SensoMetrics v8 CM

Agrocampus Ouest

An example of sorting task

J.1 J.2 J.3 J.4 J.5Angel exotic;sweet;pleasant flowery;soft fruity;strong vanilla;spicy;spirit of islands to eat;sweetAromatics Elixir strong;alcoholized strong;man heady rough;strong oldChanel5 soap;clean G4 heady toilet soapCinema flowery;lilac flowery;artificial;grass fruity;middle sweet softy; y; ;g y;Coco Mademoiselle soap;clean flowery;soft fruity;middle softness;flowery softJadoreEP soap;clean flowery;soft sweet;light softness;flowery floweryJadoreET soap;clean flowery;artificial;grass sweet;light softness;flowery floweryLinstant G3 flowery;soft fruity;strong sweet oldLolita Lempicka exotic;sweet;pleasant flowery;soft fruity;middle vanilla;spicy;spirit of islands to eat;sweetPleasures G3 strong;man fruity;strong sweet flowery

12/07/2012 Sensometrics 2012 2

Pleasures G3 strong;man fruity;strong sweet floweryPure Poison flowery;lilac flowery;soft tangy;deodorant softness;flowery softShalimar strong;alcoholized flowery;artificial;grass strong;lavander mustiness;aggressive old

An example of sorting taskConfidence ellipses for the mean points

2.0

p p

Angel

1.0

1.5

g

Lolita Lempicka

0.5

1

Dim

2 (1

3.83

%)

Aromatics ElixirCinema

-0.5

0.0

D

Chanel5Coco MademoiselleJadoreEP

Linstant

Pure Poison

Shalimar

-1.0

Coco Mademoiselle

JadoreETPleasures


-1 0 1 2

Dim 1 (16.99%)

Bootstrap technique

Real jury Virtual juryj yJ1 J2 J3 … J96 J97 J98

P1P2

J1 J1 J19 … J98P1P2P3P3

…P10P11

P3…P10P11P11

P12P11P12

=> Random re-sampling with

l t


replacement

Real jury Virtual jury

Bootstrap techniqueReal jury

J1 J2 J3 … J96 J97 J98P1P2

Virtual jury…

P1P2

Virtual jury…

P1Virtual jury

…Virtual juryVi t l j

P3…P10

P3…P10

P2P3…

P1P2P3

…P1P2P3

Virtual jury…

P1P2

Virtual jury…

P1P11P12

P11P12P10P11P12

…P10P11P12

P3…P10P11

P2P3…P10

P2P3…P12P11

P12P11P12P10P11P12

• 2 ways to use bootstrapped virtual juries :By projection (partial bootstrap)B t t ti (t t l b t t )


By procrustean rotation (total bootstrap)

Partial bootstrap1. Principal Component methodon the data of the real jury

2. Projection of the judges of a virtual jury

3a Calculation of the virtual jury’s3a. Calculation of the virtual jury’sbarycenter

3b. Calculation of the barycentersy

4. Ellipse including 95% of the points


Total bootstrap

Virtual jury 1 Virtual jury 2 Virtual jury 3 Virtual jury 200

2. Principal Component method on each virtual jury

Real jury

Virtual jury 1 Virtual jury 2 Virtual jury 3 j y

1. Principal Component method on the data of

the real jury

Expansion/Shrinkage

Translation 3. ProcrusteanTranslation

Rotation

3. Procrusteanrotation


4. Confidence ellipse including 95 % of the points

Example of a sorting task dataset

Comparison of partial and total bootstrap

Partial bootstrap Total bootstrap

3

Confidence ellipses for sorting task

2.0

Confidence ellipses for the mean points

Angel

12

.83%

)

Angel

Lolita Lempicka

Cinema Aromatics ElixirLi t t5

1.0

1.5

3.83

%)

Angel

Lolita Lempicka

-10

Dim

2 (1

3

Chanel5Shalimar

Coco MademoiselleJadoreEP

JadoreET

Pleasures

Pure Poison

Linstant

0.5

0.0

0.5

Dim

2 (1

3

Aromatics Elixir

Chanel5

Cinema

JadoreEP

Linstant

Pure Poison

Shalimar

-3 -2 -1 0 1 2 3 4

-3-2

-1 0 1 2

-1.0

-0

Coco MademoiselleJadoreEP

JadoreET Pleasures


Dim 1 (16.99%)Dim 1 (16.99%)

Example of a RANDOM sorting task dataset



2


2


1

.02%

)

10

12 12

.02%

)

10

12

0

Dim

2 (1

5.

1

234

5

6

8

9

11

-10

Dim

2 (1

5.

1

11

234

5

6

7

8

9

1 0 1 2

-1

7

2 1 0 1 2 3

-210 judges3 groups/judge

12 products


-1 0 1 2

Dim 1 (22.8%)

-2 -1 0 1 2 3

Dim 1 (22.8%)

pRandom data

Example of a RANDOM sorting task dataset



1.0


7 1.5


0.5

.53%

)

1

2

9 0.5

1.0

.53%

)

1

2

7

9

0.0

Dim

2 (1

0. 1

3

4

5

8

10

11 -0.5

0.0

Dim

2 (1

0.

1

10

11

12

3

4

5

6

8

1 0 0 5 0 0 0 5 1 0

-0.5 3

6

12

2 1 0 1 2

-1.5

-1.0

300 judges3 groups/judge

12 products

12/07/2012 Sensometrics 2012 10

-1.0 -0.5 0.0 0.5 1.0

Dim 1 (10.88%)

-2 -1 0 1 2

Dim 1 (10.88%)

pRandom data

12/07/2012 Sensometrics 2012 11

I R d lit ti d t tConfidence ellipses for the mean pointsConfidence ellipses for the mean points

I. Random qualitative dataset

0.0

0.5

1.0

32%

) 1

2

3

6

7

9 11

12

12

6.56

%)

2

35

6

78

-1.0

-0.5D

im 2

(12.

3

4

5

8

10

-2-1

0

Dim

2 (2

6

1

4

9

10

11

12 30 judges3 groups/judge12 productsRandom dataset

3 judges3 groups/judge12 productsRandom dataset

Confidence ellipses for the mean pointsConfidence ellipses for the mean points

-1.5 -1.0 -0.5 0.0 0.5 1.0

-1.5

Dim 1 (13.46%)

-3 -2 -1 0 1 2

Dim 1 (35.62%)

When the number of judges increases► The dimensionality increases

Th lli b ll

0.5

) 3

4

8 10

0.5

%) 5

6

8

9

The ellipses become smaller

-0.5

0.0

Dim

2 (9

.501

%)

1

2

3

5 7

9

12

-0.5

0.0

Dim

2 (1

0.14

%

12

3

4

7

10

11 300 judges3 groups/judge

3000 judges3 groups/judge

12/07/2012 Sensometrics 2012 12-0.5 0.0 0.5 1.0

-

Dim 1 (9.582%)

6 11

-1.0 -0.5 0.0 0.5 1.0

Dim 1 (10.85%)

312

g j g12 productsRandom dataset

g p j g12 productsRandom dataset

II Q tit ti d t tAn example of QDA (RANDOM quantitative dataset)

II. Quantitative dataset


1020

2

11

4

2

0

Dim

2 (1

0.35

%) 1

3 5

6

8

9

02

Dim

2 (1

8.43

%)

1

3

4

5

7

9

11

12

-10

D

4

7

10

12

-2

D 4

6 8

9

10

-20 -10 0 10 20

-20

Dim 1 (10 7%)

7

-4 -2 0 2 4 6

-4

Dim 1 (25 5%)

30 judges900 desc12 products

30 judges10 desc12 products

12/07/2012 Sensometrics 2012 13

Dim 1 (10.7%)Dim 1 (25.5%)

II Q tit ti d t tA simple RANDOM dataset

II. Quantitative dataset

ndesc=3 ndesc=30000

PCA on the average tableProjection of individual judgements in illustrativeProjection of the average points of the virtual juries in illustrative

12/07/2012 Sensometrics 2012 14

PCA on the average table=> A point represents a product as seen by the jury

Projection of individual judgements in illustrative=> A point is a product as seen by a judgeProjection of the average points of the virtual juries in illustrative=> A point is a product as seen by a virtual jury

12/07/2012 Sensometrics 2012 15

Th f l tl d d tThe case of completly random data


RANDOM data without structure


20

05

6.16

%)

112

2

3 4

568

9

10

10.8

2%)

10

12

-5

Dim

2 (1

6

10

11

7

-10

0

Dim

2 (1

1 11

2 3

4

5

67

8

9

-10

30 judges12 products30 descriptors -2

0-

30 judges12 products300 descriptors

12/07/2012 Sensometrics 2012 16

-10 -5 0 5 10

Dim 1 (18.96%)

-20 -10 0 10 20 30

Dim 1 (11.49%)

D t i l ti dData simulation procedure

« Pure » configuration

11 ndes

c1

1ndesc

11

ndesc

configurationAverage table

np

« Pure » nj times duplication

« Real » datasetNoise ~ N(0, sigma)« Pure »

configurationAverage table


Average table

nj*npnj*np


Average tablenj*np

12/07/2012 Sensometrics 2012 17

j pnj npnj*np

D th lli i l d th l t t f Do the ellipses include the « real » structure of the data ?

Sd Frequence

ataset 0.1 92,09%

0.5 91,5%1 91,67%

Count the number of times that a point is included in an ellipse, given its coordinates on the factorial plan


ructured

da 1 91,67%1.5 91,09%2 89,5%3 91,75%4 91,92%2

46

1

11

3

57 9

Str 4 91,92%

7 94,92%

nj 12 30 90 210

-20

2

Dim

2 (2

3.08

%)

2

4

6

α=

5%

12 88,50 88,08 89,17 92,42

30 91,42 90,00 91,00 93,92

200 94,08 94,33 95,33 93,92

-6-4 10

128

200 94,08 94,33 95,33 93,92

The proportion tends to 95% when the number of judges increases(asymptotic behavior of bootstrap techniques)

-6 -4 -2 0 2 4 6 8

Dim 1 (45.36%)

12/07/2012 Sensometrics 2012 18

(asymptotic behavior of bootstrap techniques)

C l i• One parameter must be chosen:

Conclusion• One parameter must be chosen:

• Number of dimensions for the procrustean rotations=> n = 2 in many sensometry applications

• Dimensionality problem highlighted :Confidence ellipses are essential (but may be built according to total bootstrap)

• Total bootstrap can be applied to all holistic approaches:• Napping• Sorting taskSorting task• Hierarchical sorting• Free Choice Profiling

A il bl i t th R k S Mi R th h th b t f ti• Available into the R package SensoMineR through the boot function

12/07/2012 Sensometrics 2012 19

12/07/2012 Sensometrics 2012 20

L’évolution de la taille des ellipses en fonction du L évolution de la taille des ellipses en fonction du nombre de dimensions utilisées pour les rotations

procustéennes 30 juges

12 produitsSans structure

procustéennes

12/07/2012 Sensometrics 2012 21

ncp=7ncp=2 ncp=11

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SensoMetrics v8 CM

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