An Example on Product Positioning

Transcription

1 Cluster Analysis

2 An Example on Product Positioning Caractéristiques de 24 modèles de voiture (Source : L argus de l automobile, 2004) Modèle Cylindrée Puissance Vitesse Poids Largeur Longueur (cm 3 ) (ch) (km/h) (kg) (mm) (mm) Citroën C2. Base Smart Fortwo Coupé Mini Nissan Micra Renault Clio 3.0 V Audi A3.9 TDI Peugeot HDI Peugeot V6 BVA Mercedes Classe C 270 CDI BMW 530d Jaguar S-Type 2.7 V6 Bi-Turbo BMW 745i Mercedes Classe S 400 CDI Citroën C3 Pluriel.6i BMW Z4 2.5i Audi TT.8T Aston Martin Vanquish Bentley Continental GT Ferrari Enzo Renault Scenic.9 dci Volkswagen Touran.9 TDI Land Rover Defender Td Land Rover Discovery Td Nissan X-Trail 2.2 dci

3 Data reduction To neutralize the problem of units, one replace the original datas by the standardized datas : X X p = = X M X x s p s p x p de mean 0 and standard-deviation. 3

4 The data standardized (Zscore) Case Summaries Total Std. Deviation Zscore: Zscore: Zscore: Zscore: Zscore: Zscore: MODÈLE Cylindrée Puissance Vitesse Poids Largeur Longueur Citroën C2. Base Smart Fortwo Coupé Mini Nissan Micra Renault Clio 3.0 V Audi A3.9 TDI Peugeot HDI Peugeot V6 BVA Mercedes Classe C 270 CDI BMW 530d Jaguar S-Type 2.7 V6 Bi-Turbo BMW 745i Mercedes Classe S 400 CDI Citroën C3 Pluriel.6i BMW Z4 2.5i Audi TT.8T Aston Martin Vanquish Bentley Continental GT Ferrari Enzo Renault Scenic.9 dci Volkswagen Touran.9 TDI Land Rover Defender Td Land Rover Discovery Td Nissan X-Trail 2.2 dci

5 9. Building a typology of the statistical units Searching for homogeneous groups of individuals (clusters) in the population : - Two individuals belonging to the same group are somehow close to each other (similar behaviors); - Two individuals belonging to different groups are somehow far from each other (different behaviors); Build a partition of the population into homogeneous clusters (low within-variability) which are different one from the other (high between-variability). 5

6 Dendrogramme groups Choosing the cutting level x x x Definition of the clusters 6

7 Hierarchical Classification (Ward Criterion) X X p g 2 g X 2 g 3 Ward Distance : D 2 (G i, G j ) = n i = number of cases in cluster G i n n n i i + j n j d 2 ( g, g ) i j 7

8 Distance Matrix between 24 cars Proximity Matrix Case :Citroën C2. Base 2:Smart Fortwo Coupé 3:Mini :Nissan Micra :Land Rover Discovery 24:Nissan X-Trail 2.2 d This is a dissimilarity matrix Squared Euclidean Distance 23:Land :Citroën C2 2:Smart 4:Nissan Rover 24:Nissan. Base Fortwo Coupé 3:Mini.6 70 Micra Discovery X-Trail 2.2 d p 2 2 k l = jk jl j= d (x, x ) (x x ) D Ward (Citroën C2, Nissan Micra) =.026 =.03 ( + ) 8

9 H I E R A R C H I C A L C L U S T E R A N A L Y S I S Dendrogram using Ward Method Rescaled Distance Cluster Combine C A S E Label Num Citroën C2. Base Nissan Micra Peugeot HDI 7 Citroën C3 Pluriel 4 BMW Z4 2.5i 5 Audi TT.8T 80 6 Renault Clio 3.0 V6 5 Mini Volkswagen Touran. 2 Nissan X-Trail 2.2 d 24 Audi A3.9 TDI 6 Renault Scenic.9 d 20 Land Rover Defender 22 Smart Fortwo Coupé 2 Peugeot V6 B 8 BMW 530d 0 Jaguar S-Type 2.7 V6 Mercedes Classe C 27 9 BMW 745i 2 Mercedes Classe S 40 3 Land Rover Discovery 23 Aston Martin Vanquis 7 Bentley Continental 8 Ferrari Enzo 9 9

10 Clusters Interpretation Report Ward Method Total N N N N N N Cylindrée Puissance Vitesse Poids Largeur Longueur

11 Décomposition de la somme des carrés totale X X p g g 2 g g 3 X 2 n K K i = k k + i k i= k= k= i G d (x,g) n d (g,g) d (x,g ) k Total sum of squares = (n-)p Between group = sum of squares + Within group sum of squares

12 Stage Coefficient : Somme des carrés intra-classes de la typologie en K classes Distance de Ward(,4) Cluster Combined Agglomeration Schedule Cluster Cluster 2 Coefficients Cluster Cluster 2 Next Stage Groupe contenant Stage Cluster First Appears Résultats SPSS : Somme des carrés intraclasses Part de somme des carrés totale expliquée par la typologie en K classes : (38 - Coeff[n-K])/38 Part de somme des carrés totale expliquée par la typologie en 2 classes : ( )/38 = Somme des carrés intra-classes pour la typologie en K=2 classes Somme des carrés totale = p(n-) 2

13 Autre méthode : k-means clustering Choose a few "seeds," individuals who are quite different from one another (the "seeds" can be provided by the analyst or chosen by the program) 2 Go over the file, allocating each individual to the closest seed. 3 Then, compute the mean of each group. This constitutes the new seed for the group. If all the new seeds are close to the previous ones, stop. Otherwise, go to 2. 3