Etude italian wine

knitr::opts_chunk$set(cache=FALSE)
knitr::opts_chunk$set(fig.width=10) # for rstudio
#knitr::opts_chunk$set(fig.width=6, fig.height=6) # for rstudio
#knitr::opts_chunk$set(fig.width=14, fig.height=14) # for html
options(width = 100)

Libs

library(tidyverse)

## ── Attaching packages ─────────────────────────────────────────────────────────── tidyverse 1.3.0 ──

## ✓ ggplot2 3.3.3     ✓ purrr   0.3.4
## ✓ tibble  3.0.5     ✓ dplyr   1.0.3
## ✓ tidyr   1.1.2     ✓ stringr 1.4.0
## ✓ readr   1.4.0     ✓ forcats 0.5.0

## ── Conflicts ────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

library(magrittr) # syntaxe, notamment affectation %<>%

## 
## Attaching package: 'magrittr'

## The following object is masked from 'package:purrr':
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##     extract

library(GGally)   # plot pairs better than default plot

## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2

library(plotly)   # plots interactifs

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
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read_csv

Lecture des données.

read_csv, read_tsv, read_delim, …

read_csv('wine.data.txt')

## 
## ── Column specification ────────────────────────────────────────────────────────────────────────────
## cols(
##   cultivar = col_double(),
##   alcohol = col_double(),
##   `malic-acid` = col_double(),
##   ash = col_double(),
##   `alcalinity-of-ash` = col_double(),
##   magnesium = col_double(),
##   `total-phenols` = col_double(),
##   flavonoids = col_double(),
##   `nonflavonoid-phenols` = col_double(),
##   proanthocyanins = col_double(),
##   `color-intensity` = col_double(),
##   hue = col_double(),
##   `od280-od315-of-diluted-wines` = col_double(),
##   proline = col_double()
## )

## # A tibble: 178 x 14
##    cultivar alcohol `malic-acid`   ash `alcalinity-of-… magnesium `total-phenols` flavonoids
##       <dbl>   <dbl>        <dbl> <dbl>            <dbl>     <dbl>           <dbl>      <dbl>
##  1        1    14.2         1.71  2.43             15.6       127            2.8        3.06
##  2        1    13.2         1.78  2.14             11.2       100            2.65       2.76
##  3        1    13.2         2.36  2.67             18.6       101            2.8        3.24
##  4        1    14.4         1.95  2.5              16.8       113            3.85       3.49
##  5        1    13.2         2.59  2.87             21         118            2.8        2.69
##  6        1    14.2         1.76  2.45             15.2       112            3.27       3.39
##  7        1    14.4         1.87  2.45             14.6        96            2.5        2.52
##  8        1    14.1         2.15  2.61             17.6       121            2.6        2.51
##  9        1    14.8         1.64  2.17             14          97            2.8        2.98
## 10        1    13.9         1.35  2.27             16          98            2.98       3.15
## # … with 168 more rows, and 6 more variables: `nonflavonoid-phenols` <dbl>, proanthocyanins <dbl>,
## #   `color-intensity` <dbl>, hue <dbl>, `od280-od315-of-diluted-wines` <dbl>, proline <dbl>

La 1ère colonne est interpétée comme un nombre (dbl) et non un facteur (fct) car constituée de 1, 2 ou 3 ; les 3 classes possibles.

Lecture en spécifiant les types des colonnes

tb = read_csv('wine.data.txt', col_types="fddddddddddddd")
tb

## # A tibble: 178 x 14
##    cultivar alcohol `malic-acid`   ash `alcalinity-of-… magnesium `total-phenols` flavonoids
##    <fct>      <dbl>        <dbl> <dbl>            <dbl>     <dbl>           <dbl>      <dbl>
##  1 1           14.2         1.71  2.43             15.6       127            2.8        3.06
##  2 1           13.2         1.78  2.14             11.2       100            2.65       2.76
##  3 1           13.2         2.36  2.67             18.6       101            2.8        3.24
##  4 1           14.4         1.95  2.5              16.8       113            3.85       3.49
##  5 1           13.2         2.59  2.87             21         118            2.8        2.69
##  6 1           14.2         1.76  2.45             15.2       112            3.27       3.39
##  7 1           14.4         1.87  2.45             14.6        96            2.5        2.52
##  8 1           14.1         2.15  2.61             17.6       121            2.6        2.51
##  9 1           14.8         1.64  2.17             14          97            2.8        2.98
## 10 1           13.9         1.35  2.27             16          98            2.98       3.15
## # … with 168 more rows, and 6 more variables: `nonflavonoid-phenols` <dbl>, proanthocyanins <dbl>,
## #   `color-intensity` <dbl>, hue <dbl>, `od280-od315-of-diluted-wines` <dbl>, proline <dbl>

Contenu

tb %>% summary

##  cultivar    alcohol        malic-acid         ash        alcalinity-of-ash   magnesium     
##  1:59     Min.   :11.03   Min.   :0.740   Min.   :1.360   Min.   :10.60     Min.   : 70.00  
##  2:71     1st Qu.:12.36   1st Qu.:1.603   1st Qu.:2.210   1st Qu.:17.20     1st Qu.: 88.00  
##  3:48     Median :13.05   Median :1.865   Median :2.360   Median :19.50     Median : 98.00  
##           Mean   :13.00   Mean   :2.336   Mean   :2.367   Mean   :19.49     Mean   : 99.74  
##           3rd Qu.:13.68   3rd Qu.:3.083   3rd Qu.:2.558   3rd Qu.:21.50     3rd Qu.:107.00  
##           Max.   :14.83   Max.   :5.800   Max.   :3.230   Max.   :30.00     Max.   :162.00  
##  total-phenols     flavonoids    nonflavonoid-phenols proanthocyanins color-intensity 
##  Min.   :0.980   Min.   :0.340   Min.   :0.1300       Min.   :0.410   Min.   : 1.280  
##  1st Qu.:1.742   1st Qu.:1.205   1st Qu.:0.2700       1st Qu.:1.250   1st Qu.: 3.220  
##  Median :2.355   Median :2.135   Median :0.3400       Median :1.555   Median : 4.690  
##  Mean   :2.295   Mean   :2.029   Mean   :0.3619       Mean   :1.591   Mean   : 5.058  
##  3rd Qu.:2.800   3rd Qu.:2.875   3rd Qu.:0.4375       3rd Qu.:1.950   3rd Qu.: 6.200  
##  Max.   :3.880   Max.   :5.080   Max.   :0.6600       Max.   :3.580   Max.   :13.000  
##       hue         od280-od315-of-diluted-wines    proline      
##  Min.   :0.4800   Min.   :1.270                Min.   : 278.0  
##  1st Qu.:0.7825   1st Qu.:1.938                1st Qu.: 500.5  
##  Median :0.9650   Median :2.780                Median : 673.5  
##  Mean   :0.9574   Mean   :2.612                Mean   : 746.9  
##  3rd Qu.:1.1200   3rd Qu.:3.170                3rd Qu.: 985.0  
##  Max.   :1.7100   Max.   :4.000                Max.   :1680.0

Renommage des classes en 1: Chianti (C), 2: Montepulciano (M), 3: Valpolicella (V), exemple :

tb$cultivar

##   [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
##  [48] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
##  [95] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3
## [142] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## Levels: 1 2 3

as.factor(c('C','M','V')[ tb$cultivar ]) 

##   [1] C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C
##  [48] C C C C C C C C C C C C M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M
##  [95] M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M V V V V V V V V V V V
## [142] V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V
## Levels: C M V

Modification du tibble : fonction mutate

tb %>% mutate(class=as.factor( c('C','M','V'))[ cultivar ] )

## # A tibble: 178 x 15
##    cultivar alcohol `malic-acid`   ash `alcalinity-of-… magnesium `total-phenols` flavonoids
##    <fct>      <dbl>        <dbl> <dbl>            <dbl>     <dbl>           <dbl>      <dbl>
##  1 1           14.2         1.71  2.43             15.6       127            2.8        3.06
##  2 1           13.2         1.78  2.14             11.2       100            2.65       2.76
##  3 1           13.2         2.36  2.67             18.6       101            2.8        3.24
##  4 1           14.4         1.95  2.5              16.8       113            3.85       3.49
##  5 1           13.2         2.59  2.87             21         118            2.8        2.69
##  6 1           14.2         1.76  2.45             15.2       112            3.27       3.39
##  7 1           14.4         1.87  2.45             14.6        96            2.5        2.52
##  8 1           14.1         2.15  2.61             17.6       121            2.6        2.51
##  9 1           14.8         1.64  2.17             14          97            2.8        2.98
## 10 1           13.9         1.35  2.27             16          98            2.98       3.15
## # … with 168 more rows, and 7 more variables: `nonflavonoid-phenols` <dbl>, proanthocyanins <dbl>,
## #   `color-intensity` <dbl>, hue <dbl>, `od280-od315-of-diluted-wines` <dbl>, proline <dbl>,
## #   class <fct>

Ceci ajoute une dernière colonne “class” à partir de la valeur de cultivar de chaque ligne.

Pour remplacer la valeur de cultivar par cette classe, on donne le même nom de colonne.

tb %<>%  mutate(cultivar=as.factor( c('C','M','V'))[ cultivar ] )
tb

## # A tibble: 178 x 14
##    cultivar alcohol `malic-acid`   ash `alcalinity-of-… magnesium `total-phenols` flavonoids
##    <fct>      <dbl>        <dbl> <dbl>            <dbl>     <dbl>           <dbl>      <dbl>
##  1 C           14.2         1.71  2.43             15.6       127            2.8        3.06
##  2 C           13.2         1.78  2.14             11.2       100            2.65       2.76
##  3 C           13.2         2.36  2.67             18.6       101            2.8        3.24
##  4 C           14.4         1.95  2.5              16.8       113            3.85       3.49
##  5 C           13.2         2.59  2.87             21         118            2.8        2.69
##  6 C           14.2         1.76  2.45             15.2       112            3.27       3.39
##  7 C           14.4         1.87  2.45             14.6        96            2.5        2.52
##  8 C           14.1         2.15  2.61             17.6       121            2.6        2.51
##  9 C           14.8         1.64  2.17             14          97            2.8        2.98
## 10 C           13.9         1.35  2.27             16          98            2.98       3.15
## # … with 168 more rows, and 6 more variables: `nonflavonoid-phenols` <dbl>, proanthocyanins <dbl>,
## #   `color-intensity` <dbl>, hue <dbl>, `od280-od315-of-diluted-wines` <dbl>, proline <dbl>

Remarque : L’utilisation de %<>% de la librairie magrittr évite d’avoir à faire tb = tb %>%

ggplot2

La lib ggplot2 permet de produire des graphiques de bonnes qualités et repose sur bases saines pour la construction de graphique à partir d’un jeu de données. Consultez par exemple https://www.r-graph-gallery.com/

Grammaire des graphiques de ggplot2. source: http://bloggotype.blogspot.com/2016/08/holiday-notes2-grammar-of-graphics.html

à la tidyverse/ggplot2 (encore pas très facile pour un camembert en 2021 donc on fait un barplot).

En x les classes et pour chaque classe, les effectifs, sous forme de barplot

tb %>%
  ggplot(aes(x=cultivar, fill=cultivar)) +
  geom_bar(stat = 'count')

Exo sur tidyverse / distribution classe(s)-attribut

Considérons la variable alcohol et sa distribution par classe : est-ce utile pour déterminer la classe d’un vin ?

tb %>% 
  ggplot() +
  geom_boxplot(aes(x=cultivar, y=alcohol))

Il pest possible de rajouter des geometries

tb %>% 
  ggplot(aes(x=cultivar, y=alcohol)) +
  geom_boxplot() +
  geom_point()

Les points se supperpossent : faire de la transparence et/ou du jitter

tb %>% 
  ggplot(aes(x=cultivar, y=alcohol)) +
  geom_boxplot() +
  geom_jitter(width=0.05, alpha=0.2) 

Plus moderne avec des violin plots qui tracent la courbe de densité à la place de la boiîte à moustaches

tb %>% 
  ggplot(aes(x=cultivar, y=alcohol)) +
  geom_violin(aes(fill=cultivar)) +
  geom_jitter(width=0.05, alpha=0.2) +
  theme_bw() +
  ggtitle("Distributions des degrés alcoolique par classe de vin")

Calcul des moyennes et écart-types par classe → group_by et summarise

alcohol = tb %>% 
  group_by(cultivar) %>%
  summarise(alcohol.mean = mean(alcohol), alcohol.sd = sd(alcohol))
alcohol

## # A tibble: 3 x 3
##   cultivar alcohol.mean alcohol.sd
## * <fct>           <dbl>      <dbl>
## 1 C                13.7      0.462
## 2 M                12.3      0.538
## 3 V                13.2      0.530

pivot_longer (plusieurs colonnes/variable → (variable name, variable value) )

Manip pour avoir des tuples (classe variable value)

tbg = tb %>% rowid_to_column() %>%
  pivot_longer(alcohol:proline, names_to='variable', values_to='value')
tbg

## # A tibble: 2,314 x 4
##    rowid cultivar variable              value
##    <int> <fct>    <chr>                 <dbl>
##  1     1 C        alcohol               14.2 
##  2     1 C        malic-acid             1.71
##  3     1 C        ash                    2.43
##  4     1 C        alcalinity-of-ash     15.6 
##  5     1 C        magnesium            127   
##  6     1 C        total-phenols          2.8 
##  7     1 C        flavonoids             3.06
##  8     1 C        nonflavonoid-phenols   0.28
##  9     1 C        proanthocyanins        2.29
## 10     1 C        color-intensity        5.64
## # … with 2,304 more rows

rowid sera nécessaire si on veut revenir au format de départ sinon impossible de savoir quelle mesures (d’alcool et de ash) il faut rassembler pour reconstruire le tableau de départ.

tb %>%
  pivot_longer(alcohol:proline, names_to='variable', values_to='value') %>%
  ggplot(aes(cultivar, value, color=cultivar)) +
  geom_boxplot() +
  facet_wrap(~ variable)

On remarque que proline écrase le reste.

Plot interactif

p = tb %>%
  pivot_longer(alcohol:proline, names_to='variable', values_to='value') %>%
  ggplot(aes(cultivar, value, color=cultivar)) +
  geom_boxplot() +
  facet_wrap(~ variable)
ggplotly(p)

Il va donc être judicieux de normaliser les données. Nous allons utiliser une normalisation z-score qui consiste à centrer-réduire la matrice de données.

group_by → summarise, join, mutate (normalisation)

Normalisation (z-score)

znorm = tbg %>% 
  group_by(variable) %>%
  summarize(mean=mean(value), sd=sd(value), min = min(value), max=max(value), median=median(value))
znorm

## # A tibble: 13 x 6
##    variable                        mean      sd    min     max  median
##  * <chr>                          <dbl>   <dbl>  <dbl>   <dbl>   <dbl>
##  1 alcalinity-of-ash             19.5     3.34   10.6    30     19.5  
##  2 alcohol                       13.0     0.812  11.0    14.8   13.0  
##  3 ash                            2.37    0.274   1.36    3.23   2.36 
##  4 color-intensity                5.06    2.32    1.28   13      4.69 
##  5 flavonoids                     2.03    0.999   0.34    5.08   2.13 
##  6 hue                            0.957   0.229   0.48    1.71   0.965
##  7 magnesium                     99.7    14.3    70     162     98    
##  8 malic-acid                     2.34    1.12    0.74    5.8    1.87 
##  9 nonflavonoid-phenols           0.362   0.124   0.13    0.66   0.34 
## 10 od280-od315-of-diluted-wines   2.61    0.710   1.27    4      2.78 
## 11 proanthocyanins                1.59    0.572   0.41    3.58   1.56 
## 12 proline                      747.    315.    278    1680    674.   
## 13 total-phenols                  2.30    0.626   0.98    3.88   2.36

jointure et ajout des z-score

tbg %<>% inner_join(znorm, by='variable') %>% mutate(value.z = (value-mean)/sd)
tbg

## # A tibble: 2,314 x 10
##    rowid cultivar variable              value   mean     sd   min    max median value.z
##    <int> <fct>    <chr>                 <dbl>  <dbl>  <dbl> <dbl>  <dbl>  <dbl>   <dbl>
##  1     1 C        alcohol               14.2  13.0    0.812 11.0   14.8   13.0    1.51 
##  2     1 C        malic-acid             1.71  2.34   1.12   0.74   5.8    1.87  -0.561
##  3     1 C        ash                    2.43  2.37   0.274  1.36   3.23   2.36   0.231
##  4     1 C        alcalinity-of-ash     15.6  19.5    3.34  10.6   30     19.5   -1.17 
##  5     1 C        magnesium            127    99.7   14.3   70    162     98      1.91 
##  6     1 C        total-phenols          2.8   2.30   0.626  0.98   3.88   2.36   0.807
##  7     1 C        flavonoids             3.06  2.03   0.999  0.34   5.08   2.13   1.03 
##  8     1 C        nonflavonoid-phenols   0.28  0.362  0.124  0.13   0.66   0.34  -0.658
##  9     1 C        proanthocyanins        2.29  1.59   0.572  0.41   3.58   1.56   1.22 
## 10     1 C        color-intensity        5.64  5.06   2.32   1.28  13      4.69   0.251
## # … with 2,304 more rows

Vérification de la normalisation (moyenne à 0 et écart-type à 1)

tbg %>% group_by(variable) %>% summarize(m=round(mean(value.z), 4), sd=sd(value.z))

## # A tibble: 13 x 3
##    variable                         m    sd
##  * <chr>                        <dbl> <dbl>
##  1 alcalinity-of-ash                0  1   
##  2 alcohol                          0  1   
##  3 ash                              0  1   
##  4 color-intensity                  0  1.00
##  5 flavonoids                       0  1   
##  6 hue                              0  1.00
##  7 magnesium                        0  1   
##  8 malic-acid                       0  1.00
##  9 nonflavonoid-phenols             0  1   
## 10 od280-od315-of-diluted-wines     0  1   
## 11 proanthocyanins                  0  1.00
## 12 proline                          0  1   
## 13 total-phenols                    0  1

Formatage de tableau

znorm %>% knitr::kable()

variable	mean	sd	min	max	median
alcalinity-of-ash	19.4949438	3.3395638	10.60	30.00	19.500
alcohol	13.0006180	0.8118265	11.03	14.83	13.050
ash	2.3665169	0.2743440	1.36	3.23	2.360
color-intensity	5.0580899	2.3182859	1.28	13.00	4.690
flavonoids	2.0292697	0.9988587	0.34	5.08	2.135
hue	0.9574494	0.2285716	0.48	1.71	0.965
magnesium	99.7415730	14.2824835	70.00	162.00	98.000
malic-acid	2.3363483	1.1171461	0.74	5.80	1.865
nonflavonoid-phenols	0.3618539	0.1244533	0.13	0.66	0.340
od280-od315-of-diluted-wines	2.6116854	0.7099904	1.27	4.00	2.780
proanthocyanins	1.5908989	0.5723589	0.41	3.58	1.555
proline	746.8932584	314.9074743	278.00	1680.00	673.500
total-phenols	2.2951124	0.6258510	0.98	3.88	2.355

ggplot + facet

Visu

tbg %>%
  ggplot(aes(cultivar, value.z, color=cultivar)) +
  geom_violin() +
  facet_wrap(~ variable)

On y voit mieux.

pivot_wider: (var,val) → columns

Pour revenir au format de départ (une colonne par variable)

tbz = tbg %>% 
  select(rowid, cultivar, variable, value.z) %>%
  pivot_wider(names_from = variable, values_from=value.z)
# tbz = tbg %>% 
#   select(cultivar_id, cultivar, variable, value.z) %>%
#   spread(key = variable, value=value.z)
tbz

## # A tibble: 178 x 15
##    rowid cultivar alcohol `malic-acid`    ash `alcalinity-of-… magnesium `total-phenols` flavonoids
##    <int> <fct>      <dbl>        <dbl>  <dbl>            <dbl>     <dbl>           <dbl>      <dbl>
##  1     1 C          1.51       -0.561   0.231           -1.17     1.91             0.807      1.03 
##  2     2 C          0.246      -0.498  -0.826           -2.48     0.0181           0.567      0.732
##  3     3 C          0.196       0.0212  1.11            -0.268    0.0881           0.807      1.21 
##  4     4 C          1.69       -0.346   0.487           -0.807    0.928            2.48       1.46 
##  5     5 C          0.295       0.227   1.84             0.451    1.28             0.807      0.661
##  6     6 C          1.48       -0.516   0.304           -1.29     0.858            1.56       1.36 
##  7     7 C          1.71       -0.417   0.304           -1.47    -0.262            0.327      0.491
##  8     8 C          1.30       -0.167   0.888           -0.567    1.49             0.487      0.481
##  9     9 C          2.25       -0.623  -0.716           -1.65    -0.192            0.807      0.952
## 10    10 C          1.06       -0.883  -0.352           -1.05    -0.122            1.09       1.12 
## # … with 168 more rows, and 6 more variables: `nonflavonoid-phenols` <dbl>, proanthocyanins <dbl>,
## #   `color-intensity` <dbl>, hue <dbl>, `od280-od315-of-diluted-wines` <dbl>, proline <dbl>

geom_point (bivariate analysis)

tbz %>%
  ggplot(aes(x=`alcalinity-of-ash`, y=alcohol)) +
  geom_point()

Avec des couleurs et des formes

tbz %>%
  ggplot(aes(x=`alcalinity-of-ash`, y=alcohol)) +
  geom_point(size=3, aes(color=cultivar, shape=cultivar))

http://larmarange.github.io/analyse-R/graphiques-bivaries-ggplot2.html

La librairies ggally permet de faire les analyses bivariées sous forme d’un seul plot

tb %>% 
  ggpairs(aes(color=cultivar, alpha=0.1))

La même sur les données normalisées

tbz %>% select(-rowid) %>%
  ggpairs(aes(color=cultivar, alpha=.1))

matrice de corrélations

tb %>%
  ggcorr()

## Warning in ggcorr(.): data in column(s) 'cultivar' are not numeric and were ignored

ACP

Est-ce que des groupes se distinguent à partir des données ?

tb.acp = tb %>% 
  select(-cultivar) %>% 
  as.matrix %>% 
  princomp(cor=T)
tb.acp %>% summary

## Importance of components:
##                           Comp.1    Comp.2    Comp.3    Comp.4     Comp.5     Comp.6     Comp.7
## Standard deviation     2.1692972 1.5801816 1.2025273 0.9586313 0.92370351 0.80103498 0.74231281
## Proportion of Variance 0.3619885 0.1920749 0.1112363 0.0706903 0.06563294 0.04935823 0.04238679
## Cumulative Proportion  0.3619885 0.5540634 0.6652997 0.7359900 0.80162293 0.85098116 0.89336795
##                            Comp.8     Comp.9    Comp.10    Comp.11    Comp.12     Comp.13
## Standard deviation     0.59033665 0.53747553 0.50090167 0.47517222 0.41081655 0.321524394
## Proportion of Variance 0.02680749 0.02222153 0.01930019 0.01736836 0.01298233 0.007952149
## Cumulative Proportion  0.92017544 0.94239698 0.96169717 0.97906553 0.99204785 1.000000000

La variance portée par les axes semblent être assez prometteuse.

Ajout des coordonnées projettées dans le nouveau repère à 2 dimensions (2 premières composantes principales)

names(tb.acp$score[,1:2])=c('Comp1','Comp2') 
tb$Comp1 = tb.acp$score[,1]
tb$Comp2 = tb.acp$score[,2]

visu

tb %>% 
  ggplot(aes(Comp1, Comp2, color=cultivar, shape=cultivar)) +
  geom_point() +
  ggtitle('ACP normée princomp wine')

C’est prometteur (séparation des classes par l’utilisation d’une combinaison des variables).