In this example data, there are six customers, and each is described with four attributes: Customer, Age, Income, Cards, Gender. Your task is to do clustering of the $6$ customers. Follow the steps to carry out clustering and use as much as details to describe the process.

Customer Gender Age Income$(1000)$ Cards

cusA $040503$

cusB $038482$

cusC $125304$

cusD $0691701$

cusE $019402$

cusF $0231403$

Manhattan distance metrics is adopted in the clustering. d$\_$Manhattan$($A$,$B$)=\_($i$=1)^$n$|$x$\_$i$-$y$\_$i $|$

Bottom$-$up approach Algorithm is adopted in the clustering.

Trial$-$and$-$error: K$=2.$

Initial Step:

Number of clusters: $\_\_\_\_\_\_\_\_\_\_\_$

cusA cusB cusC cusD cusE cusF

cusA $------$

cusB $-----$

cusC $----$

cusD $---$

cusE $--$

cusF $-$

Table $1.$ The distance matrix contains the distance of each pair of clusters

Step $1$

New cluster $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ formed by merging two clusters which have the smallest distance in Table $1.$

Number of clusters: $\_\_\_\_\_\_\_\_\_\_\_$

Update the distance matrix, which is denoted as Table $2.$

Step $2$

New cluster $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ formed by merging two clusters which have the smallest distance in Table $2.$

Number of clusters: $\_\_\_\_\_\_\_\_\_\_$

Update the distance matrix, which is denoted as Table $3.$

Step $3$

New cluster $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$formed by merging two clusters which have the smallest distance in Table $3.$

Number of clusters: $\_\_\_\_\_\_\_\_\_\_$

Update the distance matrix, which is denoted as Table $4.$

Step $4$

New cluster $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$formed by merging two clusters which have the smallest distance in Table $4.$

Number of clusters: $\_\_\_\_\_\_\_\_\_\_$

Update the distance matrix, which is denoted as Table $5.$

Step $5$

New cluster $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$formed by merging two clusters which have the smallest distance in Table $5.$

Number of clusters: $\_\_\_\_\_\_\_\_\_\_($Stop condition is met$)$