Dimensional Reduction using PCA on cereal nutrition
Dominika Lach
2023-12-30
INTRO
Breakfast cereal is one of the favorite breakfast foods for both children and adults. On some packages you can find words like “fit,” “high protein,” “healthy.” But is this true? It is possible to find out by decreasing the size of the dataset preserving most information PCA on cereal nutrition ingredients. Project based on dataset which contains nutritional values from 80 types of different cereals https://www.kaggle.com/datasets/crawford/80-cereals
Which breakfast cereal ingredient stores the most nutritional information? maybe not so healthy sugar? let’s check:
ANALYSIS
Descriptive stats
summary(cereal)## name mfr type calories
## Length:77 Length:77 Length:77 Min. : 50.0
## Class :character Class :character Class :character 1st Qu.:100.0
## Mode :character Mode :character Mode :character Median :110.0
## Mean :106.9
## 3rd Qu.:110.0
## Max. :160.0
## protein fat sodium fiber
## Min. :1.000 Min. :0.000 Min. : 0.0 Min. : 0.000
## 1st Qu.:2.000 1st Qu.:0.000 1st Qu.:130.0 1st Qu.: 1.000
## Median :3.000 Median :1.000 Median :180.0 Median : 2.000
## Mean :2.545 Mean :1.013 Mean :159.7 Mean : 2.152
## 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:210.0 3rd Qu.: 3.000
## Max. :6.000 Max. :5.000 Max. :320.0 Max. :14.000
## carbo sugars potass vitamins
## Min. :-1.0 Min. :-1.000 Min. : -1.00 Min. : 0.00
## 1st Qu.:12.0 1st Qu.: 3.000 1st Qu.: 40.00 1st Qu.: 25.00
## Median :14.0 Median : 7.000 Median : 90.00 Median : 25.00
## Mean :14.6 Mean : 6.922 Mean : 96.08 Mean : 28.25
## 3rd Qu.:17.0 3rd Qu.:11.000 3rd Qu.:120.00 3rd Qu.: 25.00
## Max. :23.0 Max. :15.000 Max. :330.00 Max. :100.00
## shelf weight cups rating
## Min. :1.000 Min. :0.50 Min. :0.250 Min. :18.04
## 1st Qu.:1.000 1st Qu.:1.00 1st Qu.:0.670 1st Qu.:33.17
## Median :2.000 Median :1.00 Median :0.750 Median :40.40
## Mean :2.208 Mean :1.03 Mean :0.821 Mean :42.67
## 3rd Qu.:3.000 3rd Qu.:1.00 3rd Qu.:1.000 3rd Qu.:50.83
## Max. :3.000 Max. :1.50 Max. :1.500 Max. :93.70dim(cereal)## [1] 77 16Nutritional distribution
par(mfrow = c(3, 3))
hist(cereal$calories, xlab = "Calories", main = "Calories distribution", col = wes_palette('Royal2', 11, type = ('continuous')))
hist(cereal$protein, xlab = "Protein", main = "Protein distribution", col = wes_palette('Royal2', 11, type = ('continuous')))
hist(cereal$fat, xlab = "Fat", main = "Fat distribution", col = wes_palette('Royal2', 11, type = ('continuous')))
hist(cereal$sodium, xlab = "Sodium", main = "Sodium distribution", col = wes_palette('Royal2', 11, type = ('continuous')))
hist(cereal$fiber, xlab = "Fiber", main = "Fiber distribution", col = wes_palette('Royal2', 11, type = ('continuous')))
hist(cereal$carbo, xlab = "Carbo", main = "Carbo distribution", col = wes_palette('Royal2', 11, type = ('continuous')))
hist(cereal$sugars, xlab = "Sugars", main = "Sugars distribution", col = wes_palette('Royal2', 11, type = ('continuous')))
hist(cereal$potass, xlab = "Potass", main = "Potass distribution", col = wes_palette('Royal2', 11, type = ('continuous')))
hist(cereal$vitamins, xlab = "Vitamins", main = "Vitamins distribution", col = wes_palette('Royal2', 11, type = ('continuous')))
Standardization of selected columns
nutri <- cereal[5:12]
pre <- preProcess(nutri, method = c("center", "scale"))
nutri_s <- predict(pre, nutri)Checking correlation
ggpairs(nutri_s)
par(mfrow = c(1,1))
correlation <- cor(nutri_s)
corrplot(correlation, method = "circle", type = "upper", order = "hclust", addCoef.col = "grey30", col = wes_palette("Royal2", 9, type = ('continuous')))
Potas and fieber are highly correlated
PRINCIPAL COMPONENTS ANALYSIS
pca <- prcomp(nutri_s, center = FALSE, scale = FALSE)
pca$rotation## PC1 PC2 PC3 PC4 PC5 PC6
## protein -0.43020955 -0.3010297 -0.04226036 0.44085282 -0.14487747 -0.48172465
## fat -0.19690483 0.3443189 0.33120825 0.73231694 0.01793745 0.35848190
## sodium 0.15661812 -0.3423062 0.53646747 0.04864795 0.65187105 -0.32868478
## fiber -0.54478378 -0.2028145 0.02700826 -0.32522238 0.11669172 0.21861791
## carbo 0.36093074 -0.5096970 -0.01362805 0.16664513 0.08106192 0.61175926
## sugars 0.03876167 0.4982030 0.51689413 -0.29006145 0.03667417 0.01572122
## potass -0.55911349 -0.1414933 0.16774992 -0.19764731 0.09673517 0.32758013
## vitamins 0.10221673 -0.3232657 0.55179984 -0.10126088 -0.72309213 -0.04241843
## PC7 PC8
## protein -0.51645313 0.091606439
## fat 0.23992739 0.101438647
## sodium 0.18528599 -0.028858386
## fiber 0.17625558 0.680515306
## carbo -0.43248908 0.118803916
## sugars -0.60799612 0.166507396
## potass -0.08922837 -0.689593448
## vitamins 0.21364994 -0.002523253summary(pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.6126 1.2751 1.2032 0.9435 0.80220 0.62008 0.58894
## Proportion of Variance 0.3251 0.2032 0.1810 0.1113 0.08044 0.04806 0.04336
## Cumulative Proportion 0.3251 0.5283 0.7093 0.8205 0.90098 0.94904 0.99240
## PC8
## Standard deviation 0.2466
## Proportion of Variance 0.0076
## Cumulative Proportion 1.0000fviz_eig(pca)
fviz_pca_var(pca, col.var = 'turquoise4')
fviz_pca_ind(pca, col.ind="cos2", geom = "point", gradient.cols = wes_palette("Royal2", 3, type = ('discrete')))
At a glance there are few potential nutritional ingrediens which can preserve the most information, let’s check contributions of individual variables
PC1 <- fviz_contrib(pca, choice = "var", axes = 1)
PC2 <- fviz_contrib(pca, choice = "var", axes = 2)
grid.arrange(PC1, PC2)
On the first plot almost 4 ingredients have the biggest contribution but on the second plot we can distinguish that only two ingredients can fulfill more than 50% of contribution. And YES! Sugar is here
How the components are clustered?
autoplot(pca, loadings=TRUE, loadings.colour= "rosybrown3", loadings.label=TRUE, loadings.label.size=5, loadings.label.col = "turquoise4")
fviz_cluster(clusters, geom = "point", palette = palette)
Easily detectable are three clusters in this data set. One of them contains sugar and fat, ingredients that are considered the ‘bad’ ones. The following clusters, on the other hand, contain the rest of the ‘good’ ingredients
CONCLUSIONS
Breakfast cereals are certainly tasty and eagerly eaten by most of the people, but if you want to maintain a healthy diet, don’t just read the cover of the cereal. The information about the contents is on the back of the package and is no longer as satisfying as their cover. Dimensional reduction techniques are very helpful in analyzing large data sets. But even on a small set like the one presented above, it is possible to detect variables which keep the most information included in original dataset.