Cluster analysis - Dati World

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1 Cluster analysis - Dati World Emanuele Taufer file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 1/47

2 World data Un data set sui Paesi che contiene informazioni demografiche, economiche, sulla sanità e sulle abitudini alimentari. Originariamente disponibile a single=true&gid=0 library(ggplot2) library(data.table) world=read.csv(" str(world) ## 'data.frame': 86 obs. of 102 variables: ## $ Countries ## $ Average.latitude..º. ## $ Annual.insolation..W.h.m2.day. ## $ Energy..kcal.day. ## $ Protein..g.day. ## $ Fats..g.day. ## $ Carbohydrates..g.day. ## $ Animal.Products...kcal.day. ## $ Animal.Fats..kcal.day. ## $ Bovine.Meat..kcal.day. ## $ Butter..Ghee..kcal.day. ## $ Cheese..kcal.day. ## $ Eggs..kcal.day. ## $ Fats..Animals..Raw..kcal.day. ## $ Fish..Seafood..kcal.day. ## $ Freshwater.Fish..kcal.day. ## $ Honey..kcal.day. ## $ Meat..kcal.day. ## $ Milk...Excluding.Butter..kcal.day. ## $ Milk..Whole..kcal.day. ## $ Mutton...Goat.Meat..kcal.day. ## $ Offals..Edible..kcal.day. ## $ Pelagic.Fish..kcal.day. ## $ Pigmeat..kcal.day. ## $ Poultry.Meat..kcal.day. ## $ Vegetal.Products...kcal.day. ## $ Alcoholic.Beverages..kcal.day. ## $ Apples..kcal.day. ## $ Bananas..kcal.day. ## $ Beans..kcal.day. ## $ Cereals...Excluding.Beer..kcal.day. ## $ Coconut.Oil..kcal.day. ## $ Coffee..kcal.day. ## $ Fruits...Excluding.Wine..kcal.day. ## $ Nuts..kcal.day. ## $ Olive.Oil..kcal.day. ## $ Palm.Oil..kcal.day. file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 2/47

3 ## $ Potatoes..kcal.day. ## $ Pulses..kcal.day. ## $ Rice..Milled.Equivalent...kcal.day. ## $ Rice..Paddy.Equivalent...kcal.day. ## $ Roots...Tuber.Dry.Equiv..kcal.day. ## $ Soyabean.Oil..kcal.day. ## $ Starchy.Roots..kcal.day. ## $ Sugar...Sweeteners..kcal.day. ## $ Sugar..Raw.Equivalent...kcal.day. ## $ Sugar..Raw.Equivalent..kcal.day. ## $ Sugar..Refined.Equiv..kcal.day. ## $ Vegetable.Oils..kcal.day. ## $ Vegetables..kcal.day. ## $ Wheat..kcal.day. ## $ Wine..kcal.day. ## $ Gross.national.income.per.capita..PPP.international... ## $ Population.annual.growth.rate... ## $ Population.in.urban.areas... ## $ Population.median.age..years ## $ Population.proportion.over ## $ Population.proportion.under ## $ Total.fertility.rate..per.female. ## $ Per.capita.recorded.alcohol.consumption..litres.of.pure.alcohol..among.adults...1 ## $ Population.with.sustainable.access.to.improved.drinking.water.sources...rural ## $ Population.with.sustainable.access.to.improved.drinking.water.sources...total ## $ Population.with.sustainable.access.to.improved.drinking.water.sources...urban ## $ Population.with.sustainable.access.to.improved.sanitation...rural ## $ Population.with.sustainable.access.to.improved.sanitation...total ## $ Population.with.sustainable.access.to.improved.sanitation...urban ## $ Prevalence.of.current.tobacco.use.among.adults...15.years...both.sexes ## $ Prevalence.of.current.tobacco.use.among.adults...15.years...female ## $ Prevalence.of.current.tobacco.use.among.adults...15.years...male ## $ Mean.total.cholesterol..men..mg.dl ## $ Mean.total.cholesterol..female..mg.dl ## $ Diabetes.crude.prevalence..adults.aged.20.to ## $ Systolic.blood.pressure..adults.aged.15.and.above..men..mmHg. ## $ Systolic.blood.pressure..adults.aged.15.and.above..female..mmHg. ## $ Obesity.prevalence..men... ## $ Obesity.prevalence..female... ## $ Adult.mortality.rate..probability.of.dying.between.15.to.60.years.per.1000.populat ## $ Adult.mortality.rate..probability.of.dying.between.15.to.60.years.per.1000.populat ## $ Adult.mortality.rate..probability.of.dying.between.15.to.60.years.per.1000.populat ## $ Age.standardized.mortality.rate.for.cancer..per population ## $ Age.standardized.mortality.rate.for.cardiovascular.diseases..per populatio ## $ Age.standardized.mortality.rate.for.injuries..per population ## $ Age.standardized.mortality.rate.for.non.communicable.diseases..per populat ## $ Healthy.life.expectancy..HALE..at.birth..years..both.sexes ## $ Healthy.life.expectancy..HALE..at.birth..years..female ## $ Healthy.life.expectancy..HALE..at.birth..years..male ## $ Incidence.of.tuberculosis..per population.per.year. ## $ Infant.mortality.rate..per live.births..both.sexes ## $ Infant.mortality.rate..per live.births..female ## $ Infant.mortality.rate..per live.births..male ## $ Life.expectancy.at.birth..years..both.sexes ## $ Life.expectancy.at.birth..years..female ## $ Life.expectancy.at.birth..years..male ## $ Maternal.mortality.ratio..per live.births ## $ Neonatal.mortality.rate..per live.births ## $ Prevalence.of.tuberculosis..per population. ## $ Under.5.mortality.rate..probability.of.dying.by.age.5.per.1000.live.births..both.s ## $ Under.5.mortality.rate..probability.of.dying.by.age.5.per.1000.live.births..female ## $ Under.5.mortality.rate..probability.of.dying.by.age.5.per.1000.live.births..male ## [list output truncated] file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 3/47

4 file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 4/47

5 Dati sulle abitudini alimentari Le variabili dalla # 4 alla # 52 nei dati riguardano il consumo di una varietà di alimenti misurato in kcal / giorno. Mettiamo queste varibili nell oggetto (data.frame) food. Usiamo questo sottoinsieme dei dati analizzare le abitudini alimentari utilizzando una cluster analysis food=world[,4:52] str(food) ## 'data.frame': 86 obs. of 49 variables: ## $ Energy..kcal.day. : int ## $ Protein..g.day. : int ## $ Fats..g.day. : int ## $ Carbohydrates..g.day. : num ## $ Animal.Products...kcal.day. : int ## $ Animal.Fats..kcal.day. : int ## $ Bovine.Meat..kcal.day. : int ## $ Butter..Ghee..kcal.day. : int ## $ Cheese..kcal.day. : int ## $ Eggs..kcal.day. : int ## $ Fats..Animals..Raw..kcal.day. : int ## $ Fish..Seafood..kcal.day. : int ## $ Freshwater.Fish..kcal.day. : int ## $ Honey..kcal.day. : int ## $ Meat..kcal.day. : int ## $ Milk...Excluding.Butter..kcal.day. : int ## $ Milk..Whole..kcal.day. : int ## $ Mutton...Goat.Meat..kcal.day. : int ## $ Offals..Edible..kcal.day. : int ## $ Pelagic.Fish..kcal.day. : int ## $ Pigmeat..kcal.day. : int ## $ Poultry.Meat..kcal.day. : int ## $ Vegetal.Products...kcal.day. : int ## $ Alcoholic.Beverages..kcal.day. : int ## $ Apples..kcal.day. : int ## $ Bananas..kcal.day. : int ## $ Beans..kcal.day. : int ## $ Cereals...Excluding.Beer..kcal.day.: int ## $ Coconut.Oil..kcal.day. : int ## $ Coffee..kcal.day. : int ## $ Fruits...Excluding.Wine..kcal.day. : int ## $ Nuts..kcal.day. : int ## $ Olive.Oil..kcal.day. : int ## $ Palm.Oil..kcal.day. : int ## $ Potatoes..kcal.day. : int ## $ Pulses..kcal.day. : int ## $ Rice..Milled.Equivalent...kcal.day.: int ## $ Rice..Paddy.Equivalent...kcal.day. : int ## $ Roots...Tuber.Dry.Equiv..kcal.day. : int ## $ Soyabean.Oil..kcal.day. : int file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 5/47

6 ## $ Starchy.Roots..kcal.day. : int ## $ Sugar...Sweeteners..kcal.day. : int ## $ Sugar..Raw.Equivalent...kcal.day. : int ## $ Sugar..Raw.Equivalent..kcal.day. : int ## $ Sugar..Refined.Equiv..kcal.day. : int ## $ Vegetable.Oils..kcal.day. : int ## $ Vegetables..kcal.day. : int ## $ Wheat..kcal.day. : int ## $ Wine..kcal.day. : int file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 6/47

7 1 Controllare le variabili Sembra vi siano duplicazioni nei dati: 1. Meat, Bovine.Meat, Pigmeat. C è sovrapposizione di informazioni? 2. Energy, Protein, Fats. Sono sintesi di altre variabili? (ancora, sovrapposizione) 3. Rice.paddy equivalent e Rice.milled equivalent. sembrano la stessa variabile (osservandone i valori) 4. file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 7/47

8 I dati food ripuliti Eliminiamo da food le variabli ridondanti choose=c(7:14,16:36,38:42,46:49) food=food[,choose] str(food) ## 'data.frame': 86 obs. of 38 variables: ## $ Bovine.Meat..kcal.day. : int ## $ Butter..Ghee..kcal.day. : int ## $ Cheese..kcal.day. : int ## $ Eggs..kcal.day. : int ## $ Fats..Animals..Raw..kcal.day. : int ## $ Fish..Seafood..kcal.day. : int ## $ Freshwater.Fish..kcal.day. : int ## $ Honey..kcal.day. : int ## $ Milk...Excluding.Butter..kcal.day. : int ## $ Milk..Whole..kcal.day. : int ## $ Mutton...Goat.Meat..kcal.day. : int ## $ Offals..Edible..kcal.day. : int ## $ Pelagic.Fish..kcal.day. : int ## $ Pigmeat..kcal.day. : int ## $ Poultry.Meat..kcal.day. : int ## $ Vegetal.Products...kcal.day. : int ## $ Alcoholic.Beverages..kcal.day. : int ## $ Apples..kcal.day. : int ## $ Bananas..kcal.day. : int ## $ Beans..kcal.day. : int ## $ Cereals...Excluding.Beer..kcal.day.: int ## $ Coconut.Oil..kcal.day. : int ## $ Coffee..kcal.day. : int ## $ Fruits...Excluding.Wine..kcal.day. : int ## $ Nuts..kcal.day. : int ## $ Olive.Oil..kcal.day. : int ## $ Palm.Oil..kcal.day. : int ## $ Potatoes..kcal.day. : int ## $ Pulses..kcal.day. : int ## $ Rice..Paddy.Equivalent...kcal.day. : int ## $ Roots...Tuber.Dry.Equiv..kcal.day. : int ## $ Soyabean.Oil..kcal.day. : int ## $ Starchy.Roots..kcal.day. : int ## $ Sugar...Sweeteners..kcal.day. : int ## $ Vegetable.Oils..kcal.day. : int ## $ Vegetables..kcal.day. : int ## $ Wheat..kcal.day. : int ## $ Wine..kcal.day. : int file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 8/47

9 2 Clustering con k-means Proviamo a valutare rapidamente diversi valori di k tracciando i valori di k contro il rapporto SSW / SST st.food=scale(food) # k- means clustering loop ratiowss=vector() for (i in 2:30){ km=kmeans(st.food,i,nstart=50) ratiowss[i]=km$tot.withinss/km$totss} dt=data.frame("k"=2:30,"ratiowss"=ratiowss[2:30]) ggplot(dt,aes(x=k,y=ratiowss))+geom_line(size=3) Non c è chiara indicazione, ci sono forse molti gruppi. file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 9/47

10 K=7 clusters? Proviamo ad analizzare in dettaglio il caso k=7 per avere più informazioni set.seed(1) km=kmeans(st.food,7,nstart=50) km ## K-means clustering with 7 clusters of sizes 25, 20, 8, 10, 12, 9, 2 ## ## Cluster means: ## Bovine.Meat..kcal.day. Butter..Ghee..kcal.day. Cheese..kcal.day. ## ## ## ## ## ## ## ## Eggs..kcal.day. Fats..Animals..Raw..kcal.day. Fish..Seafood..kcal.day. ## ## ## ## ## ## ## ## Freshwater.Fish..kcal.day. Honey..kcal.day. ## ## ## ## ## ## ## ## Milk...Excluding.Butter..kcal.day. Milk..Whole..kcal.day. ## ## ## ## ## ## ## ## Mutton...Goat.Meat..kcal.day. Offals..Edible..kcal.day. ## ## ## ## ## ## ## ## Pelagic.Fish..kcal.day. Pigmeat..kcal.day. Poultry.Meat..kcal.day. ## ## ## ## file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 10/47

11 ## ## ## ## Vegetal.Products...kcal.day. Alcoholic.Beverages..kcal.day. ## ## ## ## ## ## ## ## Apples..kcal.day. Bananas..kcal.day. Beans..kcal.day. ## ## ## ## ## ## ## ## Cereals...Excluding.Beer..kcal.day. Coconut.Oil..kcal.day. ## ## ## ## ## ## ## ## Coffee..kcal.day. Fruits...Excluding.Wine..kcal.day. Nuts..kcal.day. ## ## ## ## ## ## ## ## Olive.Oil..kcal.day. Palm.Oil..kcal.day. Potatoes..kcal.day. ## ## ## ## ## ## ## ## Pulses..kcal.day. Rice..Paddy.Equivalent...kcal.day. ## ## ## ## ## ## ## ## Roots...Tuber.Dry.Equiv..kcal.day. Soyabean.Oil..kcal.day. ## ## ## ## ## ## ## ## Starchy.Roots..kcal.day. Sugar...Sweeteners..kcal.day. ## ## ## ## ## file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 11/47

12 ## ## ## Vegetable.Oils..kcal.day. Vegetables..kcal.day. Wheat..kcal.day. ## ## ## ## ## ## ## ## Wine..kcal.day. ## ## ## ## ## ## ## ## ## Clustering vector: ## [1] ## [36] ## [71] ## ## Within cluster sum of squares by cluster: ## [1] ## (between_ss / total_ss = 45.9 %) ## ## Available components: ## ## [1] "cluster" "centers" "totss" "withinss" ## [5] "tot.withinss" "betweenss" "size" "iter" ## [9] "ifault" file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 12/47

13 Commenti In cluster means troviamo le coordinate dei centrodi per gruppo. I centroidi sono in uno spazio a 38 dimensioni. I valori sono standardizzati e quindi le coordinate dei centroidi sono espresse in deviazioni standard. Ad esempio il primo gruppo ha un consumo sopra le media di Carne Bovina (0.32 DS), Burro (0.97 DS), Formaggio (1.33 DS) rispetto a tutti gli altri gruppi I valori da analizzare sono troppi, vale la pena effettuare un analisi esplorativa dei risultati file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 13/47

14 3 EDA dei risultati ( ) k = 7 Per poter effettuare una EDA mettiamo i valori dei centroidi in un data.frame, che chiameremo dt. dt=data.frame(km$centers) dt ## Bovine.Meat..kcal.day. Butter..Ghee..kcal.day. Cheese..kcal.day. ## ## ## ## ## ## ## ## Eggs..kcal.day. Fats..Animals..Raw..kcal.day. Fish..Seafood..kcal.day. ## ## ## ## ## ## ## ## Freshwater.Fish..kcal.day. Honey..kcal.day. ## ## ## ## ## ## ## ## Milk...Excluding.Butter..kcal.day. Milk..Whole..kcal.day. ## ## ## ## ## ## ## ## Mutton...Goat.Meat..kcal.day. Offals..Edible..kcal.day. ## ## ## ## ## ## ## ## Pelagic.Fish..kcal.day. Pigmeat..kcal.day. Poultry.Meat..kcal.day. ## ## ## ## ## ## ## file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 14/47

15 ## Vegetal.Products...kcal.day. Alcoholic.Beverages..kcal.day. ## ## ## ## ## ## ## ## Apples..kcal.day. Bananas..kcal.day. Beans..kcal.day. ## ## ## ## ## ## ## ## Cereals...Excluding.Beer..kcal.day. Coconut.Oil..kcal.day. ## ## ## ## ## ## ## ## Coffee..kcal.day. Fruits...Excluding.Wine..kcal.day. Nuts..kcal.day. ## ## ## ## ## ## ## ## Olive.Oil..kcal.day. Palm.Oil..kcal.day. Potatoes..kcal.day. ## ## ## ## ## ## ## ## Pulses..kcal.day. Rice..Paddy.Equivalent...kcal.day. ## ## ## ## ## ## ## ## Roots...Tuber.Dry.Equiv..kcal.day. Soyabean.Oil..kcal.day. ## ## ## ## ## ## ## ## Starchy.Roots..kcal.day. Sugar...Sweeteners..kcal.day. ## ## ## ## ## ## ## ## Vegetable.Oils..kcal.day. Vegetables..kcal.day. Wheat..kcal.day. file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 15/47

16 ## ## ## ## ## ## ## ## Wine..kcal.day. ## ## ## ## ## ## ## file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 16/47

17 EDA - continua Per avere una visione migliore, si transponga il data.frame appena creato. tdt=t(dt) tdt ## ## Bovine.Meat..kcal.day ## Butter..Ghee..kcal.day ## Cheese..kcal.day ## Eggs..kcal.day ## Fats..Animals..Raw..kcal.day ## Fish..Seafood..kcal.day ## Freshwater.Fish..kcal.day ## Honey..kcal.day ## Milk...Excluding.Butter..kcal.day ## Milk..Whole..kcal.day ## Mutton...Goat.Meat..kcal.day ## Offals..Edible..kcal.day ## Pelagic.Fish..kcal.day ## Pigmeat..kcal.day ## Poultry.Meat..kcal.day ## Vegetal.Products...kcal.day ## Alcoholic.Beverages..kcal.day ## Apples..kcal.day ## Bananas..kcal.day ## Beans..kcal.day ## Cereals...Excluding.Beer..kcal.day ## Coconut.Oil..kcal.day ## Coffee..kcal.day ## Fruits...Excluding.Wine..kcal.day ## Nuts..kcal.day ## Olive.Oil..kcal.day ## Palm.Oil..kcal.day ## Potatoes..kcal.day ## Pulses..kcal.day ## Rice..Paddy.Equivalent...kcal.day ## Roots...Tuber.Dry.Equiv..kcal.day ## Soyabean.Oil..kcal.day ## Starchy.Roots..kcal.day ## Sugar...Sweeteners..kcal.day ## Vegetable.Oils..kcal.day ## Vegetables..kcal.day ## Wheat..kcal.day ## Wine..kcal.day ## ## Bovine.Meat..kcal.day ## Butter..Ghee..kcal.day ## Cheese..kcal.day ## Eggs..kcal.day ## Fats..Animals..Raw..kcal.day ## Fish..Seafood..kcal.day ## Freshwater.Fish..kcal.day ## Honey..kcal.day ## Milk...Excluding.Butter..kcal.day file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 17/47

18 ## Milk..Whole..kcal.day ## Mutton...Goat.Meat..kcal.day ## Offals..Edible..kcal.day ## Pelagic.Fish..kcal.day ## Pigmeat..kcal.day ## Poultry.Meat..kcal.day ## Vegetal.Products...kcal.day ## Alcoholic.Beverages..kcal.day ## Apples..kcal.day ## Bananas..kcal.day ## Beans..kcal.day ## Cereals...Excluding.Beer..kcal.day ## Coconut.Oil..kcal.day ## Coffee..kcal.day ## Fruits...Excluding.Wine..kcal.day ## Nuts..kcal.day ## Olive.Oil..kcal.day ## Palm.Oil..kcal.day ## Potatoes..kcal.day ## Pulses..kcal.day ## Rice..Paddy.Equivalent...kcal.day ## Roots...Tuber.Dry.Equiv..kcal.day ## Soyabean.Oil..kcal.day ## Starchy.Roots..kcal.day ## Sugar...Sweeteners..kcal.day ## Vegetable.Oils..kcal.day ## Vegetables..kcal.day ## Wheat..kcal.day ## Wine..kcal.day ## 7 ## Bovine.Meat..kcal.day ## Butter..Ghee..kcal.day ## Cheese..kcal.day ## Eggs..kcal.day ## Fats..Animals..Raw..kcal.day ## Fish..Seafood..kcal.day ## Freshwater.Fish..kcal.day ## Honey..kcal.day ## Milk...Excluding.Butter..kcal.day ## Milk..Whole..kcal.day ## Mutton...Goat.Meat..kcal.day ## Offals..Edible..kcal.day ## Pelagic.Fish..kcal.day ## Pigmeat..kcal.day ## Poultry.Meat..kcal.day ## Vegetal.Products...kcal.day ## Alcoholic.Beverages..kcal.day ## Apples..kcal.day ## Bananas..kcal.day ## Beans..kcal.day ## Cereals...Excluding.Beer..kcal.day ## Coconut.Oil..kcal.day ## Coffee..kcal.day ## Fruits...Excluding.Wine..kcal.day ## Nuts..kcal.day ## Olive.Oil..kcal.day ## Palm.Oil..kcal.day ## Potatoes..kcal.day ## Pulses..kcal.day ## Rice..Paddy.Equivalent...kcal.day ## Roots...Tuber.Dry.Equiv..kcal.day ## Soyabean.Oil..kcal.day ## Starchy.Roots..kcal.day ## Sugar...Sweeteners..kcal.day ## Vegetable.Oils..kcal.day file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 18/47

19 ## Vegetables..kcal.day ## Wheat..kcal.day ## Wine..kcal.day file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 19/47

20 EDA - continua Notiamo che il Gruppo 1 ha un consumo decisamente sopra le media per molti alimenti. L analisi dei valori nel data.frame tdt non è agevole e vale utilizzare strumenti grafici. Può essere inoltre interessante individuare, per ciascun alimento, qual è il gruppo che ne consuma di più. A tal fine si utilizzi il codice sotto maxims=vector() for (i in 1:nrow(tdt)){maxims[i]=which.max(tdt[i,])} # per ogni riga di tdt, il codice sopra indica il numero della colonna # (cioè il gruppo) con il valore più alto file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 20/47

21 Mettiamo tutte le variabili create in data.frame per analizzarle con gli strumenti grafici tdt=as.data.frame(tdt,keep.rownames = TRUE) tdt$aliments<-row.names(tdt) colnames(tdt)<-c("g1","g2","g3","g4","g5","g6","g7","aliments") world=as.data.frame(world) world$cluster=km$cluster Nota che la colonna che contiene i nomi degli alimenti nel data.frame tdt è la numero 8 Nota che la colonna che contiene i nomi dei Paesi nel data.frame world è la numero 1 file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 21/47

22 Analisi del gruppo 1 Alimenti con consumo più elevato rispetto agli altri gruppi tdt[maxims==1,8] ## [1] "Butter..Ghee..kcal.day." ## [2] "Cheese..kcal.day." ## [3] "Eggs..kcal.day." ## [4] "Fats..Animals..Raw..kcal.day." ## [5] "Milk...Excluding.Butter..kcal.day." ## [6] "Pigmeat..kcal.day." ## [7] "Alcoholic.Beverages..kcal.day." ## [8] "Apples..kcal.day." ## [9] "Olive.Oil..kcal.day." ## [10] "Sugar...Sweeteners..kcal.day." ## [11] "Vegetable.Oils..kcal.day." ## [12] "Wine..kcal.day." Nazioni del gruppo world[km$cluster==1,1] ## [1] Australia Austria ## [3] Belgium Canada ## [5] Cyprus Czech Republic ## [7] Denmark Estonia ## [9] Finland France ## [11] Germany Greece ## [13] Hungary Iceland ## [15] Italy Malta ## [17] Netherlands New Zealand ## [19] Poland Portugal ## [21] Spain Sweden ## [23] Switzerland United Kingdom ## [25] United States of America ## 86 Levels: Albania Argentina Australia Austria Bangladesh... Uzbekistan file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 22/47

23 Plot degli alimenti a più alto consumo ## ordina gli alimenti in base ai valori del centroide nel gruppo e plotta tdt$aliments <- with(tdt, factor(tdt$aliments, levels=tdt[order(-tdt$g1), ]$Aliments)) ggplot(tdt[tdt$g1>0,],aes(aliments,g1,fill=aliments))+geom_bar(stat="identity")+ggtitle("cluster 1: Alimenti file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 23/47

24 Analisi del gruppo 2 Alimenti con consumo più elevato rispetto agli altri gruppi tdt[maxims==2,8] ## [1] Beans..kcal.day. Pulses..kcal.day. ## 38 Levels: Cheese..kcal.day.... Cereals...Excluding.Beer..kcal.day. Nazioni del gruppo world[km$cluster==2,1] ## [1] Bolivia Brazil Colombia ## [4] Costa Rica Dominican Republic Ecuador ## [7] Fiji Guatemala Haiti ## [10] India Jamaica Kenya ## [13] Lesotho Mauritius Mexico ## [16] Pakistan Paraguay Peru ## [19] South Africa Trinidad and Tobago ## 86 Levels: Albania Argentina Australia Austria Bangladesh... Uzbekistan file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 24/47

25 Plot degli alimenti a più alto consumo ## ordina gli alimenti in base ai valori del centroide nel gruppo e plotta tdt$aliments <- with(tdt, factor(tdt$aliments, levels=tdt[order(-tdt$g2), ]$Aliments)) ggplot(tdt[tdt$g1>0,],aes(aliments,g2,fill=aliments))+geom_bar(stat="identity")+ggtitle("cluster 2: Alimenti file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 25/47

26 Analisi del gruppo 3 Alimenti con consumo più elevato rispetto agli altri gruppi tdt[maxims==3,8] ## [1] Vegetal.Products...kcal.day. Cereals...Excluding.Beer..kcal.day. ## [3] Nuts..kcal.day. Soyabean.Oil..kcal.day. ## [5] Vegetables..kcal.day. Wheat..kcal.day. ## 38 Levels: Beans..kcal.day. Pulses..kcal.day.... Vegetables..kcal.day. Nazioni del gruppo world[km$cluster==3,1] ## [1] Egypt Iran, Islamic Republic of ## [3] Israel Morocco ## [5] Saudi Arabia Tunisia ## [7] Turkey United Arab Emirates ## 86 Levels: Albania Argentina Australia Austria Bangladesh... Uzbekistan file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 26/47

27 Plot degli alimenti a più alto consumo tdt$aliments <- with(tdt, factor(tdt$aliments, levels=tdt[order(-tdt$g3), ]$Aliments)) ggplot(tdt[tdt$g1>0,],aes(aliments,g3,fill=aliments))+geom_bar(stat="identity")+ggtitle("cluster 3: Alimenti file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 27/47

28 Analisi del gruppo 4 Alimenti con consumo più elevato rispetto agli altri gruppi tdt[maxims==4,8] ## [1] Freshwater.Fish..kcal.day. Rice..Paddy.Equivalent...kcal.day. ## 38 Levels: Vegetal.Products...kcal.day.... Alcoholic.Beverages..kcal.day. Nazioni del gruppo world[km$cluster==4,1] ## [1] Bangladesh China Gambia Indonesia Japan ## [6] Malaysia Philippines Senegal Sri Lanka Thailand ## 86 Levels: Albania Argentina Australia Austria Bangladesh... Uzbekistan file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 28/47

29 Plot degli alimenti a più alto consumo ## ordina gli alimenti in base ai valori del centroide nel gruppo e plotta tdt$aliments <- with(tdt, factor(tdt$aliments, levels=tdt[order(-tdt$g4), ]$Aliments)) ggplot(tdt[tdt$g4>0,],aes(aliments,g4,fill=aliments))+geom_bar(stat="identity")+ggtitle("cluster 4: Alimenti file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 29/47

30 Analisi del gruppo 5 Alimenti con consumo più elevato rispetto agli altri gruppi tdt[maxims==5,8] ## [1] Bovine.Meat..kcal.day. Milk..Whole..kcal.day. Potatoes..kcal.day. ## 38 Levels: Rice..Paddy.Equivalent...kcal.day.... Nazioni del gruppo world[km$cluster==5,1] ## [1] Albania Argentina Belarus ## [4] Bosnia and Herzegovina Bulgaria Chile ## [7] Georgia Mongolia Romania ## [10] Russian Federation Ukraine Uzbekistan ## 86 Levels: Albania Argentina Australia Austria Bangladesh... Uzbekistan file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 30/47

31 Plot degli alimenti a più alto consumo ## ordina gli alimenti in base ai valori del centroide nel gruppo e plotta tdt$aliments <- with(tdt, factor(tdt$aliments, levels=tdt[order(-tdt$g5), ]$Aliments)) ggplot(tdt[tdt$g5>0,],aes(aliments,g5,fill=aliments))+geom_bar(stat="identity")+ggtitle("cluster 5: Alimenti file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 31/47

32 Analisi del gruppo 6 Alimenti con consumo più elevato rispetto agli altri gruppi tdt[maxims==6,8] ## [1] Palm.Oil..kcal.day. Roots...Tuber.Dry.Equiv..kcal.day. ## [3] Starchy.Roots..kcal.day. ## 38 Levels: Milk..Whole..kcal.day.... Pulses..kcal.day. Nazioni del gruppo world[km$cluster==6,1] ## [1] Cameroon Ethiopia Ghana Liberia Madagascar ## [6] Malawi Nigeria Sierra Leone Tanzania ## 86 Levels: Albania Argentina Australia Austria Bangladesh... Uzbekistan file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 32/47

33 Plot degli alimenti a più alto consumo ## ordina gli alimenti in base ai valori del centroide nel gruppo e plotta tdt$aliments <- with(tdt, factor(tdt$aliments, levels=tdt[order(-tdt$g6), ]$Aliments)) ggplot(tdt[tdt$g6>0,],aes(aliments,g6,fill=aliments))+geom_bar(stat="identity")+ggtitle("cluster 6: Alimenti file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 33/47

34 Analisi del gruppo 7 Alimenti con consumo più elevato rispetto agli altri gruppi tdt[maxims==7,8] ## [1] Fish..Seafood..kcal.day. Honey..kcal.day. ## [3] Mutton...Goat.Meat..kcal.day. Offals..Edible..kcal.day. ## [5] Pelagic.Fish..kcal.day. Poultry.Meat..kcal.day. ## [7] Bananas..kcal.day. Coconut.Oil..kcal.day. ## [9] Coffee..kcal.day. Fruits...Excluding.Wine..kcal.day. ## 38 Levels: Roots...Tuber.Dry.Equiv..kcal.day.... Sugar...Sweeteners..kcal.day. Nazioni del gruppo world[km$cluster==7,1] ## [1] Saint Lucia Samoa ## 86 Levels: Albania Argentina Australia Austria Bangladesh... Uzbekistan file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 34/47

35 Plot degli alimenti a più alto consumo ## ordina gli alimenti in base ai valori del centroide nel gruppo e plotta tdt$aliments <- with(tdt, factor(tdt$aliments, levels=tdt[order(-tdt$g7), ]$Aliments)) ggplot(tdt[tdt$g7>0,],aes(aliments,g7,fill=aliments))+geom_bar(stat="identity")+ggtitle("cluster 7: Alimenti file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 35/47

36 World map library(rworldmap) jd=joincountrydata2map(world,joincode="name",namejoincolumn = "Countries") FALSE 86 codes from your data successfully matched countries in the map FALSE 0 codes from your data failed to match with a country code in the map FALSE 157 codes from the map weren't represented in your data mapcountrydata(jd, namecolumntoplot="cluster", catmethod="categorical",colourpalette = "rainbow",addlegend = file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 36/47

37 Commenti La mappa individua correttamente, sembra, diverse aree mondiali a dieta simile. Si potrebbe provare a ripetere l analisi con un numero maggiore di gruppi per vedere se aumenta la precisione della rappresentazione delle diverse diete nel mondo (ad esempio, in questa soluzione, non si nota la presenza di una dieta mediterranea ) Se questa soluzione è ritenuta soddisfacente, si potrebbe analizzare ulteriormente i gruppi attraverso le CP e provare ad individuare caratteristiche generali delle diete (in relazione ad esempio, all apporto calorico, i grassi etc.) file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 37/47

38 4 Clustering gerarchico: legame singolo (min) Proviamo ad utilizzare un clustering gerarchico, confrontandolo con l algoritmo k-means, e confrontando tra loro diversi metodi di aggregazione. rownames(st.food)<-world$countries distance=dist(st.food) hc=hclust(distance,method="single") file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 38/47

39 Dendrogramma plot(hc) rect.hclust(hc, k = 8) file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 39/47

40 Ottenere i gruppi # get cluster IDs groups <- cutree(hc, k = 8) Groups=as.data.table(groups,keep.rownames = TRUE) setnames(groups,"rn","counties") Groups[groups==1,] ## Counties groups ## 1: Albania 1 ## 2: Australia 1 ## 3: Austria 1 ## 4: Bangladesh 1 ## 5: Belarus 1 ## 6: Belgium 1 ## 7: Bolivia 1 ## 8: Bosnia and Herzegovina 1 ## 9: Brazil 1 ## 10: Bulgaria 1 ## 11: Cameroon 1 ## 12: Canada 1 ## 13: Chile 1 ## 14: Colombia 1 ## 15: Costa Rica 1 ## 16: Cyprus 1 ## 17: Czech Republic 1 ## 18: Denmark 1 ## 19: Dominican Republic 1 ## 20: Ecuador 1 ## 21: Egypt 1 ## 22: Estonia 1 ## 23: Ethiopia 1 ## 24: Fiji 1 ## 25: Finland 1 ## 26: France 1 ## 27: Gambia 1 ## 28: Georgia 1 ## 29: Germany 1 ## 30: Greece 1 ## 31: Guatemala 1 ## 32: Haiti 1 ## 33: Hungary 1 ## 34: Iceland 1 ## 35: India 1 ## 36: Indonesia 1 ## 37: Iran, Islamic Republic of 1 ## 38: Israel 1 ## 39: Italy 1 ## 40: Jamaica 1 ## 41: Japan 1 ## 42: Kenya 1 ## 43: Lesotho 1 ## 44: Liberia 1 ## 45: Madagascar 1 ## 46: Malawi 1 ## 47: Malaysia 1 ## 48: Malta 1 ## 49: Mauritius 1 ## 50: Mexico 1 file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 40/47

41 ## 51: Morocco 1 ## 52: Netherlands 1 ## 53: Nigeria 1 ## 54: Pakistan 1 ## 55: Paraguay 1 ## 56: Peru 1 ## 57: Philippines 1 ## 58: Poland 1 ## 59: Portugal 1 ## 60: Romania 1 ## 61: Russian Federation 1 ## 62: Saudi Arabia 1 ## 63: Senegal 1 ## 64: Sierra Leone 1 ## 65: South Africa 1 ## 66: Spain 1 ## 67: Sri Lanka 1 ## 68: Sweden 1 ## 69: Switzerland 1 ## 70: Tanzania 1 ## 71: Thailand 1 ## 72: Trinidad and Tobago 1 ## 73: Tunisia 1 ## 74: Turkey 1 ## 75: Ukraine 1 ## 76: United Arab Emirates 1 ## 77: United Kingdom 1 ## 78: United States of America 1 ## 79: Uzbekistan 1 ## Counties groups file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 41/47

42 Clustering gerarchico: metodo di Ward rownames(st.food)<-world$countries distance=dist(st.food) hc=hclust(distance,method="ward.d2") file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 42/47

43 Dendrogramma plot(hc) rect.hclust(hc, k = 8) file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 43/47

44 Ottenere i gruppi # get cluster IDs groups <- cutree(hc, k = 8) Groups=as.data.table(groups,keep.rownames = TRUE) setnames(groups,"rn","country") Groups[groups==1,] ## Country groups ## 1: Albania 1 ## 2: Argentina 1 ## 3: Bolivia 1 ## 4: Bosnia and Herzegovina 1 ## 5: Brazil 1 ## 6: Bulgaria 1 ## 7: Chile 1 ## 8: Colombia 1 ## 9: Costa Rica 1 ## 10: Dominican Republic 1 ## 11: Ecuador 1 ## 12: Fiji 1 ## 13: Georgia 1 ## 14: India 1 ## 15: Jamaica 1 ## 16: Mauritius 1 ## 17: Mexico 1 ## 18: Mongolia 1 ## 19: Pakistan 1 ## 20: Paraguay 1 ## 21: Saudi Arabia 1 ## 22: South Africa 1 ## 23: Trinidad and Tobago 1 ## 24: Uzbekistan 1 ## Country groups file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 44/47

45 Gruppo 2 Groups[groups==2,] ## Country groups ## 1: Australia 2 ## 2: Belarus 2 ## 3: Canada 2 ## 4: Cyprus 2 ## 5: Czech Republic 2 ## 6: Estonia 2 ## 7: Finland 2 ## 8: Iceland 2 ## 9: Israel 2 ## 10: Malta 2 ## 11: New Zealand 2 ## 12: Poland 2 ## 13: Romania 2 ## 14: Russian Federation 2 ## 15: Sweden 2 ## 16: Ukraine 2 ## 17: United Arab Emirates 2 ## 18: United Kingdom 2 ## 19: United States of America 2 file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 45/47

46 World map world=data.frame(world,"cluster.ward"=groups) jd=joincountrydata2map(world,joincode="name",namejoincolumn = "Countries") FALSE 86 codes from your data successfully matched countries in the map FALSE 0 codes from your data failed to match with a country code in the map FALSE 157 codes from the map weren't represented in your data mapcountrydata(jd, namecolumntoplot="cluster.ward", catmethod="categorical",colourpalette = "rainbow",addleg file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 46/47

47 Commenti L utilizzo del legame singolo non sembra appropriato per il problema in esame. Il metodo di Ward fornisce una risposta molto simile a k-means. A differenza di k-means, sembra individuare una dieta mediterranea. Se vogliamo utilizzare k-means vale la pena utilizzare più di 7 gruppi. Il clustering gerarchico ci permette di variare il numero di gruppi individuati tagliando (con linee orizzontali) opportunamente il dendrogramma L algortmo k-means, fornendo i centroidi dei gruppi permette un analisi più approfondita delle loro caratteristiche file:///c:/users/emanuele.taufer/google%20drive/2%20corsi/3%20sqg/labs/l-10_cluster_analysis_food-df.html#(1) 47/47