1

FROM DATA MINING TO

KNOWLEDGE MINING:

SYMBOLIC DATA ANALYSIS

AND THE SODAS SOFTWARE

E. Diday

University of Paris IX Dauphine

and INRIA

AIM

FROM HUDGE DATA IN AN ECONOMIC WAY

-Extract new knowledge

-Summarize

-Concatenate

-Solve confidentiality

-Explain correlation

HOW? By working on HIGHER LEVEL UNITS as

“classes”, “categories” or ”concepts“ necessary described by

more complex data extending Data Mining to Knowledge

Mining.

2

OUTLINE

1) THE MAIN IDEA:

FIRST AND SECOND ORDER OBJECTS.

2)THE INPUT OF A SYMBOLIC DATA ANALYSIS:

SYMBOLIC DATA TABLE.

3) MAIN SOURCES OF SYMBOLIC DATA: FROM

DATA BASES, FROM CATEGORICAL VARIABLES.

4) MAIN OUTPUT OF SYMBOLIC DATA ANALYSIS

ALGORITHMS: SYMBOLIC DESCRIPTIONS AND

SYMBOLIC OBJECTS.

5) THE MAIN STEPS OF A SDA.

6) SOME TOOLS OF SYMBOLIC DATA ANALYSIS

7) SYNTHETICAL VIEW OF THE SODAS SOFTWARE

THE MAIN IDEA:

FIRST AND SECOND ORDER OBJECTS

THE ARISTOTLE ORGANON (IV B.C.) CLEARLY

DISTINGUISHES "FIRST ORDER OBJECTS" (AS THIS

HORSE OR THIS MAN) CONSIDERED AS A UNIT

DESCRIBING AN INDIVIDUAL OF THE WORLD ,

FROM "SECOND ORDER OBJECTS" (AS A HORSE

OR A MAN) ALSO TAKEN AS A UNIT DESCRIBING

A CLASS OF INDIVIDUALS.

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Class, Category, Concept

• A CLASS is a set of units (birds of an island)

• A CATEGORY is a value of a categorical variable (“swallows” is a value of the variable: “species of bird”)

• A CONCEPT is defined by an intent and an extent

• Intent: characteristic properties of the swallows

• Extent: the set of swallows

•A concept is modeled by a “symbolic object”

From standard units to concepts the statistic is not the same!

On an island there are 400 swallows, 100 ostrich, 100 penguins :

Standard Data Table Symbolic Data Table

A « conceptual »variable is added: itapplies to concepts

125NoOstrich600

swallows

Penguin

Species

70Yes2

80No1

Size (cm)FlyingOiseau

0.5n,0.5gris

0.1noir,0.9g

0.3b,0.7grey

Color

Yes

No

Yes

MigrSizeFlyingSpecies

[70, 95]NoPenguin

[85, 160]NoOstrich

[60, 85]yesSwallows

The variation due to the individuals isexpressed by intervals or histograms

Birds (individuals)

Flying No flying

1

2

Species

Flying No flying

400

200

The species is a concept , it becomes the new statistical unit

The statistic of individuals is different

from the statistic of concepts!

(concepts)

4

From Database to Concepts

QUERY

Rows : concepts

Relational

Data Base

Individuals

Concepts Description

Symbolic Data Table

Individuals description

Columns: symbolic variables

Columns: standard variables

Rows : individuals

Individuals versus Concepts

Type of environmentGeographical Position

Type of consumingWater consumer

Socio professional categoryClient

Fly AF Paris Ljubjana N° 205 in May 2006Fly AF Paris Ljubjana N° 205 5 May 06

All Reservation to Fly AF Paris Ljubjana July 2006Reservation of John to Fly AF Paris Ljubjana

MagazinesSubscription (to Time, ...)

WEB Usages (Medical Info, Weather, ...)WEB trace (Jones, temperature today,.)

Types of Item (Electrical Goods, Auto,...)Item Sold (hammer, phone, ...)

Types of Photos (Family, Mountains, ...)Photo (taken today, ...)

Team (Spane, ...)Football Player (Zidane, ...)

Species (Cardinals, Wrens, ...)Bird (this cardinal, ...)

Region (North, South, ...)Town (Paris, Lyon, ...)

Symbolic observations

(Concepts)

Classical observations

(Individuals)

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FOUR PRINCIPLES

1) ONLY TWO LEVELS OF UNITS:First level: Individuals

Second level: concepts

2) THE CONCEPTS CAN BE CONSIDERED

AS NEW INDIVIDUALS OF HIGHER LEVEL.

3) A CONCEPT IS DESCRIBED BY USING THE DESCRIPTION OF A CLASS OF INDIVIDUALS OF ITS EXTENT.

4) THE DESCRIPTION OF A CONCEPT MUST EXPRESSES THE VARIATION OF THE INDIVIDUALS OF ITS EXTENT

Units Classes Descr. Var. of the UnitsCase n° Region Bedroom Dining-

Living

Socio-Econ

Group

11401 Northern-

Metropolitan2 1 1

11402 Northern-

Metropolitan2 1 3

11403 Northern-

Metropolitan1 3 3

12315 East-Anglia 1 3 3

12316 East-Anglia 2 2 1

14524 Greater-London 1 2 3

FROM FIRST ORDER OBJECTS TO SECONDORDER OBJECTS IN OFFICIAL STATISTICS

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FROM FIRST ORDER OBJECTS TO SECOND ORDER OBJECTS

IN OFFICIAL STATISTICS

Classes Descriptive variable of the units

Region Bedroom Dining-Liv Socio-Ec grNorthern-

Metropolitan2 1 1

Northern-

Metropolitan2 1 3

Northern-

Metropolitan1 3 3

East-anglia 1 3 3East-anglia 2 2 1East-anglia 1 2 3

Classes Descriptive variables of the classes

Region Bedroom Dining-Liv Socio-Ec grNorthern-

Metropolitan

(2\3) 2, (1\3) 1 (2\3) 1, (1\3) 3 (1\3) 1, (2\3) 3

East-anglia (2\3) 1, (1\3) 2 (2\3) 2, (1\3) 3 (2\3) 3, (1\3) 1

2aC2I6

3bC2I5

1bC2I4

2cC1I3

1bC1I2

2aC1I1

Y2

Y1

ConceptsIndividuals

Initial classical data table where individuals are

described by three variables

Keeping rules after the generalization process

1, 2, 3a, b C2

1, 2a, b, c C1

Y2

Y1

Induced Symbolic Data Table with background knowledge defined by two rules:

[Y1 = a] ⇒⇒⇒⇒ [Y2 = 2] and [Y2 = 1] ⇒⇒⇒⇒ [Y1 = b]

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noFrench1.818130XXXRumbum

noAfrican1.838324XXXMirce

noBrazilian1.848429XXOlar

noSpanish1. 759123XXRenie

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

yesFrench1.857827FranceZedane

yesAfrican1.908225FranceMballo

yesBrazilian1.929023SpainPRodriguez

yesSpanish1. 848529SpainFernandez

World Cup_ _ _ _ NationalityHeightWeightAgeTeam Player

Classical data table describing players by numerical and categorical variables.

0.65[1.75, 1.85][81, 92][23, 30]no

0.85[1.85, 1.98][78, 90][21, 26]yes

Cor(Weight, Height) HeightWeightAgeWorld Cup

Symbolic Data Table obtained by generalisation for the variables age, weight and height and keeping back

the correlations between the Weight and the Height: the correlation is higher for the world cup players.

Keeping correlation after the generalization process

MORE GENERALY, WHAT IS THE INPUT OF A

SYMBOLIC DATA ANALYSIS?

SYMBOLIC DATA TABLE

+ BACKGROUND KNOWLEDGE

Schweitzer (1984): "Distributions are the

numbers of the future”

SYMBOLIC DATA TABLE :

THE CELLS CAN CONTAIN:

- SEVERAL QUALITATIVE OR QUANTITATIVE

WEIGHTED VALUES

- INTERVALS

- HISTOGRAMS

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SOME BACKGROUND KNOWLEDGE CAN BE GIVEN

VARIABLES CAN BE:

-TAXONOMIC: « A SOCIO-ECONOMIC GROUP IS

CONSIDERED TO BE "SELF-EMPLOYED" IF IT IS

"PROFESSIONAL SELF-EMPLOYED" OR "OWN ACCOUNT

NON-PROFESSIONAL".

-HIERARCHICALLY DEPENDENT :

THE VARIABLE: “DOES THE COMPANY HAS COMPUTERS? “

AND

THE VARIABLE: “ KIND OF COMPUTER” ARE

HIERARCHICALLY LINKED.

- RULES KEEPING LOGICAL DEPENDENCIES:

« IF AGE(W) IS LESS THAN 2 MONTHS THEN HEIGHT(W) IS

LESS THAN 10 ».

EuropeComp6

Glasgow Comp5

EnglandComp4

FranceComp3

LondonComp2

Paris Comp1

_ _ _ _ _ _ _ _ _Region_ _ _ _ _ _ _ _Compagnies

A TAXONOMIC VARIABLE

Europe

United King Dom

EnglandScotland France

London Glasgow Paris

The taxonomic tree associated with the variable « region ».

EuropeEurope

ScotlandGlasgow

EuropeEngland

EuropeFrance

EnglandLondon

FranceParis

PredecessorRegion

Database

relation

9

EXAMPLE OF SYMBOLIC DATA TABLE

THE CELLS CAN CONTAIN:

-SEVERAL QUALITATIVE OR

QUANTITATIVE WEIGHTED VALUES

-INTERVALS

- HISTOGRAMS

PRODUCT WEIGHT TOWN COLOUR

PRODUCT 1 [5, 9] Londres 0.1red, 0.9white

PRODUCT 2 [ 3 , 8 ] Paris, Londres

PRODUCT 3 0.3 red, 0.7 green

PRODUCT 4 [2,3]

SYMBOLIC DATA

ANALYSIS: 3 STEPS

FIRST STEP: From individuals to categories

SECOND STEP: From Categories to Concepts described

by a Symbolic Data Table.

THIRD STEP: Extract new knowledge from this symbolic

data completed by some background knowledge.

CONSEQUENCE: need of extending Standard Statistics,

Exploratory Data Analysis, and Data Mining to Symbolic

Data Tables. This is the aim of the SODAS software.

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From Standard Versus Symbolic Data and methods

Standard DataSymbolic Data

THE DATA

• Numerical: Points de R (nbres réels) • Categorical Ordinal : Points of N (naturel numbers)

• Categorical non ordered : categorical values

- Diagrams, Histograms ou Distributions

- Sequences of numbers or categories- Sequences of weighted categories

- Functions, curves

- Rules

- Taxonomies

- Graphes

Methods

• Stat descriptive (Histos, Corrélations , biplots)

•Typologie (hiérarchies, pyramids, K-means, Nuées dynamiques, Kohonen maps ,…)

•Mixture decoimposition

•Décision trees, boosting, baging, …

•Dissimilarities and their Représentation

•Rules inference and causal trees• Visualisation (points)

•factorial Analysis (ACP, AFC, …)

•Classical Regression, PLS

•Neural Network, VSM (Vector Support Machine),

Etc. • Galois Lattices (binary data)

Any standard method can be generalizedto concepts described by symbolic data

+ Specific Methods of Symbolic Data

AnalysisClass description, Haussdorf dissimilarities,

symbolic prototypes, modeling concepts by

symbolic objects…

(PLUS)

SOURCES OF SYMBOLIC DATA

.FROM DATA BASES: QUERY CREATING A

NEW CATEGORICAL VARIABLE: cartesian prod

.FROM CATEGORICAL VARIABLES:

- GIVEN (AS « TYPE OF EMPLOYMENT »)

- OBTAINED BY CLUSTERING.

.FROM EXPERT: NATIVE SYMBOLIC DATA:

Scenario of road accidents, species of insects

.FROM CONFIDENTIAL DATA

IN ORDER TO HIDE THE INITIAL DATA BY

LESS ACCURACY

11

.FROM STOCHASTIC DATA TABLE:THE PROBABILITY DISTRIBUTION , THE HISTOGRAM THE PERCENTILES OR

THE RANGE OF ANY RANDOM VARIABLE ASSOCIATED TO EACH CELL OF A

DATA TABLE

Mathematics Physics Litterature

Tom XM X P X L

Paul

XM is the random variable which associates to each

exam of TOM his mark in mathematics.

From XM several kinds of symbolic objects can be

defined by using in each cell: - Probability distr.

- Histograms

- Inter-quartile intervals

EXAMPLE

.FROM TIME SERIES

- IN DESCRIBING INTERVALS OF TIME:

( the variation of the values each week)

- IN DESCRIBING A TIME SERIES BY THE

HISTOGRAM OF ITS VALUES.

0

2 0

4 0

6 0

8 0

10 0

1 er

tr im .

2 e

tr im .

3e

tr im .

4 e

tr im .

E st

N or d

E st

O uest

N o rd

12

FROM FUZZY DATA TO SYMBOLIC DATA

height weight hair

Paul 1.60 45 yellow

Jef 1.85 80 yellow

Jim 0.65 30 black

Bill 1.95 90 black

height weight hair

small average high

Paul 0.70 0.30 0 45 yellow

Jef 0 0.50 0.50 80 yellow

Jim 0.50 0 0 30 black

Bill 0 0 0.48 90 black

height weight hair

small average high

Paul, Jef [0, 0.70] [0.30, 0.50] [0, 0.50] [45, 80] yellow

Jim, Bill [0, 0.50] 0 [0, 0.48] [30, 90] black

Symbolic Data

Fuzzy Data

0.5

small average high1

1.500 1.80 1.90

0.65 1.60 1.85 1.95

From Numerical to Fuzzy Data

Initial Data

JEF

MAIN OUTPUT OF SYMBOLIC

DATA ANALYSIS ALGORITHMS:

SYMBOLIC DESCRIPTIONS

SYMBOLIC OBJECTS.

SYMBOLIC DESCRIPTIONS

Description AGE SPC

D1 12,20,28 employee,worker

D2 [5, 33] teacher,countryman

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CONCEPTS ARE MODELED BY

SYMBOLIC OBJECTS

WHATS A CONCEPT?

A CONCEPT IS DEFINED BY AN

* INTENT : ITS CHARACTERISTIC

PROPERTIES

* EXTENT:THE SET OF INDIVIDUALS

WHICH SATISFY THESE PROPERTIES

LIKE OUR MIND, SYMBOLIC OBJECTS

MODEL CONCEPTS BY AN INTENT AND A

WAY OF COMPUTING THE EXTENT

SYMBOLIC OBJECT

It’s an animal(w) = 0.99 yes

d

y

dC

w

R

S = (a, R, dC) a(w) = [y(w)RdC]

14

TWO KINDS OF SYMBOLIC OBJECTS

BOOLEAN SYMBOLIC OBJECTS

S = (a, R, d1)

d1= 12, 20 ,28 x employee, worker]

R = (⊆⊆⊆⊆ , ⊆⊆⊆⊆ ),

a(w) = [age(w) ⊆⊆⊆⊆ 12, 20 ,28] ∧∧∧∧ [SPC(w) ⊆⊆⊆⊆employee, worker]

a(w) ∈∈∈∈ TRUE, FALSE.

S = (a, R, d):a(w) = [age(w) R1 (0.2)12, (0.8) [20 ,28]] ∧∧∧∧[SPC(w) R2 (0.4)employee, (0.6)worker]

a(w) ∈∈∈∈ [0,1].First approach: simple or flexible matching

R= (R1, R2 ): r Ri q = ∑∑∑∑j=1 ,k r j q j e (r j- min (r

j, q

j)) .

Second approach:

Probabilistic: if dependencies, copulas,

derivation of the joint distribution,

transforming the joint density in [0,1].

THE MEMBERSHIP

FUNCTION« a » MODAL CASE

15

BOOLEAN CASE:

EXT(s) = W ∈∈∈∈ ΩΩΩΩ / a(W) = TRUE.

MODAL CASE

EXTαααα (S)= EXTENTαααα (a) = W ∈∈∈∈ ΩΩΩΩ / a( W ) ≥≥≥≥ αααα.

EXTENT OF A SYMBOLIC OBJECT S:

REAL WORLD

xx

x

MODELED WORLD

INDIVIDUALS

CONCEPTS

DESCRIPTIONS

SYMBOLIC

OBJECTS

x dw

xx x

x

s = (a, R,dC)

dC

xx

xx

xwΩ

Ext(s/ΩΩΩΩ)T

R

THE LEARNING PROCESS OF SYMBOLIC OBJECTS

Learning symbolic objects modeling concepts by reducing two kinds of errors: the

individuals who are in the extent of the symbolic objects but not in the extent of the

concept, the individuals which are not in the extent of the symbolic object but are in

the extent of the concept.

16

Case 4Case 3Symbolic

Data

Case 2Case 1Classical

Data

Symbolic

Analysis

Classical

Analysis

Output

Input

THE FOUR CASES OF STATISTICAL

OR DATA MINING ANALYSIS.

WHY SYMBOLIC DATA ARE NOT STANDARD DATA?

Comparing standard data versus symbolic data

[80, 95]

Weight

0.7 Eur, 0.3 Afr[1.80, 1.95]Very Good

NationalityHeightQuality of Goal

0.3

Afr

Very Good

Quality of

Goal

95

Weight

Max

80

Weight

Min

0. 71.951.80

EurHeight

Max

Height

Min

Symbolic Data Table

Associated standard data

Consequences: . Initial variables are lost

. Variation are lost

17

1, 2(50%)Public , (50%)Private[210, 290]Toulouse

2, 3(50%)Public , (50%)Private[200, 380]Lyon

1, 3(100%)Public[320, 450]Paris

LevelKindNb of pupilsTown

0115050290210Toulouse

1105050380200Lyon

1010100450320Paris

Level 3Level 2Level 1PrivatePublicMax

Nb of pupils

Min

Nb of pupils

Town

WHY IT IS ENHANCING TO WORK ON SYMBOLIC DATA

THAN ON THEIR DECOMPOSITION IN STANDARD DATA

TABLE?

≥1.8O < 1.80

Height

Very good

goal players

Mean or bad

goal players

LOST INFORMATION BY STANDARD ENCODING

OF SYMBOLIC DATA

Example 1: in decision tree

By standard encoding of symbolic data, the variable size

desapears as it is replaced by the « Size Min » and « Size max »

The symbolic approach allows the use of the variable « size »

itself and not the variables « Size Min » and « Size max »

Explanatory Variable

Very good goal playershave generally more than

1,80m.

Here the Height is not a

minimum height or a maximum height or a

mean, but the value of the

age which discriminate the

very good players from the

others.

18

20 25 30 35

[22 27

]

[26

]33

[27 36

]

Sum of the portion of the

intervals

It is not a minimum or a maximum histogram!

Symbolic Histogram

Sum of the portion of the

intervals

x

x

x

x

x

Classical PCM

Number of

goals

…

Symbolic PCM

Lost of information by using standard coding of symbolic data in

Principal component analysis

By standard coding each concept is represented by a point

By symbolic coding

Each concept is represented by a surface which expresses the variation of the individuals of the extent of

the concept

Each concept can be described by a conjunction of properties in term of the new variables (the factors) .

Very Good

Good

Means

Very weak

Weak

Height, weight…

Number ofgoals

Very GoodGood

Very Weak

WeakMean

Height, weight…

19

AN OVERVIEW ON THE SODAS SOFTWARE

THE SODAS 2 SOFTWARE FROM ASSO

20

THE MAIN STEPS FOR A SYMBOLIC DATA

ANALYSIS IN SODAS

. PUT THE DATA IN A RELATIONAL DATA BASE

(Oracle, Acces, ...)

.DEFINE A CONTEXT BY GIVING

* The Units (Individuals,

Households,...)

* The Classes (Regions, Socio-

economics groups,...)

* The descriptive variables of the units

. BUILD A SYMBOLIC DATA TABLE WHERE

* The units are the preceding classes

* The descriptions of each class is obtained by a

generalization process applied to its members

- Histogram of a symbolic variable

- Dissimilarities between symbolic descriptions

- Clustering of symbolic descriptions

- Principal component Analysis

- Decision Tree

APPLY

SYMBOLIC DATA ANALYSIS TOOLS

- Correlation, Mean, Mean Square

- Graphical visualisation of Symbolic Objects

21

SODAS Software

Chaining

Sds file

Report

GraphGraphs

Menu

Methods

SODAS

Concatenationof summarized data

from several populations

Join two or more sets of SObased on

different underlyingpopulations

household

school

25 SO 25 SO

25 SO

DataBases

Concatenation

22

DISSIMILARITY MEASURES

A straightforward extension of similarity measures for classicaldata matrices with nominal variables.

where µ(Vj) is either the cardinality of the set Vj (if Yj is a nominal variable) or the length of the interval Vj (if Yj is a continuous variable).

Agreement Disagreement TotalAgreement αααα=µµµµ(Aj∩∩∩∩Bj) ββββ=µµµµ(Aj∩∩∩∩c(Bj)) µµµµ(Aj)

Disagreement χχχχ=µµµµ(c(Aj)∩∩∩∩Bj) δδδδ=µµµµ(c(Aj)∩∩∩∩c(Bj)) µµµµ(c(Aj))

Total µµµµ(Bj) µµµµ(c(Bj)) µµµµ(Yi)

Five different similarity measures si, i = 1, ..., 5, are defined:

The corresponding dissimilarities are di = 1 − si.

The di are aggregated on p variables by the generalisedMinkowski metric, thus obtaining:

SO_1

[ ] 5i1 ),(),(1

≤≤= ∑=

q

p

j

qjjij

i BAdwbad

s i Comparison Function Range Propertys1 αααα/(αααα+ ββββ + χχχχ) [0 ,1] m etric

s2 2αααα/(2 αααα+ ββββ+ χχχχ) [0 ,1] sem i m etric

s3 αααα/(αααα+2 ββββ+2 χχχχ) [0 ,1] m etric

s4 ½ [αααα/(αααα+ ββββ )+ αααα/(αααα+ χχχχ)] [0 ,1] sem i m etric

S 5 αααα/[(αααα+ ββββ )(αααα+ χχχχ)]½ [0 ,1] sem i m etric

DE CARVALHO’S DISSIMILARITY

MEASURES

23

Graphical Representation of a dissimilarity

Figure21: Examples of 2D and 3D ZOOM STAR:

each star describes a concept

SOE SoftwareGraphic Representation of the symbolic

description of a concept

24

Pyramid

Each level is a class of concepts modeled by a symbolic description.

PRODUCT2

WEIGHT

*2

4*

3 5* *

*

*4

6

PRODUCT1AGE

COST

P R O D U C T S WEIGHT COST AGE PROFIT

P R O D U C T 1 [2,4] [3,5] [4,6] [0,3]

P R O D U C T 2 [4,5] [3,4] [1,6] [2,7]

P R O D U C T 3 [1,6] [2,7] [5,8] [6,9]

25

x

xxxx

x

Symbolic Principal

Component AnalysisSymbolic correlation

Principal Component Analysis

26

SYMBOLIC DESCRIPTION OF CLASSES

S Y M B. O B J E C T S

S Y M B O L I CD A T A

S Y M B O L I CD A T A

S Y M B. O B J E C T S

H is t o g r a mH i s t o g r a mH i s t o g r a m , B ip l o t S t a r s , G r a p h i c s

D is s im i l a r i t i e s

C l u s t e r i n g D is c r im in a t i o n

D e c i s io nt r e eD e c i s io nt r e eD e c i s i o n t r e e

S Y M B O L I C O B J E C T S

S e le c t i o no f b e s tS y m b. O b j e c t sS e le c t i o no f b e s tS y m b. O b j e c t s

S e le c t i o n o f b e s t

S y m b o l i c. O b j e c t s

N e wS y m bN e wS y m bN e w S y m b o l i c

D a t a T a b le

G r a p h i c s o fS y m bS y m b o l i c D a t a A n a l y s i s

S y m b o l i c O b j e c t s P r o p a g a t i o n

F a c t o r i a lF a c t o r ia l A n a ly s i s F a c t o r ia lR e g r e s s i o n A n a ly s i s

E x p o r t a t i o n t o an e w D a t a b a s e

THE SODAS 2 SOFTWARE FROM ASSO

27

NEW PROBLEMS APPEAR

.QUALITY, ROBUSTNESS RELIABILITY OF

THE APPROXIMATION OF A CONCEPT BY

A SYMBOLIC OBJECT,

.THE SYMBOLIC DESCRIPTION OF A

CLASS,

.THE CONSENSUS BETWEEN SYMBOLIC

DESCRIPTIONS ETC..

MUCH HAS TO BE DONE:

SYMBOLIC

.REGRESSION, FACTORIAL ANAL.

.MULTIDIMENSIONAL SCALING,

.MIXTURE DECOMPOSITION,

.NEURAL NETWORK, KOHONEN MAP

.CONCEPT PROPAGATION between

Databases…...

Some recent advances:

- Mixture decomposition of Distributions of

distributions (by Copulas, Dirichlet and Kraft

stochastic process)

- Stochastic Symbolic Conceptual lattices

using capacity theory

- Symbolic class description

-Symbolic Regression

-NEXT FUTUR

-- Spatial symbolic clustering by pyramids

- Symbolic time series.

- Consensus between different description of

the same set of units

28

AIM ATTAINED

FROM HUDGE DATA BASES

IN AN ECONOMIC WAY

WE ARE ABLE TO: -Extract new knowledge

-Summarize

-Concatenate

-Solve confidentiality

-Explain Correlation

HOW? By working on HIGHER LEVEL UNITS

extending Data Mining to Knowledge Mining.

CONCLUSION

Symbolic Data Analysis is an extension of standard data

analysis therefore

First principle: any Symbolic Data Mining method must

have as a special case method of Data Mining on standard

data.

Second principle : the output must be a symbolic

description or a symbolic object

New problems appear as the quality, robustness and

reliability of the modelling of a concept by a symbolic

object, the symbolic description of a class, the consensus

between symbolic descriptions etc..

Due to the intensive development of the information

technology the great chapters of the standard statistics will

have to be think in these new terms.

29

References

SPRINGER, 2000 :

“Analysis of Symbolic Data”

H.H., Bock, E. Diday, Editors . 450 pages.

JASA (Journal of the American Statistical Association)

“From the Statistic of Data to the Statistic of Knowledge:

Symbolic Data Analysis” Billard, Diday June, 2003 .

Electronic Journal of S. D. A.: ESDA

E. Diday, R. Verde, Y. Lechevallier editors

WILEY 2006: To be published

SYMBOLIC DATA ANALYSIS AND THE SODAS SOFTWARE Diday, Noirhomme (editors)

SYMBOLIC DATA ANALYSIS : conceptual statistics and data mining Billard , Diday

Download SODAS with documentation and examples :

www.ceremade.dauphine.frthen LISE, then SODAS