mining event histories: some new insights on personal swiss...

Mining Event Histories

Mining Event Histories:Some New Insights on Personal Swiss Life Courses

Gilbert Ritschard

Dept of Econometrics and Laboratory of Demography, University of Genevahttp://mephisto.unige.ch

PaVie Seminar, Lausanne, October 22, 2008

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http://mephisto.unige.ch


My talk is about life courses,So, let me start with an example of scientific life course

date event1970-1979 Studies in econometrics1980-1992 Mathematical Economics1985-... Work with Social scientists (Family studies)

Interest in Statistics for social sciences1990-1995 Interest in Neural Networks2000-... KDD and data mining (Clustering, supervised learning)2003-... Work with historians, demographers, psychologists

(longitudinal data)2005-... KDD and Data mining approaches

for analysing life course data2007-... Start a SNF project on “Mining Event Histories”

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Outline

1 Sequence Analysis in Social Sciences

2 Survival Trees

3 Characterizing, rendering and clustering sequence data

4 Mining Frequent Episodes

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Mining Event HistoriesSequence Analysis in Social Sciences

Table of content


2 Survival Trees



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Mining Event HistoriesSequence Analysis in Social SciencesMotivation

Section content

1 Sequence Analysis in Social SciencesMotivationWhat kind of data?Issues with life course dataMethods for Longitudinal Data

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Motivation

Individual life course paradigm.Following macro quantities (e.g. #divorces, fertility rate, meaneducation level, ...) over timeinsufficient for understanding social behavior.Need to follow individual life courses.

Data availabilityLarge panel surveys in many countries(SHP, CHER, SILC, GGP, ...)Biographical retrospective surveys (FFS, ...).Statistical matching of censuses, population registers and otheradministrative data.

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Motivation

Need for suited methods for discovering interesting knowledgefrom these individual longitudinal data.Social scientists use

Essentially Survival analysis (Event History Analysis)More rarely sequential data analysis (Optimal Matching,Markov Chain Models)

Could social scientists benefit from data-mining approaches?Which methods?Are there specific issues with those methods for socialscientists?

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Motivation: KD in Social sciences

In KDD (Knowledge discovery in databases) and data mining,focus on prediction and classification.Improve prediction and classification errors.

In Social science, aim is understanding/explaining (social)behaviors.Hence focus is on process rather than output.

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Mining Event HistoriesSequence Analysis in Social SciencesWhat kind of data?

Section content


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What kind of data?

What kind of data are we dealing with?Mainly categorical longitudinal data describing life courses

Data can be in different forms ...

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ontology of longitudinal data (Aristotelean tree)

Longitudinal data

States

one state per time unit t

not

several states at each t

not

not

Events

time stamped events

notevent sequence

not

notspell duration

not

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Alternative views of Individual Longitudinal Data

Table: Time stamped events, record for Sandra

ending secondary school in 1970 first job in 1971 marriage in 1973

Table: State sequence view, Sandra

year 1969 1970 1971 1972 1973civil status single single single single marriededucation level primary secondary secondary secondary secondaryjob no no first first first

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Transforming time stamped events into state sequencesExample: the “BioFam” data

Data from the retrospective survey conducted in 2002 by theSwiss Household Panel (SHP)(with support of Federal Statistical Office, Swiss NationalFund for Scientific Research, University of Neuchatel.)Retrospective survey: 5560 individualsRetained familial life events: Leaving Home, First childbirth,First marriage and First divorce.Age 15 to 45 → 2601 remaining individuals, born between1909 et 1957.

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Creating state sequences

Example of time stamped data:individual LHome marriage childbirth divorce

1 1989 1990 1992 NA

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Deriving the states

Need one state for each combination of events:

LHome marriage childbirth divorce0 no no no no1 yes no no no2 no yes yes/no no3 yes yes no no4 no no yes no5 yes no yes no6 yes yes yes no7 yes/no yes yes/no yes

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From events to states

Example of transformation :events:

individual LHome marriage childbirth divorce1 1989 1990 1992 NA

states:

individual ... 1988 1989 1990 1991 1992 1993 ...1 ... 0 0 1 3 3 6 ...

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Mining Event HistoriesSequence Analysis in Social SciencesIssues with life course data

Section content


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Issues with life course data

Incomplete sequencesCensored and truncated data:Cases falling out of observation before experiencing an event ofinterest.Sequences of varying length.

Time varying predictors.Example: When analysing time to divorce, presence of childrenis a time varying predictor.

Data collected by clustersExample: Household panel surveys.Multi-level analysis to account for unobserved sharedcharacteristics of members of a same cluster.

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Multi-level: Simple linear regression example

y = 3.2 + 0.2 x

y = 6.2 - 0.8 x

y = 15.6 - 0.8 x

y = 12.5 - 0.8 x

0

1

2

3

4

5

6

7

8

9

1 3 5 7 9 11 13 15

Education

Chi

ldre

n

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Mining Event HistoriesSequence Analysis in Social SciencesMethods for Longitudinal Data

Section content


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Classical statistical approachesSurvival Approaches

Survival or Event history analysis (Blossfeld and Rohwer, 2002)Focuses on one event.Concerned with duration until event occursor with hazard of experiencing event.

Survival curves: Distribution of duration until event occurs

S(t) = p(T ≥ t) .

Hazard models: Regression like models for S(t, x) or hazardh(t) = p(T = t | T ≥ t)

h(t, x) = g(t, β0 + β1x1 + β2x2(t) + · · ·

).

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Survival curves (Switzerland, SHP 2002 biographical survey)

Women

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80

AGE (years)

Surv

ival

pro

babi

lity

Leaving home Marriage 1st Chilbirth Parents' deathLast child left Divorce Widowing19/11/2008gr 22/95


Analysis of sequences

Frequencies of given subsequencesEssentially event sequences, e.g. (First job → Marriage).Subsequences considered as categories ⇒ Methods forcategorical data apply (Frequencies, cross tables, log-linearmodels, logistic regression, ...).

Markov chain modelsState sequences.Focuses on transition rates between states.Does the rate also depend on previous states?How many previous states are significant?

Optimal Matching (Abbott and Forrest, 1986) .State sequences.Edit distance (Levenshtein, 1966; Needleman and Wunsch,1970) between pairs of sequences.Clustering of sequences.

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Typology of methods for life course data

IssuesQuestions duration/hazard state/event sequencingdescriptive • Survival curves: • Frequencies of given

Parametric patterns(Weibull, Gompertz, ...) • Optimal matching

and non parametric clustering, MDS(Kaplan-Meier, Nelson- • Rendering sequencesAalen) estimators. • Discovering typical

episodescausality • Hazard regression models • Markov models

(Cox, ...) • Mobility trees• Survival trees • Discriminating episodes

• Sequence HeterogeneityAnalysis (Anova)

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Mining Event HistoriesSurvival Trees

Table of content


2 Survival Trees



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Mining Event HistoriesSurvival TreesMarriage survival, SHP biographical data

Section content

2 Survival TreesMarriage survival, SHP biographical dataSurvival Tree PrincipleExampleSocial Science Issues

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SHP biographical retrospective surveyhttp://www.swisspanel.ch

SHP retrospective survey: 2001 (860) and 2002 (4700 cases).We consider only data collected in 2002.Data completed with variables from 2002 wave (language).

Characteristics of retained data for divorce(individuals who get married at least once)

men women TotalTotal 1414 1656 30701st marriage dissolution 231 308 539

16.3% 18.6% 17.6%

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http://www.swisspanel.ch


Distribution by birth cohortBirth year

year

Fre

quen

cy

1910 1920 1930 1940 1950 1960

010

020

030

040

050

0

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Marriage duration until divorceSurvival curves

0 8

0.85

0.9

0.95

1

vie

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 10 20 30 40

prob

. de

surv

Durée du mariage, Femmes

1942 et avant

1943-1952

1953 et après

0 8

0.85

0.9

0.95

1

vie

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 10 20 30 40pr

ob. d

e su

rvDurée du mariage, Hommes

1942 et avant

1943-1952

1953 et après

0 8

0.85

0.9

0.95

1

vie

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 10 20 30 40

prob

. de

surv

Durée du mariage, Femmes

1942 et avant

1943-1952

1953 et après

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Marriage duration until divorceHazard model

Discrete time model (logistic regression on person-year data)exp(B) gives the Odds Ratio, i.e. change in the odd h/(1− h)when covariate increased by 1 unit.

exp(B) Sig.birthyr 1.0088 0.002university 1.22 0.043child 0.73 0.000language unknwn 1.47 0.000

French 1.26 0.007German 1 refItalian 0.89 0.537

Constant 0.0000000004 0.000

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Mining Event HistoriesSurvival TreesSurvival Tree Principle

Section content


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Mining Event HistoriesSurvival TreesSurvival Tree Principle

Survival trees: Principle

Target is survival curve or some other survival characteristic.Aim: Partition data set into groups thatdiffer as much as possible (max between class variability)

Example: Segal (1988) maximizes difference in KM survivalcurves by selecting split with smallest p-value of Tarone-WareChi-square statistics

TW =∑

i

wi

(di1 − E(Di )

)(w2

i var(Di ))1/2

are as homogeneous as possible (min within class variability)Example: Leblanc and Crowley (1992) maximize gain indeviance (-log-likelihood) of relative risk estimates.

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Mining Event HistoriesSurvival TreesExample

Section content


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Divorce, Switzerland, Differences in KM Survival Curves I

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Divorce, Switzerland, Differences in KM Survival Curves II

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0.6

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1.0

Cohort <=1940 & Non French Speaking & University

Cohort <=1940 & Non French Speaking & < University

Cohort <=1940 & French Speaking

Cohort > 1940 & No Child & University

Cohort > 1940 & No Child & < University

Cohort > 1940 & Child & German or Italian Speaking

Cohort > 1940 & Child & French or Unknown Speaking

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Divorce, Switzerland, Relative risk

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Hazard model with interaction

Adding interaction effects detected with the tree approachimproves significantly the fit (sig ∆χ2 = 0.004)

exp(B) Sig.born after 1940 1.78 0.000university 1.22 0.049child 0.94 0.619language unknwn 1.50 0.000

French 1.12 0.282German 1 refItalian 0.92 0.677

b_before_40*French 1.46 0.028b_after_40*child 0.68 0.010

Constant 0.008 0.00019/11/2008gr 37/95

Mining Event HistoriesSurvival TreesSocial Science Issues

Section content


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Mining Event HistoriesSurvival TreesSocial Science Issues

Issues with survival trees in social sciences

1 Dealing with time varying predictorsSegal (1992) discusses few possibilities, none being reallysatisfactory.Huang et al. (1998) propose a piecewise constant approachsuitable for discrete variables and limited number of changes.Room for development ...

2 Multi-level analysisHow can we account for multi-level effects in survival trees,and more generally in trees?Conjecture: Should be possible to include unobserved sharedeffect in deviance-based splitting criteria.

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Mining Event HistoriesCharacterizing, rendering and clustering sequence data

Table of content


2 Survival Trees



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Mining Event HistoriesCharacterizing, rendering and clustering sequence dataLife trajectories

Section content

3 Characterizing, rendering and clustering sequence dataLife trajectoriesCharacterizing sets of sequences

EntropyLongitudinal within sequence entropies

Distances between sequences: ClusteringHeterogeneity analysis and sequence discriminationMultidimensional Scaling representation of sequences

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Sequence analysis

Survival approaches not useful in a unitary (holistic)perspective of the whole life course.Sequence analysis of whole collection of life events bettersuited for such holistic approach (Billari, 2005).

Rendering sequencesColorize your life courses

Results from the analysis of the retrospective Swiss HouseholdPanel (SHP) survey.Focus on visualization of life course data.

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Evolution tendencies in familial life course trajectories

Sequence analysis techniques permit to test hypotheses aboutevolution in these familial life trajectories. (Elzinga and Liefbroer,2007):

De-standardization: Some states and events of familial life areshared by decreasing proportions of the population, occur atmore dispersed ages and their duration is also more scattered.De-institutionalization: Social and temporal organization oflife courses becomes less driven by normative, legal orinstitutional rules.Differentiation: Number of distinct steps lived by individualincreases.

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Mining Event HistoriesCharacterizing, rendering and clustering sequence dataCharacterizing sets of sequences

Section content




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Characterizing sets of sequences

Sequence of transversal measures (between entropy, ...)id t1 t2 t3 · · ·1 B B D · · ·2 A B C · · ·3 B B A · · ·

Summary of longitudinal measures (sequence entropy, ...)id t1 t2 t3 · · ·1 B B D · · ·2 A B C · · ·3 B B A · · ·

Other global characteristics: Central sequence, Sequencediversity, ...

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Entropy

Entropy: Measure of uncertainty regarding state predictability.

pi , proportion of cases (or time points) in state i .Shannon h(p) =

∑i −pi log2(pi )

Other types of entropies: Quadratic (Gini), Daroczy, ...Two ways of using entropies.

(Transversal) entropy of the state at each time (age) point:Entropy increases with diversity of states observed at eachtime point (age).(Longitudinal) entropy of each individual sequences: Entropyincreases with diversity of states during the observed lifecourse and varies with the time spend in each state.

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Illustrative data

Data from the 2002 SHP biographical surveyInterested in relationship between

Cohabitational trajectories (10 states)Professional trajectories (8 states)

We use the coding retained by Gauthier (2007)Focus on ages 20 to 45 (sequence length = 26 years)1503 cases (751 women, 752 men)

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Transversal entropy at each time (age) point

Living Arrangement Trajectories

Age

Ent

ropy

A20 A23 A26 A29 A32 A35 A38 A41 A44

0.3

0.4

0.5

0.6

0.7

0.8

Professional Trajectories

Age

Ent

ropy

A20 A23 A26 A29 A32 A35 A38 A41 A44

0.3

0.4

0.5

0.6

0.7

0.8 1910−1940 1941−1950 1951−1957

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Men : Living Arrangement Trajectories

Age

Ent

ropy

A20 A23 A26 A29 A32 A35 A38 A41 A44

0.3

0.4

0.5

0.6

0.7

0.8

Women : Living Arrangement Trajectories

Age

Ent

ropy

A20 A23 A26 A29 A32 A35 A38 A41 A44

0.3

0.4

0.5

0.6

0.7

0.8 1910−1940 1941−1950 1951−1957

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Men: Professional Trajectories

Age

Ent

ropy

A20 A23 A26 A29 A32 A35 A38 A41 A44

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Women: Professional Trajectories

Age

Ent

ropy

A20 A23 A26 A29 A32 A35 A38 A41 A44

0.2

0.3

0.4

0.5

0.6

0.7

0.8 1910−1940 1941−1950 1951−1957

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Hypothesis about longitudinal entropies

Cohabitational and professional life trajectoriesbecome less stablemore diversified

Their entropy tends to increase for younger generations.Are increases in professional trajectories related to increases incohabitational trajectories?

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Entropy of cohabitational trajectories

●●●●●●●●●●●●●●

●

●●

●

●●●●●●●

1910−1940 1941−1950 1951−1957

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Men: Living Arrangment Trajectories

●

1910−1940 1941−1950 1951−19570.

00.

10.

20.

30.

40.

50.

60.

7

Women: Living Arrangment Trajectories

p(F > f ) = .000∗∗∗ p(F > f ) = .073∗all 2 by 2 differences significant coh3 significantly (.02) different from coh1

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Entropy of professional trajectories

●●

●

●

●

1910−1940 1941−1950 1951−1957

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Men: Professional Trajectories

1910−1940 1941−1950 1951−19570.

00.

10.

20.

30.

40.

50.

60.

7

Women: Professional Trajectories

p(F > f ) = .002∗∗∗ p(F > f ) = .001∗∗∗coh3 not significantly different from coh2

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Correlation between cohabitational and professional entropies

Overall Men Women1910-1940 0.08 ∗ 0.11 ∗ 0.19 ∗∗∗1941-1950 0.12 ∗∗ 0.14 ∗∗ 0.30 ∗∗∗1951-1957 0.15 ∗∗ 0.25 ∗∗∗ 0.31 ∗∗∗

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Mining Event HistoriesCharacterizing, rendering and clustering sequence dataDistances between sequences: Clustering

Section content




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Clustering, Multidimensional scaling and more

Once you are able to compute 2 by 2 distances betweensequences you can among others:Cluster sequencesAnalyse the trajectory heterogeneity (Generalized ANOVA)Make scatter plot representation of sets of sequences usingmultidimensional scaling.

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Distances between sequences

Edit distance (known as Optimal matching in Social sciences)(Levenshtein, 1966; Needleman and Wunsch, 1970; Abbott andForrest, 1986)

d(x , y) Total cost of insert, deletion and substitution changesrequired to transform sequence x into y .Different solutions depending on indel and substitution costs.

Other metrics proposed by (Elzinga, 2008)LCP: Longest common prefix (also longest common postfix)LCS: Longest common subsequence(same as OM with indel cost = 1, and substitution cost = 2).NMS: Number of matching subsequences...

Elzinga (2008) proposes a nice formalization of these metrics.

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Clustering with OM distances: Dendrograms[1

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24]

[132

6][4

12]

[109

3][7

92]

[15]

[175

][2

24]

[783

][1

304]

[561

][1

075]

[122

][1

283]

[924

][6

40]

[641

][7

26]

[101

2][1

303]

[143

3][1

063]

[998

][4

38]

[463

][9

70]

[105

2][1

330]

[143

6][1

446]

[137

1][3

1][6

7][4

88]

[782

][1

089]

[110

7][1

274]

[80]

[163

][3

40]

[556

][5

74]

[110

8][1

297]

[143

2][5

53]

[402

][7

89]

[519

][9

87]

[103

7][1

279]

[222

][3

07]

[499

][1

201]

[444

][8

18]

[456

][6

60]

[956

][9

64]

[995

][1

374]

[26]

[157

][8

11]

[104

7][5

5][7

9][6

6][8

13]

[468

][1

148]

[116

5][1

357]

[97]

[692

][1

135]

[101

7][1

485]

[269

][1

219]

[113

6][1

133]

[464

][5

30]

[127

1][4

71]

[765

][1

281]

[149

][1

81]

[784

][8

07]

[981

][1

358]

[639

][1

175]

[111

8][1

117]

[747

][7

64]

[133

2][2

40]

[500

][5

39]

[503

][1

256]

[123

4][1

496]

[132

7][1

2][1

8][4

5][4

6][5

6][6

3][9

6][1

32]

[144

][1

59]

[169

][1

80]

[189

][2

15]

[246

][2

63]

[264

][2

95]

[297

][3

58]

[429

][4

41]

[442

][4

57]

[467

][5

06]

[558

][5

62]

[568

][5

69]

[585

][5

95]

[596

][5

98]

[664

][7

05]

[717

][7

46]

[761

][7

72]

[775

][7

76]

[777

][8

55]

[863

][8

67]

[879

][8

97]

[950

][9

96]

[100

5][1

067]

[108

3][1

084]

[110

0][1

101]

[111

3][1

114]

[114

4][1

147]

[125

8][1

260]

[134

4][1

345]

[135

4][1

376]

[149

8][1

499]

[72]

[414

][1

353]

[59]

[938

][4

93]

[945

][5

59]

[850

][2

96]

[144

3][1

019]

[111

6][6

2][5

84]

[952

][2

17]

[251

][9

92]

[583

][6

50]

[675

][1

60]

[494

][1

079]

[250

][6

71]

[23]

[119

1][1

64]

[350

][8

37]

[140

5][1

406]

[141

][7

98]

[566

][9

37]

[103

8][1

259]

[165

][7

90]

[16]

[623

][1

225]

[425

][1

321]

[20]

[22]

[814

][1

264]

[225

][2

37]

[110

9][1

18]

[619

][1

018]

[118

5][9

31]

[216

][3

92]

[146

5][9

34]

[141

9][1

15]

[126

8][1

143]

[122

1][4

96]

[511

][8

62]

[184

][1

142]

[121

0][4

35]

[346

][6

69]

[138

0][5

18]

[115

4][6

36]

[114

9][6

97]

[899

][1

119]

[117

][3

05]

[405

][4

66]

[932

][9

36]

[228

][8

75]

[781

][1

45]

[202

][1

273]

[145

7][1

70]

[147

8][4

79]

[688

][1

322]

[155

][1

93]

[943

][1

207]

[226

][9

06]

[119

6][1

9][7

78]

[127

6][2

35]

[313

][6

96]

[243

][6

74]

[763

][8

96]

[921

][5

34]

[918

][2

38]

[834

][1

488]

[510

][8

68]

[128

4][1

313]

[145

4][8

02]

[766

][1

173]

[144

0][2

36]

[342

][7

33]

[799

][1

470]

[801

][2

84]

[331

][3

02]

[976

][1

213]

[720

][7

70]

[137

][5

36]

[117

9][6

01]

[100

9][1

307]

[294

][9

02]

[137

3][2

06]

[332

][1

430]

[578

][1

073]

[917

][1

302]

[131

1][3

0][1

20]

[690

][8

40]

[418

][4

58]

[128

7][1

177]

[232

][2

85]

[145

5][3

11]

[132

0][4

51]

[809

][6

83]

[124

7][1

79]

[947

][8

15]

[126

3][8

80]

[905

][1

21]

[140

3][2

86]

[140

8][7

08]

[554

][1

34]

[434

][6

57]

[762

][2

76]

[110

4][3

83]

[2]

[651

][6

52]

[102

][9

12]

[201

][2

75]

[391

][1

395]

[133

6][3

90]

[134

0][1

458]

[39]

[627

][1

155]

[820

][1

453]

[50]

[110

3][1

88]

[507

][1

98]

[86]

[711

][1

19]

[128

5][1

349]

[291

][8

00]

[448

][8

49]

[604

][1

126]

[148

9][6

0][4

00]

[404

][5

81]

[913

][4

13]

[871

][1

111]

[771

][8

66]

[119

0][5

79]

[139

7][1

398]

[38]

[985

][7

04]

[124

6][3

61]

[698

][7

10]

[124

5][1

97]

[616

][1

473]

[127

0][9

61]

[836

][8

9][2

47]

[804

][5

45]

[106

][1

267]

[105

][1

024]

[659

][1

085]

[207

][1

346]

[135

2][3

20]

[107

0][2

34]

[373

][3

74]

[573

][1

474]

[106

1][1

449]

[120

2][1

312]

[239

][6

26]

[299

][9

60]

[105

6][1

125]

[14]

[680

][8

89]

[885

][3

62]

[821

][5

3][3

96]

[575

][4

20]

[136

5][6

67]

[54]

[888

][5

72]

[145

6][1

54]

[729

][2

18]

[125

5][1

080]

[118

0][1

206]

[140

][4

19]

[486

][8

60]

[916

][7

3][1

102]

[701

][8

91]

[214

][1

416]

[848

][5

44]

[107

2][3

28]

[138

8][7

93]

[980

][1

360]

[602

][6

72]

[823

][5

93]

[756

][1

235]

[132

9][1

94]

[622

][5

16]

[681

][3

63]

[116

4][5

14]

[702

][7

85]

[138

1][8

12]

[141

3][1

157]

[407

][6

03]

[978

][9

94]

[835

][1

242]

[147

5][4

69]

[113

9][1

277]

[883

][6

87]

[144

2][5

1][1

01]

[85]

[287

][1

090]

[443

][9

04]

[325

][6

78]

[753

][1

409]

[146

8][1

492]

[112

][1

041]

[230

][1

350]

[769

][1

305]

[547

][1

097]

[132

3][9

90]

[108

8][1

128]

[101

3][1

059]

[136

8][1

029]

[131

][9

22]

[100

6][3

67]

[126

1][1

56]

[476

][2

78]

[886

][1

50]

[662

][3

66]

[314

][1

160]

[724

][4

78]

[830

][8

53]

[48]

[118

3][1

193]

[725

][1

288]

[293

][1

112]

[125

2][5

57]

[262

][1

053]

[120

8][5

02]

[768

][8

10]

[124

9][6

1][8

32]

[143

][1

168]

[546

][3

36]

[703

][2

41]

[427

][2

67]

[105

5][1

447]

[100

3][1

167]

[119

5][1

39]

[116

9][9

93]

[109

1][8

39]

[620

][6

35]

[213

][1

158]

[977

][1

134]

[107

6][1

239]

[136

1][1

53]

[629

][1

174]

[828

][8

87]

[100

4][1

166]

[454

][1

393]

[890

][9

35]

[132

8][2

77]

[645

][1

186]

[104

5][1

317]

[146

1][5

09]

[907

][9

08]

[563

][1

057]

[666

][1

184] [3]

[323

][6

53]

[654

][1

266]

[126

][1

394]

[354

][2

83]

[911

][1

015]

[134

1][5

26]

[138

5][3

6][1

29]

[523

][1

78]

[110

6][2

56]

[242

][8

45]

[846

][1

13]

[203

][7

74]

[322

][1

087]

[309

][1

316]

[694

][1

194]

[127

8][6

93]

[126

5][9

19]

[803

][2

74]

[738

][1

205]

[339

][5

40]

[894

][3

71]

[125

0] [7]

[424

][1

82]

[308

][1

490]

[44]

[282

][3

00]

[148

6][6

08]

[100

7][1

189]

[142

6][3

64]

[140

0][7

94]

[124

4][9

82]

[5]

[121

1][4

89]

[723

][1

044]

[112

9][1

427]

[329

][4

03]

[132

4][2

89]

[399

][4

30]

[408

][7

35]

[927

][8

70]

[105

4][1

121]

[127

2][1

290]

[35]

[580

][5

87]

[142

0][2

98]

[303

][3

33]

[341

][1

152]

[453

][1

423]

[621

][1

081]

[379

][7

00]

[452

][4

90]

[431

][5

70]

[676

][7

07]

[21]

[49]

[148

7][1

159]

[137

0][6

5][1

00]

[88]

[791

][4

83]

[668

][7

18]

[594

][8

54]

[825

][1

343]

[529

][8

38]

[104

8][1

229]

[43]

[744

][4

26]

[369

][1

131]

[436

][1

431]

[123

3][1

096]

[87]

[773

][8

72]

[137

8][1

3][5

82]

[605

][1

30]

[416

][2

48]

[749

][9

53]

[954

][2

11]

[113

8][6

86]

[119

2][3

4][4

47]

[103

4][2

52]

[882

][1

87]

[138

6][6

10]

[527

][8

95]

[147

7][2

33]

[116

2][1

163]

[930

][1

231]

[142

2][3

21]

[140

2][4

84]

[577

][1

362]

[37]

[498

][1

300]

[52]

[312

][1

026]

[112

7][1

292]

[93]

[107

][7

48]

[841

][1

301]

[541

][1

294]

[133

8][8

4][1

141]

[910

][1

286]

[140

1][1

47]

[345

][9

68]

[249

][1

031]

[136

7][1

74]

[126

2][6

25]

[691

][7

54]

[145

2][3

44]

[102

1][5

67]

[847

][7

13]

[118

7] [8]

[555

][1

212]

[355

][1

241]

[69]

[571

][3

3][1

467]

[714

][1

48]

[245

][2

72]

[822

][8

65]

[121

7][1

464]

[387

][6

18]

[141

0][2

08]

[900

][1

91]

[624

][6

48]

[117

8][3

16]

[334

][1

216]

[125

4][5

91]

[989

][1

0][9

4][9

5][3

56]

[377

][4

60]

[551

][5

92]

[649

][6

77]

[928

][9

42]

[109

8][1

124]

[121

8][1

407]

[142

8][9

46]

[70]

[115

6][5

99]

[140

4][1

83]

[109

2][7

80]

[521

][8

06]

[817

][9

65]

[105

1][1

237]

[138

3][7

1][1

172]

[338

][1

451]

[423

][1

425]

[135

][9

01]

[151

][1

060]

[533

][7

88]

[372

][1

335]

[401

][6

47]

[564

][1

153]

[874

][1

318]

[138

2][9

1][1

314]

[158

][1

309]

[150

1][2

71]

[966

][2

59]

[148

1][1

001]

[398

][4

46]

[732

][8

58]

[983

][1

36]

[537

][6

09]

[351

][3

86]

[432

][6

89]

[750

][6

06]

[612

][6

15]

[728

][7

55]

[103

3][1

243]

[145

9][7

36]

[903

][1

014]

[113

7][4

7][1

04]

[172

][3

76]

[394

][5

89]

[878

][1

035]

[123

8][1

348]

[142

9][1

480]

[149

7][4

77]

[116

][6

65]

[859

][1

150]

[138

4][1

424]

[330

][7

37]

[105

8][4

17]

[550

][1

463]

[607

][8

3][3

35]

[133

][3

75]

[487

][1

25]

[661

][1

293]

[111

][8

29]

[742

][9

79]

[108

2][1

130] [4]

[385

][5

38]

[684

][7

40]

[876

][1

414]

[141

5][1

46]

[185

][9

23]

[974

][3

10]

[353

][7

30]

[613

][6

14]

[124

][2

65]

[406

][4

62]

[915

][9

91]

[127

5][1

500]

[186

][2

79]

[347

][3

93]

[459

][6

70]

[864

][8

84]

[898

][9

09]

[962

][9

63]

[103

2][1

049]

[110

5][1

176]

[125

7][1

295]

[597

][1

008]

[17]

[119

9][6

46]

[106

5][1

306]

[133

4][2

4][1

351]

[114

0][1

77]

[861

][1

441]

[27]

[209

][4

50]

[90]

[231

][7

22]

[739

][9

58]

[107

7][3

70]

[881

][1

227]

[122

8][1

363]

[365

][1

434]

[411

][1

122]

[395

][9

73]

[797

][1

392]

[474

][7

67]

[481

][7

31]

[869

][1

151]

[25]

[472

][8

51]

[972

][1

016]

[137

2][1

90]

[513

][1

095]

[148

4][3

37]

[525

][9

59]

[118

1][1

310]

[92]

[102

0][1

337]

[137

9][5

12]

[104

2][1

094]

[827

][1

389]

[969

][1

200]

[497

][8

26]

[106

2][1

435]

[147

6][6

8][9

8][4

10]

[656

][7

09]

[719

][1

099]

[129

8][1

469]

[288

][3

01]

[758

][4

70]

[515

][4

61]

[824

][5

86]

[123

2][8

31]

[139

9][7

8][8

57]

[939

][1

28]

[843

][1

396]

[786

][1

291]

[176

][4

82]

[535

][1

96]

[110

][7

21]

[926

][9

71]

[107

8][3

04]

[449

][8

05]

[102

5][1

064]

[111

5] [6]

[57]

[127

][1

42]

[200

][2

53]

[260

][2

68]

[397

][6

31]

[638

][6

43]

[644

][8

42]

[892

][9

49]

[102

8][1

030]

[112

0][1

145]

[114

6][1

198]

[120

4][1

282]

[150

3][7

5][8

2][1

08]

[440

][4

91]

[751

][7

96]

[134

2][1

71]

[548

][1

027]

[106

6][3

59]

[873

][1

209]

[378

][1

002]

[58]

[161

][1

66]

[168

][1

73]

[195

][2

23]

[261

][4

22]

[475

][4

80]

[590

][6

00]

[617

][6

28]

[699

][7

15]

[787

][8

56]

[877

][9

67]

[984

][1

000]

[105

0][1

224]

[130

8][1

319]

[141

7][1

482]

[148

3][1

491]

[150

2][2

9][1

67]

[199

][3

68]

[389

][4

33]

[445

][4

85]

[611

][6

30]

[734

][1

086]

[113

2][1

170]

[132

5][1

377]

[144

8][1

110]

[143

7][1

296]

[109

][2

20]

[229

][2

80]

[384

][4

21]

[655

][9

20]

[975

][2

19]

[380

][1

223]

[147

1][7

4][7

6][7

7][2

12]

[266

][5

49]

[759

][9

48]

[104

3][1

289]

[143

9] [9]

[473

][8

08]

[988

][1

182]

[123

0][1

299]

[64]

[315

][1

52]

[816

][1

444]

[381

][4

95]

[501

][7

45]

[852

][9

51]

[999

][1

010]

[125

3][1

366]

[142

1][1

466]

[757

][9

9][6

63]

[205

][7

41]

[11]

[103

][2

44]

[348

][6

79]

[682

][8

93]

[925

][1

226]

[123

6][1

251]

[133

9][1

347]

[139

0][1

479]

[149

5][2

8][3

2][2

54]

[522

][5

31]

[716

][9

14]

[117

1][1

240]

[136

9][1

411]

[141

8][1

460]

[146

2][8

1][3

49]

[695

][3

82]

[727

]

050

0010

000

1500

020

000

Cohabitational trajectories, Ward method

(OM Distances, Indel=1, Subst. Cost based on Trans. Rate)Individual trajectories

Hei

ght

1 2 5 6 7 13 24 29 30 34 36 37 38 42 43 46 50 53 62 64 68 69 76 84 86 92 95 97 101

104

112

116

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137

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149

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629

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733

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827

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1000

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1011

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1020

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1024

1025

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1038

1040

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1120

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1123

1128

1130

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1189

1191

1195

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1199

1201

1204

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1215

1219

1222

1228

1238

1243

1247

1253

1258

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1267

1270

1274

1275

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1279

1282

1290

1297

1302

1303

1307

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1318

1320

1324

1325

1329

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1339

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1348

1358

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1371

1374

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1498

1499

1501

1408 12 15 89 98 114

150

174

192

260

281

355

391

410

465

471

475

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531

539

567

600

617

619

635

636

646

651

658

659

678

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765

789

807

809

818

842

847

886

906

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1007

1081

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1104

1110

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1405

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1442

1471

1484 87 30

512

0719

610

6911

94 498

1047 64

912

317

119

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985

525

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332

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09 922

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1911

01 143

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112

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64 182

216

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2 48 331

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241

790

710

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53 270

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1 463

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491

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212

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625

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367

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168

373

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210

2910

9211

2511

4311

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0212

3213

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4914

86 40

502

82 146

285

370

519

557

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830

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1455 9

122 20

549

654

559

371

574

175

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111

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76 138

1064 72

123 67 75 34

535

936

144

559

060

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974

376

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487

310

6111

3113

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81 47 385

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1072 91

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4 10 336

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19 610

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75 3510

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17 20 49 55 110

221

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183

614

16 59 901

1126 43

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099

7 7857

210

36 7919

484

810

010

08 838

780

119

620

660

262

328

947

1200

1257 62

226

711

90 857 74

655

1317

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164

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905

564

1326

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418

1231 95

013

1213

3814

9110

7610

5311

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114

54 284

1108

1158 28

679

612

17 280

565

1139

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9810

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1237 26 169

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1097 24

563 67

311 56 13

114

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322

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342

342

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344

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648

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551

653

654

255

357

357

564

164

466

367

470

976

077

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481

382

283

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496

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0011

0511

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35 559

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614

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59 295

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1423 79

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5810

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1281 41

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058 81 99 482

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535

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793

547

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1474 69

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158

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311

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338

1218

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714

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75 107

462

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371

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1085

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057

710

7411

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1167

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355

511

4913

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88 4512

52 239

342

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736

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07 374 94

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4810

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616

754

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158

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51 726

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013

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21 54

222

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103

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254

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65 732

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1062 44 368

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274

275

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320

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310

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394

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41 93 390

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618

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126

161

211

53 356

551

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298

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520

537

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2113

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184

253

398

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629

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437

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865

867

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928

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1321

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31 70 581

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24 473

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810

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859

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369

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613

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244

812

66

050

0010

000

1500

020

000

Professional trajectories, Ward method

(OM Distances, Indel=1, Subst. Cost based on Trans. Rate)Individual trajectories

Hei

ght

LA Prof19/11/2008gr 58/95


LA, State distribution by age, within cluster

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 1 : Conjugal Trajectories (16 %)

Fre

q. (

n=23

5)

0.0

0.2

0.4

0.6

0.8

1.0

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 2 : Parental Trajectories, Slow Transition (19 %)

Fre

q. (

n=28

5)

0.0

0.2

0.4

0.6

0.8

1.0

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 3: Parental Trajectories, Fast Transition (48 %)

Fre

q. (

n=71

4)

0.0

0.2

0.4

0.6

0.8

1.0

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 4 : Nestalgic Trajectories (7 %)

Fre

q. (

n=11

0)

0.0

0.2

0.4

0.6

0.8

1.0

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 5 : Solo or Reconstituted Family Trajectories (11 %)

Fre

q. (

n=15

9)

0.0

0.2

0.4

0.6

0.8

1.0

Biological father and motherOne biological parentOne biological parent with her/his partnerAloneWith partnerPartner and biological childPartner and non biological childBiological child and no partnerFriendsOther

19/11/2008gr 59/95


LA, Most frequent sequences by cluster

3.4%

3.4%

3%

2.5%

2.5%

2.1%

2.1%

2.1%

2.1%

1.7%

Type 1 : Conjugal Trajectories (16 %)

Fre

q. (

n=23

5)

A20 A23 A26 A29 A32 A35 A38 A41 A44

1.1%

1.1%

1.1%

1.1%

0.7%

0.7%

0.7%

0.7%

0.7%

0.7%


Fre

q. (

n=28

5)

A20 A23 A26 A29 A32 A35 A38 A41 A44

4.5%

3.5%

2.5%

2.4%

2.4%

2.2%

2%

1.8%

1.7%

1.5%


Fre

q. (

n=71

4)

A20 A23 A26 A29 A32 A35 A38 A41 A44

61.8%

1.8%1.8%0.9%0.9%0.9%0.9%0.9%0.9%0.9%


Fre

q. (

n=11

0)

A20 A23 A26 A29 A32 A35 A38 A41 A44

3.1%

1.9%

1.9%

1.9%

1.9%

1.3%

1.3%

1.3%

1.3%

1.3%


Fre

q. (

n=15

9)

A20 A23 A26 A29 A32 A35 A38 A41 A44

Biological father and motherOne biological parentOne biological parent with her/his partnerAloneWith partnerPartner and biological childPartner and non biological childBiological child and no partnerFriendsOther

19/11/2008gr 60/95


LA, Sequence diversity within cluster

19/11/2008gr 61/95


LA, Birth year distribution by clusterType 1 : Conjugal Trajectories (16 %)

Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06


Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06


Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06


Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06


Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06

Overall

Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06

19/11/2008gr 62/95


Prof, State distribution by age, within cluster

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 1 : Full Time Trajectoires (53 %)

Fre

q. (

n=79

5)

0.0

0.2

0.4

0.6

0.8

1.0

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 2 : Mixed Part Time − Home Trajectories (13 %)

Fre

q. (

n=15

5)

0.0

0.2

0.4

0.6

0.8

1.0

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 3 : At Home Trajectories (16 %)

Fre

q. (

n=27

7)

0.0

0.2

0.4

0.6

0.8

1.0

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 4 : Part Time Trajectories (7 %)

Fre

q. (

n=10

1)

0.0

0.2

0.4

0.6

0.8

1.0

A20 A23 A26 A29 A32 A35 A38 A41 A44

Type 5 : Missing Data (11 %)

Fre

q. (

n=17

5)

0.0

0.2

0.4

0.6

0.8

1.0

MissingFull timePart timeNegative breakPositive breakAt homeRetiredEducation

19/11/2008gr 63/95


Prof, Most frequent sequences by cluster

56.6%

8.4%

3.8%

2.8%2.4%2.3%1.9%1.8%0.8%0.6%

Type 1 : Full Time Trajectoires (53 %)

Fre

q. (

n=79

5)

A20 A23 A26 A29 A32 A35 A38 A41 A44

2.6%

2.6%

2.6%

1.9%

1.9%

1.9%

1.9%

1.9%

1.3%

1.3%


Fre

q. (

n=15

5)

A20 A23 A26 A29 A32 A35 A38 A41 A44

5.4%

4%

4%

3.2%

3.2%

3.2%

2.9%

2.2%

2.2%

2.2%


Fre

q. (

n=27

7)

A20 A23 A26 A29 A32 A35 A38 A41 A44

5%

5%

5%

4%

2%

2%

2%

2%

2%

2%


Fre

q. (

n=10

1)

A20 A23 A26 A29 A32 A35 A38 A41 A44

34.9%

4.6%

3.4%

3.4%

2.9%

2.3%

2.3%1.7%1.7%1.7%


Fre

q. (

n=17

5)

A20 A23 A26 A29 A32 A35 A38 A41 A44

MissingFull timePart timeNegative breakPositive breakAt homeRetiredEducation

19/11/2008gr 64/95


Prof, Sequence diversity within cluster

19/11/2008gr 65/95


Prof, Birth year distribution by clusterType 1 : Full Time Trajectoires (53 %)

Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06


Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06


Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06


Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06


Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06

Overall

Birth year

Den

sity

1910 1920 1930 1940 1950 1960

0.00

0.01

0.02

0.03

0.04

0.05

0.06

19/11/2008gr 66/95

Mining Event HistoriesCharacterizing, rendering and clustering sequence dataHeterogeneity analysis and sequence discrimination

Section content




19/11/2008gr 67/95


Heterogeneity of set of sequences

Sum of squares can be expressed in terms of the distancesbetween each pair of points

SS =n∑

i=1(yi − y)2 =

1n

n∑i=1

n∑j=i+1

(yi − yj)2

=1n

n∑i=1

n∑j=i+1

dij

Setting dij to the OM, LCP, LCS, ... distance, we get ameasure of diversity or heterogeneity of sequences.Can apply ANOVA principle to sequences.

19/11/2008gr 68/95


Heterogeneity analysisProfessional trajectories by sex

19/11/2008gr 69/95


Sequence Tree

19/11/2008gr 70/95

Mining Event HistoriesCharacterizing, rendering and clustering sequence dataMultidimensional Scaling representation of sequences

Section content




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Multidimensional Scaling: Principle

Let D be a distance matrix between sequences.D computed using OM, LPS, LCS, ... metrics.Multidimensional Scaling consists in

Finding a set of real valued variables (f1, f2) such that theδij =

√(fi1 − fj1)2 + (fi2 − fj2)2 best approximate the

distances between sequences.Plotting the points in the (f1, f2) space.

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Multidimensional Scaling

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010

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Multidimensional scaling representation, colored cluster of cohabitation

MDS axis 1

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xis

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Type 1 : Conjugal Trajectories (16 %)Type 2 : Parental Trajectories, Slow Transition (19 %)Type 3: Parental Trajectories, Fast Transition (48 %)Type 4 : Nestalgic Trajectories (7 %)Type 5 : Solo or Reconstituted Family Trajectories (11 %)

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010

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S a

xis

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Type 1 : Full Time Trajectoires (53 %)Type 2 : Mixed Part Time − Home Trajectories (13 %)Type 3 : At Home Trajectories (16 %)Type 4 : Part Time Trajectories (7 %)Type 5 : Missing Data (11 %)

19/11/2008gr 73/95

Mining Event HistoriesMining Frequent Episodes

Table of content


2 Survival Trees



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Mining Event HistoriesMining Frequent Episodes

Mining Frequent Episodes

(Time stamped) event sequencesWhat can we expect from frequent episodes mining?

GSP (Srikant and Agrawal, 1996)MINEPI, WINEPI (Mannila et al., 1997)TCG, TAG (Bettini et al., 1996)SPADE (Zaki, 2001)

Are there specific issues when applying these methods insocial sciences?

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Mining Event HistoriesMining Frequent EpisodesWhat Is It About?

Section content

4 Mining Frequent EpisodesWhat Is It About?Example: Counting Alternate Episode StructuresFrequent and discriminant episodes

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Frequent episodes. What is it?

Episode: Collection of events occurring frequently together.Mining typical (frequent) episodes:

Specialized case of mining frequent itemsets.Time dimension ⇒ Partially ordered events.

More complex than unordered itemsets: User mustspecify time constraints (and episode structure constraints).select a counting method.

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Episode structure constraints

For people who leave home within 2 years from their 17, what aretypical events occurring until they get married and have a firstchild?

LH,17

w = 2

??

w = 1

C1

M(0, 4)

(0,3)

(0, 1, 10)

elastic

event constraints

parallel

node constraint

edge constraints

19/11/2008gr 78/95


Counting methods (Joshi et al., 2001)

20 21 22 23 24

U UUC C C

Searching (U,C)min gap= 1, max gap= 2, win size= 2

indiv. with episode COBJ = 1

windows with episode CWIN = 3

min win. with episode CminWIN = 2

distinct occurrences CDIS_o = 5

dist. occ. without overlap CDIS = 3

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Mining Event HistoriesMining Frequent EpisodesExample: Counting Alternate Episode Structures

Section content


19/11/2008gr 80/95

Mining Event HistoriesMining Frequent EpisodesExample: Counting Alternate Episode Structures

Example: Counting alternate structures (COBJ, no max gap)

0%

5%

10%

15%

20%

25%

30%

Child <

Marr

iage

Marriag

e < C

hild

Child =

Marr

iage

Child <

Job

Job <

Chil

d

Child =

Job

Child <

Edu

c end

Educ e

nd <

Child

Child =

Edu

c end

Marriag

e < Jo

b

Job <

Marr

iage

Marriag

e = Jo

b

Marriag

e < Edu

c end

Educ e

nd <

Marriag

e

Marriag

e = Edu

c end

Job <

Edu

c end

Educ e

nd <

Job

Job =

Edu

c end

Switzerland, SHP 2002 biographical survey (n = 5560).19/11/2008gr 81/95

Mining Event HistoriesMining Frequent EpisodesFrequent and discriminant episodes

Section content


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Frequent episodes, cohabitational and professional trajectories0.

00.

10.

20.

30.

40.

50.

6

(Bio

logi

cal f

athe

r an

d m

othe

r)

(With

par

tner

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nd b

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(Bio

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cal f

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With

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0.0

0.1

0.2

0.3

0.4

0.5

(Ful

l tim

e)

(Edu

catio

n)

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n>F

ull t

ime)

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catio

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ime)

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ome>

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)

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19/11/2008gr 83/95


Discriminant episodes, professional trajectories, women

FullTime Mixed AtHome PartTime

(Full time>At home)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


(Full time)−(Full time>At home)

0.0

0.1

0.2

0.3

0.4

0.5


(At home>Part time)

0.0

0.1

0.2

0.3

0.4

FullTime Mixed AtHome PartTime Missing

(Full time>Part time)

0.0

0.1

0.2

0.3

0.4

0.5

Mixed AtHome PartTime

(Full time>At home)−(At home>Part time)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Mixed AtHome PartTime

(Full time)−(At home>Part time)

0.00

0.05

0.10

0.15

0.20

0.25

19/11/2008gr 84/95


Discriminant episodes, professional trajectories, men

FullTime Mixed Missing

(Missing)

0.0

0.1

0.2

0.3

0.4

FullTime Mixed PartTime Missing

(Education>Missing)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35


(Full time)

0.0

0.1

0.2

0.3

0.4

0.5

0.6


(Education>Full time)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35


(Education)−(Education>Full time)

0.00

0.05

0.10

0.15

0.20

0.25

0.30


(Education)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

19/11/2008gr 85/95

Mining Event HistoriesSummary

Summary

Data mining approaches (survival trees, clustering sequences,frequent episodes) have promising future in life courseanalysis.

Complement classical statistical outcomes with new insights.

Their use within social sciences raises specific issues:Accounting for multi-level effects when growing survival tree ormining association rules.Handling time varying predictors in survival trees.Selecting relevant counting methods (event dependent)?Suitable criteria for measuring association strength betweenfrequent episodes....

19/11/2008gr 86/95


Our TraMineR R-package

Let me finish with an Add ...

TraMineR, a free life trajectory mining toolfor the free open source R statistical environment.downloadable from http://cran.r-project.org (CRAN)see also http://mephisto.unige.ch/biomining

19/11/2008gr 87/95

http://cran.r-project.org/web/packages/TraMineR/

http://cran.r-project.org

http://mephisto.unige.ch/biomining

http://mephisto.unige.ch/biomining


Thank You!Thank You!

19/11/2008gr 88/95

Mining Event HistoriesAppendixZoomed tree

Divorce, Switzerland, Differences in KM Survival CurvesI

Return

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Mining Event HistoriesAppendixZoomed tree

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19/11/2008gr 89/95

Mining Event HistoriesAppendixFor Further Reading

For Further Reading I

Abbott, A. and J. Forrest (1986). Optimal matching methods forhistorical sequences. Journal of Interdisciplinary History 16,471–494.

Bettini, C., X. S. Wang, and S. Jajodia (1996). Testing complextemporal relationships involving multiple granularities and itsapplication to data mining (extended abstract). In PODS ’96:Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGARTsymposium on Principles of database systems, New York, pp.68–78. ACM Press.

19/11/2008gr 90/95


For Further Reading II

Billari, F. C. (2005). Life course analysis: Two (complementary)cultures? Some reflections with examples from the analysis oftransition to adulthood. In R. Levy, P. Ghisletta, J.-M. Le Goff,D. Spini, and E. Widmer (Eds.), Towards an InterdisciplinaryPerspective on the Life Course, Advances in Life CourseResearch, Vol. 10, pp. 267–288. Amsterdam: Elsevier.

Blossfeld, H.-P. and G. Rohwer (2002). Techniques of EventHistory Modeling, New Approaches to Causal Analysis (2nded.). Mahwah NJ: Lawrence Erlbaum.

Elzinga, C. H. (2008). Sequence analysis: Metric representationsof categorical time series. Sociological Methods and Research.forthcoming.

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For Further Reading III

Elzinga, C. H. and A. C. Liefbroer (2007). De-standardization offamily-life trajectories of young adults: A cross-nationalcomparison using sequence analysis. European Journal ofPopulation 23, 225–250.

Gauthier, J.-A. (2007). Empirical categorizations of socialtrajectories: A sequential view on the life course. Thèse,Université de Lausanne, Faculté des sciences sociales et politique(SSP), Lausanne.

Huang, X., S. Chen, and S. Soong (1998). Piecewise exponentialsurvival trees with time-dependent covariates. Biometrics 54,1420–1433.

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For Further Reading IV

Joshi, M. V., G. Karypis, and V. Kumar (2001). A universalformulation of sequential patterns. In Proceedings of theKDD’2001 workshop on Temporal Data Mining, San Fransisco,August 2001.

Leblanc, M. and J. Crowley (1992). Relative risk trees for censoredsurvival data. Biometrics 48, 411–425.

Levenshtein, V. (1966). Binary codes capable of correctingdeletions, insertions, and reversals. Soviet Physics Doklady 10,707–710.

Mannila, H., H. Toivonen, and A. I. Verkamo (1997). Discovery offrequent episodes in event sequences. Data Mining andKnowledge Discovery 1(3), 259–289.

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For Further Reading VNeedleman, S. and C. Wunsch (1970). A general method

applicable to the search for similarities in the amino acidsequence of two proteins. Journal of Molecular Biology 48,443–453.

Segal, M. R. (1988). Regression trees for censored data.Biometrics 44, 35–47.

Segal, M. R. (1992). Tree-structured methods for longitudinaldata. Journal of the American Statistical Association 87(418),407–418.

Srikant, R. and R. Agrawal (1996). Mining sequential patterns:Generalizations and performance improvements. In P. M. G.Apers, M. Bouzeghoub, and G. Gardarin (Eds.), Advances inDatabase Technologies – 5th International Conference onExtending Database Technology (EDBT’96), Avignon, France,Volume 1057, pp. 3–17. Springer-Verlag.

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For Further Reading VI

Zaki, M. J. (2001). SPADE: An efficient algorithm for miningfrequent sequences. Machine Learning 42(1/2), 31–60.

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