Clustering K-means CLARA
Islam Islamov
2/7/2022
The dataset that I used was taken from here –> https://www.kaggle.com/jackdaoud/marketing-data
The data is from a shop, that operates both online and offline, including catalogues too. Below 2 methods have been performed on this dataset –> Kmeans and Clara. In both cases the results were almost the same, meaning that the optimal number of clusters were chosen correctly.
As for the additional information for the data, it was provided within the codes. Overall, it contains Incomes,Number of complaints,Number of online/offline purchases, Different products and number of times they were purchased(meat,fruits,fish etc.)
You will see how different columns were renamed or completely changed and been saved in new columns.
marketing <-read.csv("C:\\Users\\Lelo\\Desktop\\marketing_data.csv")I used following libraries, in order to work with the dataset.
library(ClusterR)## Loading required package: gtoolslibrary(factoextra)## Loading required package: ggplot2## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(flexclust)## Loading required package: grid## Loading required package: lattice## Loading required package: modeltools## Loading required package: stats4library(fpc)
library(clustertend)
library(cluster)
library(ClusterR)
library(pdp)marketing$AcceptedCmp1 <- NULL
marketing$AcceptedCmp2 <- NULL
marketing$AcceptedCmp3 <- NULL
marketing$AcceptedCmp4 <- NULL
marketing$AcceptedCmp5 <- NULL
marketing$MntGoldProds <- NULL
marketing$Response <- NULL
marketing$Dt_Customer <- NULL
marketing$Country <- NULLBecause I can not clearly see what is the name of first column I will change the name to just customerID.
colnames(marketing)[1] <- "customerID"Also I will replace NumDealsPurchases with DiscountedPurchases.
colnames(marketing)[colnames(marketing) == "NumDealsPurchases"] <- "DiscountedPurchases"Next I need the age of customers (2021-the birth year).
marketing$age <- 2021 - marketing$Year_Birth
marketing$Year_Birth <- NULL
table(marketing$age)##
## 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
## 2 5 3 5 13 15 18 30 29 27 42 32 38 42 45 39 39 53 77 52
## 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
## 89 83 69 74 79 87 77 71 51 44 50 74 42 45 44 36 49 51 53 43
## 65 66 67 68 69 70 71 72 73 74 75 76 77 78 80 81 121 122 128
## 55 49 50 35 52 43 29 30 21 16 16 8 7 7 1 1 1 1 1Now I will eliminate those customers with “unrealistic” ages like 100 or above, if you want you can remove those below too, based on your research.
marketing <- marketing[!(marketing$age=="121" | marketing$age=="122" | marketing$age=="128"), ]Lets look at our rows once more and find what we can eliminate next or change. We can see some rows like Education, which we will not need since we will not focus on it.
marketing$Education <- NULLWe can see row called MartialStatus which we can change a bit and replace it with another row, that will represent those in a relation with 1 and others with 0.
marketing$partner <- ifelse(marketing$Marital_Status == "Married" | marketing$Marital_Status == "Together", 1, 0) Since we have kind of identical columns, we can get rid of the former(MartialStatus).
marketing$Marital_Status <- NULLNow lets look at other rows such as Income. We need to make it numeric for later.
marketing$Income <- substr(marketing$Income, 2, nchar(marketing$Income))Now if we look at our data we can see that $ signs are not there anymore. After that we will make our Income numbers even easier to read(no . or , in them).
marketing$Income <- sapply(marketing$Income, function(v) {as.numeric(gsub("\\,","", (v)))})Later we can check the min and maximum amounts of Income.
max(marketing$Income, na.rm = T)## [1] 666666min(marketing$Income, na.rm = T)## [1] 1730median(marketing$Income, na.rm = T)## [1] 51373sum(is.na(marketing$Income))## [1] 24mean(marketing$Income, na.rm = T)## [1] 52236.58UPDATE: Since I did not know I used the previous codes, but I learnt this one too.
Or we can just use following function.
summary(marketing$Income)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 1730 35246 51373 52237 68487 666666 24Now we can see that there are income numbers that are big- like 150-160k or +. But the one that grabs attention is the following one - 666 666. We presume that it is an outlier since it is too huge .
max(marketing$Income, na.rm = T)## [1] 666666So we will delete it, also we can get rid of all the NA values.
marketing <- marketing[!(marketing$Income == "666666"), ]
marketing <- na.omit(marketing)Now we will make our data even smaller with the help of gathering up all children in one column, regardless of “type”.
marketing$Number_of_kids <- marketing$Kidhome + marketing$Teenhome
marketing$Kidhome <- NULL
marketing$Teenhome <- NULL
summary(marketing)## customerID Income Recency MntWines
## Min. : 0 Min. : 1730 Min. : 0.00 Min. : 0.0
## 1st Qu.: 2815 1st Qu.: 35234 1st Qu.:24.00 1st Qu.: 24.0
## Median : 5454 Median : 51371 Median :49.00 Median : 175.5
## Mean : 5585 Mean : 51959 Mean :49.02 Mean : 305.3
## 3rd Qu.: 8418 3rd Qu.: 68487 3rd Qu.:74.00 3rd Qu.: 505.0
## Max. :11191 Max. :162397 Max. :99.00 Max. :1493.0
## MntFruits MntMeatProducts MntFishProducts MntSweetProducts
## Min. : 0.00 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.: 2.00 1st Qu.: 16.0 1st Qu.: 3.00 1st Qu.: 1.00
## Median : 8.00 Median : 68.0 Median : 12.00 Median : 8.00
## Mean : 26.33 Mean : 167.0 Mean : 37.65 Mean : 27.05
## 3rd Qu.: 33.00 3rd Qu.: 232.2 3rd Qu.: 50.00 3rd Qu.: 33.00
## Max. :199.00 Max. :1725.0 Max. :259.00 Max. :262.00
## DiscountedPurchases NumWebPurchases NumCatalogPurchases NumStorePurchases
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 1.000 1st Qu.: 2.000 1st Qu.: 0.000 1st Qu.: 3.000
## Median : 2.000 Median : 4.000 Median : 2.000 Median : 5.000
## Mean : 2.325 Mean : 4.088 Mean : 2.672 Mean : 5.807
## 3rd Qu.: 3.000 3rd Qu.: 6.000 3rd Qu.: 4.000 3rd Qu.: 8.000
## Max. :15.000 Max. :27.000 Max. :28.000 Max. :13.000
## NumWebVisitsMonth Complain age partner
## Min. : 0.000 Min. :0.000000 Min. :25.00 Min. :0.0000
## 1st Qu.: 3.000 1st Qu.:0.000000 1st Qu.:44.00 1st Qu.:0.0000
## Median : 6.000 Median :0.000000 Median :51.00 Median :1.0000
## Mean : 5.321 Mean :0.009042 Mean :52.09 Mean :0.6456
## 3rd Qu.: 7.000 3rd Qu.:0.000000 3rd Qu.:62.00 3rd Qu.:1.0000
## Max. :20.000 Max. :1.000000 Max. :81.00 Max. :1.0000
## Number_of_kids
## Min. :0.0000
## 1st Qu.:0.0000
## Median :1.0000
## Mean :0.9476
## 3rd Qu.:1.0000
## Max. :3.0000ncol(marketing)## [1] 17nrow(marketing)## [1] 2212Now for clustering we need to check if our data is clusterable at all. Since we will no need our id column we will add the rest to our new data - cluster as you showed in K-Means & PAM - codes (html)File.
cluster <- marketing[2:17]Scaling data - we have different variables
cluster_z <- as.data.frame(lapply(cluster, scale))Check data with Hopkins statistics, if close to 1 then the data is clusterable if not then vice versa
get_clust_tendency(cluster_z, 2, graph= FALSE)## $hopkins_stat
## [1] 0.8799351
##
## $plot
## NULLWe can see it on graph too.
get_clust_tendency(cluster_z, 2, graph=TRUE, gradient=list(low="red", mid="white", high="blue"), seed = 123)## $hopkins_stat
## [1] 0.8799351
##
## $plot
# or
di<-dist(cluster_z, method="euclidean")
fviz_dist(di, show_labels = FALSE)+ labs(title="our data")
We can see that it is close to 1, so, obviously it will be clusterable Also when looking at the graph we can clearly see blocks of specific colored lines meaning that most probably the dataset is clusterable
Lets check it as SILHOUETTE INDEX method too:
# Number 1 - Kmeans
a <- fviz_nbclust(cluster_z, FUNcluster = kmeans, method = "silhouette") + theme_classic() + ggtitle("optimal numbers of clusters - kmeans")# Number 2 - Clara
b <- fviz_nbclust(cluster_z, FUNcluster = cluster::clara, method = "silhouette") + theme_classic() + ggtitle("optimal numbers of clusters - CLARA")
grid.arrange(a,b, ncol=1)
Variance explained and AIC method Optimal number of clusters - elbow
opt2<-Optimal_Clusters_KMeans(cluster_z, max_clusters=10, plot_clusters = TRUE)
opt3<-Optimal_Clusters_KMeans(cluster_z, max_clusters=10, plot_clusters=TRUE, criterion="AIC")
We saw earlier that best number of clusters is 2, however we may also put is as 3 or even 4 Due to the size of our data it will be in our interest to segment it in many clusters. Optimal number being 3.
KMEANS_3 <- kmeans(cluster_z, 3)
fviz_cluster(list(data=cluster_z, cluster=KMEANS_3$cluster),
ellipse.type="norm", geom="point", stand=FALSE, palette="jco", ggtheme=theme_classic())
Better graphics(from Lecture)
fviz_cluster(list(data=cluster_z, cluster=KMEANS_3$cluster), geom = "point", ellipse.type = "norm") 
fviz_cluster(list(data=cluster_z, cluster=KMEANS_3$cluster), geom = "point", ellipse.type = "convex")
Silhouette plot
sil<-silhouette(KMEANS_3$cluster, dist(cluster_z))
fviz_silhouette(sil)## cluster size ave.sil.width
## 1 1 1010 0.32
## 2 2 603 0.11
## 3 3 599 0.13
We can see 3 groups(clusters) Also we know that the closer the output to 1 is the better for us Meaning that group elements are in right cluster In our case it is first group 0.32 The others however, are very close to 0 meaning that the group(sample) is on the border of two clusters and it is unknown to which it really belongs
We already saw some info regarding the clusters as: number of clusters - 3 size of clusters - 1010,603 and 599 respectively average silhouette width - 0.32 , 0.11 , 0.13 respectively in order
But we may look at other info too such as: Average(mean) characteristics of our clusters based on different columns as a boxplot:
groupBWplot(cluster_z, KMEANS_3$cluster, alpha=0.05)
or we may calculate the average for each of them separately and see as numbers to which cluster they are assigned:
KMEANS_3$cluster## [1] 3 2 1 1 1 3 3 1 2 2 3 1 3 1 2 1 1 1 1 1 2 2 1 2 2 1 2 2 1 3 2 3 1 2 1 3 3
## [38] 1 3 3 1 2 3 1 1 3 1 2 2 2 1 3 1 3 1 1 1 1 3 2 1 1 1 1 2 1 2 3 1 1 3 3 2 1
## [75] 3 3 1 3 3 1 3 3 2 2 1 1 1 1 3 1 1 3 1 3 3 1 1 1 3 2 2 3 2 2 2 2 2 2 3 3 2
## [112] 1 1 1 1 2 2 2 3 2 2 3 1 1 2 2 1 2 3 3 3 2 1 1 3 1 3 1 1 1 3 3 2 1 1 1 1 1
## [149] 2 2 3 3 1 3 1 1 1 1 1 3 1 1 3 2 1 3 2 2 3 3 2 1 3 3 3 2 2 1 1 2 2 1 3 1 1
## [186] 1 2 3 1 3 3 1 2 3 2 2 2 2 2 2 2 2 2 2 2 1 2 3 1 3 1 1 1 1 1 2 1 2 3 1 2 3
## [223] 3 1 3 2 3 1 2 2 2 2 1 1 1 1 1 3 1 3 1 1 2 1 1 1 2 2 2 1 2 2 2 1 1 3 3 3 3
## [260] 2 1 2 2 1 1 1 1 2 1 1 2 1 3 2 2 3 1 1 1 2 2 3 1 3 1 1 2 3 2 3 3 3 1 3 1 1
## [297] 2 1 3 3 2 1 1 3 1 3 3 1 1 1 1 3 3 2 3 2 1 3 2 1 1 3 1 3 3 1 1 1 3 1 1 1 2
## [334] 3 1 1 3 2 3 2 3 2 2 1 2 1 3 1 1 1 1 3 1 1 1 1 1 2 1 3 1 1 1 1 1 1 1 1 2 1
## [371] 1 1 1 1 3 1 1 1 2 1 2 1 1 3 1 2 3 2 1 1 1 1 1 2 1 1 3 2 1 3 3 2 3 1 2 2 2
## [408] 2 3 1 1 3 3 3 1 1 3 1 2 2 3 2 3 3 1 3 1 2 1 3 2 3 3 3 3 3 1 1 3 1 2 3 1 1
## [445] 1 2 2 1 3 1 1 1 1 1 1 2 1 3 1 2 1 3 1 1 1 3 3 2 2 1 2 2 3 1 1 1 2 1 3 3 3
## [482] 3 2 3 2 2 2 3 3 2 1 2 1 3 2 1 2 2 2 1 1 2 2 1 1 1 1 1 2 1 1 1 3 3 2 1 1 2
## [519] 1 3 2 2 1 1 1 2 3 3 3 3 3 1 3 1 1 1 2 1 1 1 1 1 1 1 1 1 3 3 2 2 2 2 2 2 2
## [556] 1 1 1 1 2 1 1 1 1 1 2 1 3 3 1 3 1 2 2 2 1 3 3 2 1 3 3 2 1 1 2 1 1 2 1 3 1
## [593] 1 1 3 1 2 1 2 3 2 2 1 1 3 2 3 3 3 1 3 3 1 2 3 3 3 1 1 1 1 3 1 1 1 2 1 2 2
## [630] 3 2 3 3 2 3 1 1 1 1 1 1 1 2 2 3 3 1 2 1 3 2 2 2 3 1 1 1 1 2 2 3 3 3 3 3 3
## [667] 2 1 1 1 2 2 2 3 3 2 1 3 2 3 2 1 1 2 1 1 1 2 3 3 2 2 1 1 1 1 1 3 1 2 2 1 3
## [704] 3 3 2 2 1 1 1 1 3 1 2 3 2 3 1 2 1 1 1 1 1 1 2 2 1 1 1 2 3 1 3 3 1 3 1 2 1
## [741] 2 3 2 2 1 1 1 3 2 2 1 3 2 3 3 1 2 2 1 1 1 3 3 1 1 3 1 2 1 1 2 3 1 1 1 2 1
## [778] 1 1 2 3 1 1 1 1 1 3 2 2 2 2 2 3 1 2 3 1 3 2 3 1 2 3 2 3 3 1 1 3 1 2 2 3 1
## [815] 1 3 1 1 2 3 3 1 3 3 3 1 2 1 3 1 1 1 1 3 1 2 1 2 1 1 1 2 1 2 1 1 3 1 1 1 2
## [852] 2 1 2 2 1 3 3 1 2 3 3 1 2 1 2 1 1 1 3 3 1 1 3 2 2 2 1 3 1 1 1 1 1 1 1 1 1
## [889] 1 1 2 2 2 2 2 2 3 1 1 1 3 3 3 1 1 1 1 1 2 2 1 1 2 2 2 1 1 3 2 1 1 2 1 3 3
## [926] 2 3 3 3 1 2 1 2 1 2 1 3 3 1 3 1 3 1 3 1 1 1 2 1 2 3 3 3 2 3 2 1 1 1 3 1 1
## [963] 1 3 2 2 2 1 1 1 3 1 1 1 1 1 1 1 3 3 2 2 3 1 3 2 3 1 1 1 2 3 2 1 1 2 1 2 3
## [1000] 3 1 2 2 3 1 1 3 1 1 1 2 3 3 3 1 3 1 1 1 2 2 1 2 1 1 1 2 1 1 2 2 2 3 2 3 3
## [1037] 2 2 1 1 1 1 2 3 3 3 2 3 3 1 1 1 1 1 1 1 1 3 3 1 1 2 1 1 1 1 2 2 2 1 1 2 2
## [1074] 1 3 3 3 2 2 2 3 3 1 3 1 1 1 1 1 3 1 1 1 1 1 3 2 1 1 2 1 1 2 1 2 1 1 1 1 1
## [1111] 2 1 2 3 1 1 1 2 2 2 2 1 3 3 1 1 3 1 2 3 1 3 1 1 2 1 2 2 1 1 1 1 2 2 2 1 2
## [1148] 3 3 3 2 1 2 1 1 1 3 2 1 1 2 2 1 1 1 3 3 2 1 2 2 1 2 1 1 1 3 1 1 1 2 1 1 1
## [1185] 2 3 3 2 1 3 2 1 1 1 1 3 3 2 2 1 3 2 1 3 3 2 2 1 1 1 1 1 1 3 3 3 1 1 1 1 3
## [1222] 3 3 3 2 1 3 1 2 2 3 2 3 1 1 2 1 1 1 1 1 1 1 2 3 2 2 2 2 3 1 2 2 2 1 3 3 3
## [1259] 1 1 2 3 1 2 3 3 3 1 2 2 2 1 1 3 3 1 1 1 2 3 2 2 3 1 3 3 1 2 2 3 1 2 3 3 1
## [1296] 3 3 1 1 2 2 3 3 3 2 1 2 2 2 3 2 1 1 1 1 1 1 2 3 3 3 3 1 3 3 3 3 2 2 1 2 1
## [1333] 1 1 2 2 3 3 1 2 1 3 3 1 1 3 2 2 3 3 1 2 1 3 3 3 1 2 1 1 2 2 2 2 2 3 1 1 1
## [1370] 2 3 3 1 1 3 3 2 3 3 1 3 3 1 2 1 3 1 1 3 3 2 2 2 3 3 1 1 1 2 2 3 1 2 2 2 1
## [1407] 1 2 1 2 2 2 1 1 2 2 3 1 2 1 2 2 2 2 2 1 1 1 1 3 3 3 2 2 2 3 2 2 2 1 1 3 2
## [1444] 1 3 1 2 1 1 1 1 1 1 1 2 1 1 1 3 3 2 1 2 2 1 2 3 1 1 1 1 1 2 2 3 3 3 1 2 3
## [1481] 3 1 1 1 2 2 1 3 3 1 2 2 3 2 3 1 3 1 1 3 3 2 3 1 1 1 2 1 2 2 2 2 1 3 1 3 3
## [1518] 1 1 3 1 1 1 1 3 3 1 2 3 1 1 3 1 2 2 3 3 2 1 3 2 1 3 1 3 2 2 3 2 2 2 1 3 3
## [1555] 2 3 3 1 2 2 2 3 2 2 1 2 1 2 1 2 3 2 1 1 1 1 1 1 3 2 1 1 1 1 3 1 1 2 2 2 3
## [1592] 1 1 1 2 1 3 1 2 3 3 3 2 3 1 1 1 1 3 1 1 3 1 1 2 2 3 3 2 2 1 1 2 2 3 2 3 3
## [1629] 1 2 3 1 2 3 3 3 3 3 3 3 1 3 3 2 2 3 1 1 2 1 1 1 1 3 2 1 3 2 2 1 1 1 3 2 1
## [1666] 1 2 2 3 2 3 2 1 3 3 1 1 1 1 1 1 3 3 1 2 1 1 1 1 1 1 1 1 1 2 1 1 3 1 3 2 2
## [1703] 1 1 1 1 1 1 2 1 1 1 1 1 1 3 1 3 3 1 2 1 3 2 1 2 1 1 1 1 1 2 1 1 3 1 1 1 1
## [1740] 3 3 3 3 1 1 1 1 3 2 3 2 3 3 2 2 3 3 2 2 2 1 1 1 1 1 3 1 3 1 1 3 3 3 1 3 1
## [1777] 1 2 1 1 1 2 1 2 1 1 1 1 1 1 2 2 3 2 3 2 1 1 3 2 2 2 1 1 1 1 1 1 3 2 2 3 1
## [1814] 1 1 2 3 1 1 1 3 2 2 2 2 2 2 3 2 3 1 1 1 1 3 1 1 3 1 1 2 1 1 3 3 1 1 2 1 1
## [1851] 1 1 3 1 3 1 1 1 1 2 3 1 1 3 3 2 2 2 2 2 1 1 3 1 1 1 1 1 3 3 1 1 1 1 3 2 3
## [1888] 2 1 2 2 3 3 1 3 3 1 2 3 3 3 3 2 1 1 2 1 1 3 3 3 1 1 3 1 2 3 1 1 3 1 1 2 3
## [1925] 1 1 1 1 1 1 1 1 1 1 1 1 2 3 1 1 3 3 3 3 2 2 1 2 1 1 3 2 2 2 3 3 2 3 1 3 1
## [1962] 1 1 1 1 3 2 3 3 2 2 2 1 2 3 1 1 3 3 1 1 2 3 1 2 1 1 3 2 1 1 1 1 2 1 3 1 3
## [1999] 1 1 3 2 3 1 1 1 1 2 1 1 2 2 3 3 2 2 3 1 1 3 1 3 2 1 1 2 2 1 1 1 2 3 3 2 1
## [2036] 1 3 3 1 2 1 1 2 3 1 2 1 2 1 1 3 3 3 3 3 3 2 1 1 1 1 1 2 2 2 1 1 3 3 3 1 2
## [2073] 2 2 1 3 1 1 1 3 3 3 2 2 2 3 3 1 3 2 1 2 1 1 1 3 1 1 1 1 1 3 1 1 1 3 2 1 2
## [2110] 1 1 1 2 3 2 1 3 1 1 2 3 1 1 2 2 3 3 1 2 3 3 1 3 1 1 1 1 2 1 1 3 3 2 2 1 1
## [2147] 1 1 2 2 1 3 3 3 1 2 1 1 3 1 1 1 2 3 1 2 1 1 3 3 3 1 2 1 2 1 1 3 1 3 3 3 2
## [2184] 2 1 3 3 1 3 2 2 2 3 1 1 1 3 1 1 3 2 1 1 1 1 1 2 2 1 1 3 3Their sizes
KMEANS_3$size## [1] 1010 603 599Center of clusters
KMEANS_3$centers## Income Recency MntWines MntFruits MntMeatProducts MntFishProducts
## 1 -0.8011642 0.01615891 -0.7883576 -0.5407587 -0.6472894 -0.5610513
## 2 0.2546222 -0.04479088 0.4890158 -0.1461561 -0.1523677 -0.1926934
## 3 1.0945553 0.01784375 0.8370026 1.0589289 1.2448081 1.1399932
## MntSweetProducts DiscountedPurchases NumWebPurchases NumCatalogPurchases
## 1 -0.5380002 -0.1851260 -0.7427176 -0.7267831
## 2 -0.1580878 0.8111058 0.8332688 0.1028930
## 3 1.0662890 -0.5043732 0.4134953 1.1218805
## NumStorePurchases NumWebVisitsMonth Complain age partner
## 1 -0.8127355 0.4573161 0.02999220 -0.23050169 -0.002121785
## 2 0.5589274 0.2585598 -0.02543459 0.32906910 0.047560858
## 3 0.8077289 -1.0313870 -0.02496672 0.05739239 -0.044300825
## Number_of_kids
## 1 0.3672128
## 2 0.3332878
## 3 -0.9546870Lets look at more results
mean values of Income for all variables in dataset for each cluster
aggregate(data = marketing, Income ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster Income
## 1 1 34711.93
## 2 2 57440.13
## 3 3 75521.61mean values of Recency of purchase for all variables in dataset for each cluster
aggregate(data = marketing, Recency ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster Recency
## 1 1 49.48713
## 2 2 47.72305
## 3 3 49.53589TYPES OF PURCHASES
mean number of puchases online(Web purchases)
aggregate(data = marketing, NumWebPurchases ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster NumWebPurchases
## 1 1 2.051485
## 2 2 6.373134
## 3 3 5.222037mean number of puchases from catalogue
aggregate(data = marketing, NumCatalogPurchases ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster NumCatalogPurchases
## 1 1 0.5445545
## 2 2 2.9734660
## 3 3 5.9565943mean number of puchases from store itself(on site purchases)
aggregate(data = marketing, NumStorePurchases ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster NumStorePurchases
## 1 1 3.164356
## 2 2 7.623549
## 3 3 8.432387Number of average visits for variables of each cluster
aggregate(data = marketing, NumWebVisitsMonth ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster NumWebVisitsMonth
## 1 1 6.430693
## 2 2 5.948590
## 3 3 2.819699Mean number of complaints
aggregate(data = marketing, Complain ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster Complain
## 1 1 0.011881188
## 2 2 0.006633499
## 3 3 0.006677796We can also see average age by clusters too
aggregate(data = marketing, age ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster age
## 1 1 49.38911
## 2 2 55.93698
## 3 3 52.75793Mean number of people who have family or in a relationship
aggregate(data = marketing, partner ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster partner
## 1 1 0.6445545
## 2 2 0.6683250
## 3 3 0.6243740Mean number of kids that we summed previously
aggregate(data = marketing, Number_of_kids ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster Number_of_kids
## 1 1 1.2227723
## 2 2 1.1973466
## 3 3 0.2320534Mean number of discounted purchases
aggregate(data = marketing, DiscountedPurchases ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster DiscountedPurchases
## 1 1 1.968317
## 2 2 3.885572
## 3 3 1.353923MEAN NUMBER DIFFERENT PRODUCTS
mean values of Amount spent on Wine of purchase for all variables in dataset for each cluster
aggregate(data = marketing, MntWines ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster MntWines
## 1 1 39.35644
## 2 2 470.24378
## 3 3 587.62771Mean of fruits purchased
aggregate(data = marketing, MntFruits ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster MntFruits
## 1 1 4.837624
## 2 2 20.520730
## 3 3 68.415693Mean of meat products purchased
aggregate(data = marketing, MntMeatProducts ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster MntMeatProducts
## 1 1 21.87228
## 2 2 132.86070
## 3 3 446.18364Mean of fish purchased
aggregate(data = marketing, MntFishProducts ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster MntFishProducts
## 1 1 6.918812
## 2 2 27.094527
## 3 3 100.088481Mean of sweet products purchased
aggregate(data = marketing, MntSweetProducts ~ KMEANS_3$cluster, mean)## KMEANS_3$cluster MntSweetProducts
## 1 1 4.939604
## 2 2 20.550580
## 3 3 70.861436Now let’s conclude all what we saw previously
First, we can easily state that best group among our clusters is the 3rd one as: They have : least amount of complaints on average 0.006 the biggest number of purchases on average in the store 8.432 the biggest number of catalogue purchases 5.956 the second most web purchases on average 5.222 highest incomes on average 75521.61 highest mean number of recent purchases 49.5 lowest mean number of discounted purchases 1.353923 They buy the most products and in biggest volume
Second group is mostly the one who has everything in between 1st and 3rd groups:
The lowest number of recent purchases 47.723 The most purchases with discount( way ahead of others) 3.885 Relatively high number of purchases in store 7.623 Mostly buy online 6.373 All in all it is visible that they buy somewhere between the 1st and 3rd group in almost all parameters
First group :
They are making up the biggest average among those who like to complain They are visiting the shop the most, however still buy the least Spend the least Earn the least When they decide to buy, they buy wine. Basically, people who buy wine and like to complain.
Now lets do the clustering but with a different method - CLARA. Esentially we will have to do same steps as before but adjusted for CLARA
clara_3 <- eclust(cluster_z,'clara',k=3,hc_metric = 'euclidean', graph = FALSE)
plot_clara_3 <- fviz_cluster(clara_3, geom = c("point")) + ggtitle('CLARA with 3 clusters')
plot_clara_3
summary(clara_3)## Object of class 'clara' from call:
## fun_clust(x = x, k = k)
## Medoids:
## Income Recency MntWines MntFruits MntMeatProducts
## [1,] 1.3795608 0.69033883 0.1740542 0.3439618 1.1503456
## [2,] 0.3187672 -0.17342426 0.6157674 -0.3102242 -0.0581029
## [3,] -0.8588085 -0.06977269 -0.7775561 -0.6121562 -0.6244238
## MntFishProducts MntSweetProducts DiscountedPurchases NumWebPurchases
## [1,] 2.1973124 0.8019625 -0.6882765 -0.3968204
## [2,] -0.3404791 -0.6582115 -0.6882765 1.7912144
## [3,] -0.6873715 -0.4391854 0.3509506 -0.3968204
## NumCatalogPurchases NumStorePurchases NumWebVisitsMonth Complain
## [1,] 0.4535402 0.6747250 -1.7815938 -0.0954985
## [2,] -0.2296269 0.9823285 0.2797544 -0.0954985
## [3,] -0.9127940 -0.5556886 0.6920240 -0.0954985
## age partner Number_of_kids
## [1,] -0.007379094 -1.3492980 -1.26431204
## [2,] 1.103580215 0.7407911 0.06997147
## [3,] -0.349212728 0.7407911 0.06997147
## Objective function: 3.305778
## Numerical information per cluster:
## size max_diss av_diss isolation
## [1,] 503 13.95248 4.289437 2.568499
## [2,] 483 11.64255 3.687221 3.016241
## [3,] 1226 11.08847 2.751931 2.872696
## Average silhouette width per cluster:
## [1] 0.09493994 0.11401638 0.31694491
## Average silhouette width of best sample: 0.2221515
##
## Best sample:
## [1] 10 56 197 206 356 416 418 422 458 535 680 732 781 795 844
## [16] 863 884 930 955 966 981 1024 1053 1118 1168 1209 1355 1418 1540 1652
## [31] 1681 1719 1736 1758 1772 1775 1858 1912 1939 1948 1955 2096 2109 2111 2157
## [46] 2195
## Clustering vector:
## [1] 1 2 3 3 3 1 2 3 2 2 1 3 1 3 2 3 3 3 3 3 3 3 3 3 2 3 2 2 3 1 3 1 3 3 3 1 1
## [38] 3 1 1 3 2 1 3 3 1 3 2 2 3 3 1 3 1 3 3 3 3 1 3 3 3 3 3 3 3 2 1 3 3 1 1 3 3
## [75] 1 2 3 2 1 3 1 1 3 2 3 3 3 3 2 3 3 1 3 1 2 3 3 3 1 2 2 1 3 3 3 2 2 2 1 1 2
## [112] 3 3 3 3 2 2 2 1 1 2 1 3 3 2 3 3 2 2 1 1 2 3 3 1 3 1 3 3 3 1 1 2 3 3 3 3 3
## [149] 2 2 1 1 3 2 3 3 3 3 3 1 3 3 2 2 3 1 2 3 1 2 3 3 1 1 1 3 2 3 3 3 3 3 2 3 3
## [186] 3 2 1 3 1 1 3 2 2 2 2 2 3 2 2 2 2 3 3 3 3 3 1 3 2 3 3 3 3 3 2 3 3 1 3 3 2
## [223] 2 3 2 3 2 3 3 2 2 2 3 3 3 3 3 2 3 1 3 3 2 3 3 3 3 2 2 3 3 3 2 3 3 1 1 1 1
## [260] 2 3 3 3 3 3 3 3 3 3 3 2 3 2 2 3 2 3 3 3 3 3 2 3 1 3 3 2 1 2 2 2 1 3 1 3 3
## [297] 2 3 1 1 2 3 3 1 3 1 1 3 3 3 3 1 1 3 1 2 3 1 2 3 3 1 3 1 1 3 3 3 1 3 3 3 3
## [334] 1 3 3 2 2 1 2 1 2 2 3 3 3 1 3 3 3 3 1 3 3 3 3 3 2 3 1 3 3 3 3 3 3 3 3 2 3
## [371] 3 3 3 3 1 3 3 3 3 3 2 3 3 1 3 3 2 2 3 3 3 3 3 2 3 3 1 3 3 2 2 2 1 3 2 2 2
## [408] 2 2 3 3 1 1 1 3 3 1 3 2 3 2 3 2 2 3 1 3 2 3 1 2 1 1 2 1 1 3 3 1 3 2 1 3 3
## [445] 3 3 3 3 1 3 3 3 3 3 3 3 3 2 3 3 3 2 3 3 3 1 2 3 2 3 3 3 1 3 3 3 2 3 2 1 2
## [482] 2 2 1 2 2 2 1 2 3 3 2 3 1 3 3 2 2 2 3 3 2 3 3 3 3 3 3 2 3 3 3 1 1 2 3 3 2
## [519] 3 1 2 2 3 3 3 2 1 1 1 2 2 3 1 3 3 3 2 3 3 3 3 3 3 3 3 3 2 2 2 3 3 2 2 2 2
## [556] 3 3 3 3 2 3 3 3 3 3 2 3 1 1 3 2 3 2 2 3 3 1 1 3 3 1 1 2 3 3 2 3 3 3 3 2 3
## [593] 3 3 1 3 3 3 2 1 3 3 3 3 2 2 1 1 1 3 1 1 3 2 2 1 2 3 3 3 3 1 3 3 3 2 3 2 2
## [630] 1 3 1 1 2 1 3 3 3 3 3 3 3 3 2 1 1 3 3 3 1 3 3 2 2 3 3 3 3 2 1 1 2 1 1 1 1
## [667] 2 3 3 3 1 2 3 1 1 2 3 2 2 1 2 3 3 2 3 3 3 2 1 1 2 3 3 3 3 3 3 2 3 3 3 3 1
## [704] 1 1 3 3 3 3 3 3 1 3 3 1 1 1 3 3 3 3 3 3 3 3 2 2 3 3 3 2 1 3 1 1 3 1 3 2 2
## [741] 3 1 3 3 3 3 3 2 3 3 3 1 3 1 1 3 2 2 3 3 3 1 1 3 3 1 3 2 3 3 2 1 3 3 3 2 3
## [778] 3 3 3 2 3 3 3 3 3 2 2 2 2 2 3 1 3 3 1 3 1 3 1 3 3 1 2 1 1 3 3 1 3 1 2 1 3
## [815] 3 1 3 3 3 2 2 3 1 1 1 3 3 3 2 3 3 3 3 1 3 2 3 3 3 3 3 2 3 3 1 3 1 3 3 3 2
## [852] 2 3 2 2 3 2 1 3 2 2 1 3 3 3 3 3 3 3 1 1 3 3 1 2 2 3 3 3 3 3 3 3 3 3 3 3 3
## [889] 3 3 3 2 2 2 2 2 1 3 3 3 2 1 1 3 3 3 3 3 2 2 3 3 2 3 2 3 3 1 2 3 3 2 3 1 1
## [926] 3 1 1 1 3 2 3 3 3 3 3 2 1 3 1 3 1 3 2 3 3 3 2 3 2 1 1 1 3 1 3 3 3 3 2 3 3
## [963] 3 1 2 2 3 3 3 3 1 3 3 3 3 3 3 3 2 2 2 2 1 3 1 3 1 3 3 3 2 1 2 3 3 2 3 3 1
## [1000] 1 3 2 2 2 3 3 1 3 3 3 2 1 2 2 3 2 3 3 3 2 2 3 3 3 3 3 1 3 3 2 3 3 1 3 1 1
## [1037] 3 2 3 3 3 3 3 1 1 3 2 1 1 3 3 3 3 3 3 3 3 1 1 3 3 3 3 3 3 3 3 2 3 3 3 2 2
## [1074] 3 2 2 2 2 2 2 1 1 3 1 3 3 3 3 3 1 3 3 3 3 3 2 2 3 3 3 3 3 2 3 2 3 3 3 3 3
## [1111] 2 3 2 2 3 3 3 3 3 3 3 3 1 2 3 3 3 3 3 2 3 1 3 3 3 3 2 2 3 3 3 3 3 2 2 3 2
## [1148] 1 1 2 2 3 3 3 3 3 1 3 3 3 3 3 3 3 3 1 1 3 3 2 2 3 2 3 3 3 1 3 3 3 2 3 3 3
## [1185] 3 1 1 2 3 1 2 3 3 3 3 1 1 2 2 3 1 1 3 1 1 2 2 3 3 3 3 3 3 1 1 1 3 3 3 3 1
## [1222] 1 1 1 3 3 1 3 3 2 1 3 1 3 3 2 3 3 3 3 3 3 3 2 1 3 2 2 2 1 3 2 2 2 3 1 1 2
## [1259] 3 3 3 2 3 3 1 1 1 3 3 1 1 3 3 3 1 3 3 3 3 1 2 2 1 3 1 2 3 3 3 2 3 2 1 1 3
## [1296] 2 1 3 3 3 3 1 1 1 2 3 1 2 2 1 2 3 3 3 3 3 3 2 1 2 1 1 3 1 1 2 1 2 2 3 2 3
## [1333] 3 3 2 2 1 2 3 2 3 1 1 3 3 1 3 3 1 1 3 2 3 1 1 1 3 2 3 3 2 2 3 3 2 1 3 3 3
## [1370] 2 2 2 3 3 2 1 3 1 1 3 1 1 3 2 3 1 3 3 1 1 2 2 3 1 1 3 3 3 2 2 1 3 2 2 2 3
## [1407] 3 2 3 3 2 2 3 3 3 2 1 3 2 3 3 3 2 2 2 3 3 3 3 2 1 1 3 3 2 1 2 2 2 3 3 1 3
## [1444] 3 1 3 3 3 3 3 3 3 3 3 2 3 3 3 1 1 2 3 2 2 3 3 1 3 3 3 3 3 2 2 1 1 3 3 2 1
## [1481] 1 3 3 3 3 3 3 1 1 3 2 2 1 2 1 3 1 3 3 1 1 3 1 3 3 3 2 3 3 2 2 3 3 1 3 1 1
## [1518] 3 3 1 3 3 3 3 2 2 3 3 1 3 3 2 3 3 3 1 1 2 3 1 3 3 2 3 1 3 3 1 2 2 3 3 1 1
## [1555] 2 1 1 3 2 2 2 1 3 3 3 3 3 2 3 3 1 3 3 3 3 3 3 3 1 2 3 3 3 3 1 3 3 2 2 1 1
## [1592] 3 3 3 3 3 1 3 2 1 1 3 2 1 3 3 3 3 1 3 3 1 3 3 2 2 1 1 2 2 3 3 2 3 1 3 1 1
## [1629] 3 2 1 1 2 1 1 1 1 1 1 1 3 1 1 3 2 1 3 3 2 3 3 3 3 1 3 3 2 3 3 3 3 3 1 2 3
## [1666] 3 3 2 1 3 1 2 3 1 1 3 3 3 3 3 3 1 1 3 1 3 3 3 3 3 3 3 3 3 2 3 3 1 3 1 2 2
## [1703] 3 3 3 3 3 3 2 3 3 3 3 3 3 1 3 1 1 3 2 3 2 2 3 3 3 3 3 3 3 2 3 3 1 3 3 3 3
## [1740] 1 1 1 1 3 3 3 3 2 2 1 2 1 1 2 2 1 1 2 3 2 3 3 3 3 3 1 3 1 3 3 1 1 2 3 1 3
## [1777] 3 2 3 3 3 2 3 2 3 3 3 3 3 3 2 1 1 2 2 2 3 3 1 3 3 2 3 3 3 3 3 1 1 2 3 2 3
## [1814] 3 3 2 2 3 3 3 1 2 3 2 2 2 3 1 2 1 3 3 3 3 1 3 3 1 3 3 2 3 3 1 1 3 3 2 3 3
## [1851] 3 3 1 3 1 3 3 3 3 3 1 3 3 2 1 2 2 2 2 2 3 3 1 3 3 3 3 3 1 1 3 3 3 3 1 1 1
## [1888] 2 3 3 3 1 1 3 1 1 3 2 1 1 1 1 2 1 3 3 3 3 2 1 1 3 3 1 3 2 1 3 3 2 3 3 2 1
## [1925] 3 3 3 3 3 3 3 3 3 3 3 3 2 1 3 3 1 1 1 1 3 2 3 2 3 3 1 3 3 2 1 1 3 2 3 1 3
## [1962] 3 3 3 3 1 3 1 1 2 2 2 3 3 1 3 3 1 1 3 3 2 1 3 3 3 3 1 2 3 3 3 3 2 3 1 3 1
## [1999] 3 3 1 2 1 3 2 3 3 2 3 3 3 2 1 1 3 3 1 3 3 1 3 1 2 3 3 2 2 3 3 3 2 1 1 2 3
## [2036] 3 1 1 3 2 3 3 2 1 3 3 3 2 3 3 1 1 1 1 2 1 2 3 3 3 3 3 3 3 2 3 3 1 1 1 3 3
## [2073] 2 2 3 1 3 3 3 1 1 1 2 2 3 1 2 3 1 3 3 3 3 3 3 1 3 3 3 3 3 1 3 3 3 1 2 3 3
## [2110] 3 3 3 2 1 2 3 1 3 3 3 1 3 3 1 2 1 1 3 2 1 1 3 1 3 3 3 3 2 3 3 1 1 2 3 3 3
## [2147] 3 3 3 2 3 1 1 2 3 2 3 3 1 3 3 3 3 1 3 2 3 3 2 2 1 3 3 3 2 3 3 1 3 1 1 1 2
## [2184] 2 3 1 1 3 2 3 3 1 1 3 3 3 1 3 3 1 2 3 3 3 3 3 2 1 3 3 1 2
##
## Silhouette plot information for best sample:
## cluster neighbor sil_width
## 2096 1 2 0.2666778561
## 1742 1 2 0.2643744719
## 1743 1 2 0.2643744719
## 568 1 2 0.2606505045
## 1201 1 2 0.2599908647
## 938 1 2 0.2561264149
## 1045 1 2 0.2558665074
## 2152 1 2 0.2546131835
## 2153 1 2 0.2546131835
## 1167 1 2 0.2527405123
## 1035 1 2 0.2481811154
## 1036 1 2 0.2481811154
## 737 1 2 0.2474252253
## 1960 1 2 0.2472504770
## 674 1 2 0.2468510811
## 675 1 2 0.2468510811
## 689 1 2 0.2458495191
## 918 1 2 0.2455964213
## 2032 1 2 0.2415098266
## 1186 1 2 0.2374282620
## 1900 1 2 0.2366170637
## 1756 1 2 0.2351511902
## 1757 1 2 0.2351511902
## 432 1 2 0.2350531342
## 1683 1 2 0.2328234422
## 1938 1 2 0.2322083195
## 582 1 2 0.2321126828
## 1772 1 2 0.2318911847
## 664 1 2 0.2311908044
## 665 1 2 0.2311908044
## 173 1 2 0.2308211733
## 1324 1 2 0.2280119286
## 1553 1 2 0.2273075241
## 1554 1 2 0.2273075241
## 600 1 2 0.2269660640
## 847 1 2 0.2268707199
## 800 1 2 0.2265141285
## 2180 1 2 0.2260948888
## 1012 1 2 0.2256731942
## 1346 1 2 0.2254992772
## 1157 1 2 0.2254629692
## 1609 1 2 0.2246751680
## 798 1 2 0.2246165733
## 927 1 2 0.2217065534
## 488 1 2 0.2209431892
## 1500 1 2 0.2209068038
## 1835 1 2 0.2206389385
## 1793 1 2 0.2177349532
## 1204 1 2 0.2171783174
## 1205 1 2 0.2171783174
## 823 1 2 0.2166289142
## 1356 1 2 0.2163341249
## 806 1 2 0.2158541182
## 870 1 2 0.2158133027
## 871 1 2 0.2158133027
## 1227 1 2 0.2139489657
## 334 1 2 0.2137231443
## 1941 1 2 0.2133953934
## 1325 1 2 0.2123870833
## 1520 1 2 0.2111836835
## 985 1 2 0.2097346240
## 1497 1 2 0.2097036696
## 2013 1 2 0.2074165799
## 2014 1 2 0.2074165799
## 339 1 2 0.2071501582
## 174 1 2 0.2065190225
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## 513 1 2 0.2057084259
## 514 1 2 0.2057084259
## 1718 1 2 0.2054077457
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## 754 1 2 0.2053052421
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## 1501 1 2 0.2030221384
## 1 1 2 0.2028715416
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## 983 1 2 0.2011898286
## 703 1 2 0.2002329400
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## 190 1 2 0.1981283523
## 766 1 2 0.1971166276
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## 1221 1 2 0.1947697814
## 1480 1 2 0.1941555330
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## 2022 1 2 0.1925276968
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## 2056 1 2 0.1915069888
## 322 1 2 0.1906569887
## 2117 1 2 0.1902493505
## 1503 1 2 0.1890140458
## 1631 1 2 0.1881771079
## 633 1 2 0.1880623387
## 690 1 2 0.1874840342
## 166 1 2 0.1872223366
## 611 1 2 0.1868262344
## 612 1 2 0.1868262344
## 1319 1 2 0.1867871958
## 1821 1 2 0.1867245476
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## 6 1 2 0.1850086881
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## 2130 1 2 0.1754342120
## 2131 1 2 0.1754342120
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## 71 1 2 0.1751006866
## 1885 1 2 0.1734904436
## 1488 1 2 0.1733520199
## 2106 1 2 0.1731426778
## 284 1 2 0.1725942896
## 142 1 2 0.1713210382
## 329 1 2 0.1700643549
## 318 1 2 0.1694535791
## 705 1 2 0.1692956797
## 2082 1 2 0.1671191439
## 1910 1 2 0.1652589305
## 1911 1 2 0.1652589305
## 1768 1 2 0.1650153702
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## 645 1 2 0.1589758367
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## 1529 1 2 0.1585349922
## 1431 1 2 0.1583525859
## 630 1 2 0.1575829689
## 999 1 2 0.1559146095
## 1637 1 2 0.1556280114
## 1394 1 2 0.1544491643
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## 304 1 2 0.1538847842
## 352 1 2 0.1538429969
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## 307 1 2 0.1531387138
## 137 1 2 0.1522389771
## 1996 1 2 0.1472610465
## 1998 1 2 0.1470950623
## 2141 1 2 0.1458589999
## 2142 1 2 0.1458589999
## 2200 1 2 0.1447753073
## 1436 1 2 0.1440537972
## 1597 1 2 0.1431016721
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## 1983 1 2 0.1393490370
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## 288 1 2 0.1392711752
## 292 1 2 0.1380271240
## 796 1 2 0.1375861513
## 1132 1 2 0.1371970981
## 119 1 2 0.1370703498
## 1865 1 2 0.1368899364
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## 135 1 2 0.1344654686
## 1968 1 2 0.1333364525
## 1969 1 2 0.1333364525
## 1838 1 2 0.1326625971
## 1401 1 2 0.1310724579
## 2187 1 2 0.1307067822
## 902 1 2 0.1305095068
## 704 1 2 0.1304388860
## 1256 1 2 0.1293176324
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## 315 1 2 0.1279978412
## 1830 1 2 0.1271461288
## 2159 1 2 0.1264023900
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## 2076 1 2 0.1243031960
## 397 1 2 0.1234677632
## 1343 1 2 0.1231163986
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## 2051 1 2 0.1195243121
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## 1495 1 2 0.1152849425
## 763 1 2 0.1148981031
## 169 1 2 0.1148862523
## 1337 1 2 0.1138743330
## 1988 1 2 0.1131683046
## 2121 1 2 0.1120924001
## 1386 1 2 0.1119119071
## 1342 1 2 0.1118555104
## 59 1 2 0.1114137792
## 2164 1 2 0.1110589729
## 635 1 2 0.1106582119
## 413 1 2 0.1105962815
## 414 1 2 0.1105962815
## 793 1 2 0.1105956866
## 1879 1 2 0.1105931627
## 360 1 2 0.1100092005
## 533 1 2 0.1094569326
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## 824 1 2 0.1081776089
## 1545 1 2 0.1076787222
## 426 1 2 0.1054326922
## 1148 1 2 0.1052294631
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## 188 1 2 0.1051109191
## 2133 1 2 0.1041193202
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## 473 1 2 0.1038164331
## 1059 1 2 0.1029573134
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## 951 1 2 0.1026000565
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## 13 1 2 0.1001063683
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## 1828 1 2 0.0988146939
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## 300 1 2 0.0961219536
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## 130 1 2 0.0940723816
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## 2001 1 2 0.0940165730
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## 430 1 2 0.0929624715
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## 191 1 2 0.0887940766
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## 1442 1 2 0.0878405092
## 1917 1 2 0.0876951748
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## 30 1 2 0.0856846757
## 1902 1 2 0.0855275649
## 2102 1 2 0.0829877000
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## 1049 1 2 0.0808665903
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## 1215 1 2 0.0784705046
## 442 1 2 0.0784485203
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## 520 1 2 0.0602315911
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## 256 1 2 0.0552158370
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##
## 1035 dissimilarities, summarized :
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.5055 3.6653 4.9245 5.1487 6.2369 13.7790
## Metric : euclidean
## Number of objects : 46
##
## Available components:
## [1] "sample" "medoids" "i.med" "clustering" "objective"
## [6] "clusinfo" "diss" "call" "silinfo" "data"
## [11] "nbclust"Silhouette index
fviz_silhouette(clara_3)## cluster size ave.sil.width
## 1 1 503 0.09
## 2 2 483 0.11
## 3 3 1226 0.32
The I will do the same way of grouping as I did above for Kmeans aggregate(data = marketing, Income ~ KMEANS_3$cluster, mean) —> replace KMEANS_3 with clara_3
mean values of Income for all variables in dataset for each cluster
aggregate(data = marketing, Income ~ clara_3$cluster, mean)## clara_3$cluster Income
## 1 1 76321.11
## 2 2 64228.55
## 3 3 37129.68mean values of Recency of purchase for all variables in dataset for each cluster
aggregate(data = marketing, Recency ~ clara_3$cluster, mean)## clara_3$cluster Recency
## 1 1 52.01193
## 2 2 46.40994
## 3 3 48.81974TYPES OF PURCHASES
mean number of puchases online(Web purchases)
aggregate(data = marketing, NumWebPurchases ~ clara_3$cluster, mean)## clara_3$cluster NumWebPurchases
## 1 1 4.771372
## 2 2 7.043478
## 3 3 2.643556mean number of puchases from catalogue
aggregate(data = marketing, NumCatalogPurchases ~ clara_3$cluster, mean)## clara_3$cluster NumCatalogPurchases
## 1 1 5.972167
## 2 2 3.944099
## 3 3 0.817292mean number of puchases from store itself(on site purchases)
aggregate(data = marketing, NumStorePurchases ~ clara_3$cluster, mean)## clara_3$cluster NumStorePurchases
## 1 1 8.347913
## 2 2 8.523810
## 3 3 3.693312Number of average visits for variables of each cluster
aggregate(data = marketing, NumWebVisitsMonth ~ clara_3$cluster, mean)## clara_3$cluster NumWebVisitsMonth
## 1 1 2.564612
## 2 2 5.331263
## 3 3 6.448613Mean number of complaints
aggregate(data = marketing, Complain ~ clara_3$cluster, mean)## clara_3$cluster Complain
## 1 1 0.005964215
## 2 2 0.010351967
## 3 3 0.009787928We can also see average age by clusters too
aggregate(data = marketing, age ~ clara_3$cluster, mean)## clara_3$cluster age
## 1 1 51.70974
## 2 2 58.23188
## 3 3 49.81974Mean number of people who have family or in a relationship
aggregate(data = marketing, partner ~ clara_3$cluster, mean)## clara_3$cluster partner
## 1 1 0.5367793
## 2 2 0.7225673
## 3 3 0.6598695Mean number of kids that we summed previously
aggregate(data = marketing, Number_of_kids ~ clara_3$cluster, mean)## clara_3$cluster Number_of_kids
## 1 1 0.2067594
## 2 2 0.9337474
## 3 3 1.2569331Mean number of discounted purchases
aggregate(data = marketing, DiscountedPurchases ~ clara_3$cluster, mean)## clara_3$cluster DiscountedPurchases
## 1 1 1.357853
## 2 2 2.844720
## 3 3 2.516313Conclusion on 3 cluster CLARA 1st GROUP: # The wealthiest # Leaders in recency of puchases # Buy mostly from catalogue # Less likely to are in a relationship or have family # Tend to buy products which are not on discount # Less likely to complain
2nd GROUP: # Mostly buy online # Are biggest group of those who buy on-site too # Biggest number of visits of shop # Have relatively higher number of complaints # On average the oldest among all groups # Likely to have family or be in a relationship # Buy products on discount the most
3rd GROUP: # Earn the least # Mostly the last in other aspects. # The least valuable group for the shop
In order to be sure if the number of clusters right, we will use following codes. But before that we need to create 4 clusters(CLARA) to compare it with previous results. First, check for 4 clusters
clara_4 <- eclust(cluster_z,'clara',k=4,hc_metric = 'euclidean', graph = FALSE)
plot_clara_4 <- fviz_cluster(clara_4, geom = c("point")) + ggtitle('CLARA with 4 clusters')
plot_clara_4
Now we can compare 3 and 4 clusters, in terms of which option is more approptiate We will use Calinski-Harabasz index in order to understand which option is better one. The higher the result the better, meaning that 3 clusters is just the way to go.
round(calinhara(cluster_z, clara_4$cluster),digits=2) ## [1] 486.69round(calinhara(cluster_z, clara_3$cluster),digits=2) ## [1] 585.89So, again even in the case with CLARA the first group was the most valuable for the shop in terms of almost all aspects. It would be better to separate the group in more clusters, however, because of the nature of our data it is best to keep it within a range of 3-4 clusters. But still our result showed that 3 is the optimal number of cluters for this dataset.