Hierarchical Clustering - linkage(y)

Hi,

I don't fully understand the linkage function and its outputs.

>> x=[1 2 6 8]';
>> y=pdist(x)

y =

     1     5     7     4     6     2

>> Z=linkage(y)

Z =

     1     2     1
     3     4     2
     5     6     4

For Z, what does the first and second column stand for? What is the third column? How was the third column calculated based on the input data x and y?

Answer 1

[Salad Box]

Only just figured it out.

The first and second columns are the new group number after clustering.

4 elements in x each was given a group number from 1 to 4.

The system will then group element 1 and 2 in x together and give a new group number '5'.

The system will then group element 6 and 8 in x together and give a new group number '6'.

The system will at last group '5' and '6' together while group 5 looks like (1,2), and group 6 looks like (6,8).

the third column is the distance between the two group.

first number in column 3 is 1, that is the difference between elements 1 and 2.

second number in column 3 is 2, that is the difference between elements 6 and 8.

third number in column 3 is 4. That is the tricky one. group 5 and group 6 would look like (1,2) and (6,8). Matlab use the shortest euclidean distance by default. Therefore the shortest between two groups will be the 2 from group 5 and the 6 from group 6 with the distance 6-2=4.

Ta-da!