How can i partition market basket items into clusters? - r

Question

I have a data set as follows: (i took a simple example but the real data set is much bigger)
V1 V2 V3 V4
1 1 0 0 1
2 0 1 1 0
3 0 0 1 0
4 1 1 1 1
5 0 1 1 0
6 1 0 0 1
7 0 0 0 1
8 0 1 1 1
9 1 0 1 0
10 0 1 1 0
...
where V1, V2,V3...Vn are items and 1,2,3,4...1000 are transactions. I want to partition these items into k clusters such that in each cluster i have the items that appear the most frequently together in the same transactions.
To determine the number times each couple of items appear together i tried crosstable, i got the following results:
V1 V2 V3 V4
V1 4 1 2 3
V2 1 5 5 2
V3 2 5 7 2
V4 3 2 2 5
For this small example if i want to create 2 clusters (k=2) such that a cluster must contain 2 items (to maintain the balance between clusters), i will get:
Cluster1={V1,V4}
Cluster2={V2,V3}
because:
1) V1 appears more frequently with V4 (V1,V4)=3 > (V1,V3) > (V1,V2) and same for V4.
2) V2 appears more frequently with V2 (V2,V3)=5 > (V2,V4) > (V2, V1) and same for V3.
How can i do this partition with R and for a bigger set of data ?

Answer 1

I think you are asking about clustering. It is not quite the same as what you are doing above, but you could use hclust to look for similarity between variables with a suitable distance measure.
For example
plot(hclust(dist(t(df),method="binary")))
produces the following...
You should look at ?dist to see if this distance measure is meaningful in your context, and ?hclust for other things you can do once you have your dendrogram (such as identifying clusters).
Or you could use your crosstab as a distance matrix (perhaps take the reciprocal of the values, and then as.dist).

Answer 2

library(data.table)
data:
df<-
fread("
V1 V2 V3
1 1 0 0
2 0 0 1
3 0 0 1
4 1 1 1
5 0 0 1
6 1 0 0
7 0 0 0
8 0 1 1
9 1 0 1
10 0 1 1
")[,-1]
code:
setDT(df)
sapply(names(df),function(x){
df[get(x)==1,lapply(.SD,sum,na.rm=T),.SDcols=names(df)]
})
result:
V2 V3 V4
V2 4 1 2
V3 1 3 3
V4 2 3 7

Answer 3

df <- read.table(text="
ID V1 V2 V3
1 1 0 0
2 0 0 1
3 0 0 1
4 1 1 1
5 0 0 1
6 1 0 0
7 0 0 0
8 0 1 1
9 1 0 1
10 0 1 1
", header = TRUE)
k = 3 # number of clusters
library(dplyr)
df %>%
# group and count on all except the first id column
group_by_at(2:ncol(df)) %>%
# get the counts, and collect all the transaction ids
summarize(n = n(), tran_ids = paste(ID, collapse = ',')) %>%
ungroup() %>%
# grab the top k summarizations
top_n(k, n)
# V1 V2 V3 n tran_ids
# <int> <int> <int> <int> <chr>
# 1 0 0 1 3 2,3,5
# 2 0 1 1 2 8,10
# 3 1 0 0 2 1,6

Answer 4

You can transpose your table and use standard methods of clustering. Thus, you will cluster the items. The features are the transactions.
Geometrical approaches can be used like kmeans. Alternatively, you can use mixture models which provide information criteria (like BIC) for selecting the number of clusters. Here is an R script
require(VarSelLCM)
my.data <- as.data.frame(t(df))
# To consider Gaussian mixture
# Alternatively Poisson mixture can be considered by converting each column into integer.
for (j in 1:ncol(my.data)) my.data[,j] <- as.numeric(my.data[,j])
## Clustering by considering all the variables as discriminative
# Number of clusters is between 1 and 6
res.all <- VarSelCluster(my.data, 1:6, vbleSelec = FALSE)
# partition
res.all#partitions#zMAP
# shiny application
VarSelShiny(res.all)
## Clustering with variable selection
# Number of clusters is between 1 and 6
res.selec <- VarSelCluster(my.data, 1:6, vbleSelec = TRUE)
# partition
res.selec#partitions#zMAP
# shiny application
VarSelShiny(res.selec)