Categorization or free sorting task in sensory analysis

Transcription

1 Categorization or free sorting task in sensory analysis Marine Cadoret, Sébastien Lê, Jérôme Pagès Applied Mathematics Department Agrocampus Ouest, Rennes (France) 15 march 2012

2 Outline 1 Application in sensory analysis 2 Analysis of sorting data: a multidimensional approach 2/ 16

3 Categorization (or free sorting) task Used in sensory analysis since the end of the 80 s Holistic approach (global) Each judge is asked to make group of objects according to their resemblances: 2 objects are together if he/she perceives them as similar 2 objects are in 2 different groups if he/she perceives them as different No criteria are imposed to judges Simultaneous evaluation The number of groups have to be between 2 and I 1 (with I the number of objects) A verbalization task can be asked to describe the groups provided ( qualified categorization) 3/ 16

4 Example of products Data 98 judges consumers perfumes for carried women: out a qualified categorization on 12 luxury perfumes: Angel Lolita Lempicka L'instant Cinéma J'adore (ET) J'adore (EP) Shalimar Aromatics Coco Chanel n 5 Elixir Mademoiselle Pure Poison Pleasures Products are presented anonymously 3 4/ 16

5 Example of products 98 judges - 12 perfumes for women: Products are presented anonymously 4/ 16

6 Example of categorization 5/ 16

7 Example of categorization sweet, vanilla heady flower, green 5/ 16

8 Elements of interest 1 Arom. El. Chanel n 5 Shalimar Coco Melle J adore EP i J adore ET L instant Pleasures Pure Pois. Cinéma Loli. Lemp. I Angel Objectives: Representation (map) of the products 6/ 16

9 Elements of interest Judge 1 Judge 2... Judge j... Judge J 1 Arom. El. G1 G2 G5 G3 Chanel n 5 G1 G4 G5 G3 Shalimar G1 G1 G4 G4 Coco Melle G2 G1 G2 G2 J adore EP G3 G1 G1 G1 i J adore ET G2 G1 G1 G2 L instant G2 G1 G2 G1 Pleasures G2 G1 G1 G1 Pure Pois. G4 G2 G2 G2 Cinéma G3 G3 G3 G2 Loli. Lemp. G2 G3 G3 G2 I Angel G3 G5 G3 G1 Objectives: Representation (map) of the products 6/ 16

10 Elements of interest Judge 1 Judge 2... Judge j... Judge J 1 Arom. El. G1 G2 G5 G3 Chanel n 5 G1 G4 G5 G3 Shalimar G1 G1 G4 G4 Coco Melle G2 G1 G2 G2 J adore EP G3 G1 G1 G1 i J adore ET G2 G1 G1 G2 L instant G2 G1 G2 G1 Pleasures G2 G1 G1 G1 Pure Pois. G4 G2 G2 G2 Cinéma G3 G3 G3 G2 Loli. Lemp. G2 G3 G3 G2 I Angel G3 G5 G3 G1 Objectives: Representation (map) of the products 6/ 16

11 Elements of interest Judge 1 Judge 2... Judge j... Judge J 1 Arom. El. heady floral, green G5 strong, acid Chanel n 5 heady G4 G5 strong, acid Shalimar heady soft G4 old Coco Melle fresh soft G2 sweet J adore EP vanilla soft G1 floral i J adore ET fresh soft G1 sweet L instant fresh soft G2 floral Pleasures fresh soft G1 floral Pure Pois. G4 floral, green G2 sweet Cinéma vanilla G3 G3 sweet Loli. Lemp. fresh G3 G3 sweet I Angel vanilla bitter G3 floral Objectives: Representation (map) of the products Representation (map) of the words 6/ 16

12 Elements of interest Judge 1 Judge 2... Judge j... Judge J 1 Arom. El. heady floral, green G5 strong, acid Chanel n 5 heady G4 G5 strong, acid Shalimar heady soft G4 old Coco Melle fresh soft G2 sweet J adore EP vanilla soft G1 floral i J adore ET fresh soft G1 sweet L instant fresh soft G2 floral Pleasures fresh soft G1 floral Pure Pois. G4 floral, green G2 sweet Cinéma vanilla G3 G3 sweet Loli. Lemp. fresh G3 G3 sweet I Angel vanilla bitter G3 floral Objectives: Representation (map) of the products Representation (map) of the words Representation (map) of the judges 6/ 16

13 Outline 1 Application in sensory analysis 2 Analysis of sorting data: a multidimensional approach 7/ 16

14 The dataset Judge 1 Judge 2... Judge j... Judge J 1 Arom. El. heady floral, green G5 strong, acid Chanel n 5 heady G4 G5 strong, acid Shalimar heady soft G4 old Coco Melle fresh soft G2 sweet J adore EP vanilla soft G1 floral i J adore ET fresh soft G1 sweet L instant fresh soft G2 floral Pleasures fresh soft G1 floral Pure Pois. G4 floral, green G2 sweet Cinéma vanilla G3 G3 sweet Loli. Lemp. fresh G3 G3 sweet I Angel vanilla bitter G3 floral One judge = One categorical variable 8/ 16

15 The dataset Judge 1 Judge 2... Judge j... Judge J 1 Arom. El. heady floral, green G5 strong, acid Chanel n 5 heady G4 G5 strong, acid Shalimar heady soft G4 old Coco Melle fresh soft G2 sweet J adore EP vanilla soft G1 floral i J adore ET fresh soft G1 sweet L instant fresh soft G2 floral Pleasures fresh soft G1 floral Pure Pois. G4 floral, green G2 sweet Cinéma vanilla G3 G3 sweet Loli. Lemp. fresh G3 G3 sweet I Angel vanilla bitter G3 floral One judge = One categorical variable One label = The sequence of words used to describe the group 8/ 16

16 The dataset Judge 1 Judge 2... Judge j... Judge J 1 Arom. El. heady floral, green G5 strong, acid Chanel n 5 heady G4 G5 strong, acid Shalimar heady soft G4 old Coco Melle fresh soft G2 sweet J adore EP vanilla soft G1 floral i J adore ET fresh soft G1 sweet L instant fresh soft G2 floral Pleasures fresh soft G1 floral Pure Pois. G4 floral, green G2 sweet Cinéma vanilla G3 G3 sweet Loli. Lemp. fresh G3 G3 sweet I Angel vanilla bitter G3 floral One judge = One categorical variable One label = The sequence of words used to describe the group Analyzed using Multiple Correspondence Analysis (MCA; Lebart et al., 1977) 8/ 16

17 Disjunctive data table The data are taken into account through the disjunctive data table: a judge is represented by his/her groups 1 Judge 1 Judge j Judge J 1 k K i x ik I I 1 I k I K x ik = 1 if the object i belongs to group k (of judge j) and 0 otherwise I k : number of objects belonging to group k (of judge j) 9/ 16

18 Representation of the objects in MCA Distance between 2 objects i and l: d 2 (i, l) = 1 J k I I k (x ik x lk ) 2 2 objects are closer than they were put in the same group by a great number of judges 2 objects are all the more distant than they were put in different groups by a great number of judges Inversely proportional role of I k (group size): a product isolated by a great number of judges will be highlighted on the first dimension 10/ 16

19 Representation of the perfumes MCA factor map Angel Dim 2 (13.64%) Lolita Lempicka Cinéma L'instant Coco Mademoiselle Pure Poison J'adore (ET) Pleasures J'adore (EP) Aromatics Elixir Chanel n 5 Shalimar Dim 1 (17.8%) 11/ 16

20 Representation of the perfumes MCA factor map Angel Dim 2 (13.64%) Lolita Lempicka Cinéma L'instant Coco Mademoiselle Pure Poison J'adore (ET) Pleasures J'adore (EP) Aromatics Elixir Chanel n 5 Shalimar Arom. El. Shalimar J adore (EP) J adore (ET) Arom. El Shalimar J adore (EP) J adore (ET) Alone Dim 1 (17.8%) 11/ 16

21 Representation of the words in MCA Individual representation of the words (non-aggregated data): words of each judge will appear on the map Representation of the words themselves that makes sense: Distance between two words k and h: d 2 (k, h) = i I ( xik I k x ih I h ) 2 Two words will be closer than they were associated to the same products Representation of the words being interpreted with the one of the products: Coordinate of the word k on the axis of rank s: G s (k) = 1 λs I i=1 x ik I k F s (i) Double barycentric property: a word will be on the side of the products it were associated and a product will be on the side of the words it were associated 12/ 16

22 Representation of the words and of the perfumes aseptisé neutre discret estival poivré caractère barbe à papa épicé musc camphre corsé fort épicé chocolat nourriture épicé soirée sucré faible fruité sucré doux propreté fraîcheur savon fruité muguet fruité discret fruité discret (13.64%) Dim 2 pollen naturel sucré nature muguet léger caractère fort enivrant fleuri fin suave acidulé désodorisant chaud sucré fruité chocolat vanille sucré chaud chaud vanillé épicé fort intense MCA factor map odeur prenante fort attaquant fête sucré miel fort fruité fort fort particulier Dim 1 (17.8%) femme d âge mûr fleuri suffocant léger masculin poivré fort sucré épicé épicé homme eau de Cologne entêtant attaque toilettes savon savon fort prononcé parfum à WC WC médicament plante savon fort savon toilettes fort pain d'épices amande entêtant fruité pourri printemps agressif chimique piquant savon fort fort fleuri toilettes ancien eau de Cologne fort mauvais chimique non-naturel artificiel capiteux grand-mère pourri décomposition fleuri désodorisant désodorisant fort nauséabond oriental métallique médicament épicé agrume frais fleuri doux citronnelle sucré anti-moustique eau de Cologne hôpital oriental cire particulier fort médicament citronné renfermé agressif fort lavande eau de Cologne 13/ 16

23 Representation of the words and of the perfumes aseptisé neutre discret estival poivré caractère barbe à papa épicé musc camphre corsé fort épicé chocolat nourriture épicé soirée sucré faible fruité sucré doux propreté fraîcheur savon fruité muguet fruité discret fruité discret Dim 2 (13.64%) pollen naturel sucré nature muguet chaud sucré fruité chocolat vanille sucré chaud chaud vanillé épicé fort intense Cinéma J'adore (ET) J'adore (EP) Pleasures léger caractère fort enivrant fleuri fin suave acidulé désodorisant Lolita Lempicka L'instant Coco Mademoiselle MCA factor map Angel Pure Poison odeur prenante fête sucré miel fort fruité fort fort particulier Dim 1 (17.8%) fort attaquant Chanel n 5 Shalimar Aromatics Elixir femme d âge mûr fleuri suffocant léger masculin poivré fort sucré épicé épicé homme eau de Cologne entêtant attaque toilettes savon savon fort prononcé parfum à WC WC médicament plante savon fort savon toilettes fort pain d'épices amande entêtant fruité pourri printemps agressif chimique piquant savon fort fort fleuri toilettes ancien eau de Cologne fort mauvais chimique non-naturel artificiel capiteux grand-mère pourri décomposition fleuri désodorisant désodorisant fort nauséabond oriental métallique médicament épicé agrume frais fleuri doux citronnelle sucré anti-moustique eau de Cologne hôpital oriental cire particulier fort médicament citronné renfermé agressif fort lavande eau de Cologne 13/ 16

24 Representation of the judges in MCA MCA Looking for dimension z s such as: max j η2 (z s, j) Coordinate of judge j on axis of rank s: η 2 (F s, j) (squared correlation ratio) Representation linked to the two others: a judge will have a coordinate higher on the axis than his/her categorization corresponds to the oppositions on the axis 14/ 16

25 Representation of the judges Groups representation Dim 2 (13.64%) Dim 1 (17.8%) 15/ 16

26 Representation of the judges Groups representation Dim 2 (13.64%) Judges Aromatics Elixir Chanel n Shalimar Coco Mademoiselle J adore (EP) J adore (ET) L instant Pleasures Pure Poison Cinéma Lolita Lempicka Angel Dim 1 (17.8%) 15/ 16

27 Representation of the judges Groups representation Dim 2 (13.64%) Judges Aromatics Elixir Chanel n Shalimar Coco Mademoiselle J adore (EP) J adore (ET) L instant Pleasures Pure Poison Cinéma Lolita Lempicka Angel Dim 1 (17.8%) 15/ 16

28 Conclusion Different representations (products, words, judges) related to each other The global approach provides also: Basic results (Number of groups used, number of words used to describe the groups, co occurrences matrix, etc.) Confidence ellipses around the position of products Available in the free software and the packages using: Directly and the fast function The Graphical User Interface Rcommander in RExcel Excel macro Information: 16/ 16