThe hunter shot the elk

.91.87Predication

.66.76Centroid

The glass was broken

The student was broken

The student dropped the glass

.83.62Predication

.71.70Centroid

The table was cleanThe student was clean

The student washed the table

Metaphors

My lawyer is a shark shark(lawyer)

lawyer

My lawyer is a shark

The meaning of my lawyer is a shark is not a simplecombination of the meaning of lawyer andthe meaning of shark

Metaphors

Look for words that are similar to shark but also close to lawyer

sharks

vicious

agressive

lawyer

Metaphors

lawyer

viciousagressive

Metaphors

Much more neighbors of the predicate need to be consideredAccording to Kintsch, predication fails if number of neighbors is less than 100!

An incremental algorithm(Lemaire & Bianco, 2003)

Does not work on a predefine set of neigbors but look for them progressively

This kid is intelligent 1... 2... 3 clever 4... 5 brilliant 6... 7... 8... 9 sage

This kid is a scientist1... 2... 3............................................................................................................................................................................97 invention ......................................................................................... 128 knowledge.............................................138 wonderful

Experiment

Does the model account for the processing time of various kind of metaphors?12 texts, 4 conditions :

Synonym (child / kid)Conventional metaphor (child / scientist)Original metaphor (child / sage)Bad metaphor (child / colonel)

Subjects (N=49)

Subjects

Synonym

Conv. met.

Unconv. Met.

Bad met.

Types of metaphors

ionnal ti

Subjects and model

Correlation: .62

Simulation

Types of metaphors

Subjects

Synonym

Conv. met.

Unconv. Met.

Bad met.

Types of metaphors

ionnal

Models based on LSA

Free text assessment

Assessing the content of a student essayRely on a domain-specific corpusCompare the student essay with a reference text:

Pre-graded essaysText to be summarizedPortions of a text course

Trusso Haley et al. (2005) published a good state-of-the-art report (Tech. Rep. Open University)

Intelligent Essay Assessor

Foltz et al. (1999)Holistic score:

Compare student essay with pre-graded essaysGive the grade of the closest one

Gold standard scoreCompare student essay with a teacher essayGive the grade according to the semantic similarityCorrelation with teacher's grades around .8

Summary Street

Wade-Stein & E. Kintsch (2003)Helps the student to summarize a textIndicate the part of the text that are well or not well summarizedAn experiment with 60 6th grade students has shown a positive effect

Summary StreetIntroductionLSA techniqueTestsCognitive modelsLimitsCompeting models

ApexIntroductionLSA techniqueTestsCognitive modelsLimitsCompeting models

Dessus & Lemaire (1999, 2001,2002)Compare student essay with relevant portions of the courseThe course is structured :

#T The first chapter

#N In the first part, we will study the way...

#N Now, I will present a method...

#T The second chapter

#N ...

Correlation with teacher's grades : .62Not only for grading but for engaging students in a revising processCan be used at a distance

Outline

Strengths and limits

LSA strengthsfully automaticvectorial representation allows:

esay representation of sequence of words easy comparisons between words or texts

a cognitive model of learning and representation

LSA weaknessesno syntax processingrepresentations are not explicitnot incrementalparagraphs are bag of words

Outline

Competing models

Cognitive models of semantic memory could mimic:

the human semantic associations orthe human construction of these associations over a long period of time

Semantic networks are good model of semantic associations BUT... they do not account for the construction of these associations

Features

Input (corpus, word association norms)Knowledge representation (vector-based, network-based)Addition of a new text (incrementally or not)Unit of context (paragraph, sliding window)Use of high-order co-occurrences (yes/no)Compositionality (representing the meaning of a text from the meaning of its words)

Input: corpus Knowledge representation: vector-basedAddition of a new text: not incrementalUnit of context: paragraphUse of high-order co-occurrences: yesCompositionality: easy

HAL(Burgess, 1998)

Word co-occurrence matrix built from a N-word sliding window

vector = concatenation of row and columnbarn = <0,2,4,3,6,0,5,0,0,0>Measure of similarity = Euclidian distance

HAL(Burgess, 1998)

Input: corpus Knowledge representation: vector-basedAddition of a new text: incrementalUnit of context: sliding windowUse of high-order co-occurrences: noCompositionality: easy

Word association space(Steyvers et al., in press)

Based on association norms for 5,000 wordsWord/word matrix scaled to 200-500 dimensions

Word association space(Steyvers et al., in press)

Input: association norms Knowledge representation: vector-basedAddition of a new text: not incrementalUnit of context: N/AUse of high-order co-occurrences: noCompositionality: easy

PMI-IR(Turney, 2001)

Based on Mutual Information (Church & Hanks, 89)

compares the probability of two words occuring together with the probability of the words occuring separately

MI(A,B)=log2(p(A,B)/p(A).p(B))

TOEFL test: 1 problem word/4 choicesscore

1(choice)=hits(problem AND choice)/hits(choice)

score2(choice)=hits(problem NEAR choice)/hits(choice)

Input: webKnowledge representation: N/AAddition of a new text: incrementalUnit of context: web pageUse of high-order co-occurrences: noCompositionality: hard

ICAN(Lemaire & Denhière, 2004)

Network-based representationbetter for quickly retrieving neighborsbetter for representing asymmetrical relations

electric

connector

networkrope

wire.7

.5.4 .3

... if you have such a [device, connect the cable to the network connector] then switch ...

Create or reinforce co-occurrence links

electric

connector

networkrope

wire.7

.5.4 .3

device.5

connect

.8cable

electric

connector

network

wire.7

.5.4 .3

Create or slightly reinforce 2nd-order co-occurrence links

electric

connector

networkrope

wire.7

.5.4 .3

device.5

connect

.4.3.8

electric

connector

network

wire.7

.5.4 .3

Create or slightly reinforce 2nd-order co-occurrence links

Sligthly decrease other links

electric

connector

networkrope

wire.6

.5.4 .2

device.5

connect

.4.3.8

electric

connector

network

wire.7

.5.4 .3

3.2 million word corpus of texts for childrenTest on 1200 pairs of words (from association norms)Average weights:

stem/1st associate: .415

stem/2nd associate: .269

stem/3rd associate: .236stem/last associates: .098

Correlation with human data: .50

Input: corpusKnowledge representation: network-basedAddition of a new text: incrementalUnit of context: sliding windowUse of high-order co-occurrences: yesCompositionality: hard

Web pages

Testslsa.colorado.edu

Referenceswww-leibniz.imag.fr/~blemaire/lsa.html

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