I am reading this book http://infolab.stanford.edu/~ullman/mmds/ch9.pdf there is an exercise 9.3.2 a) it says

Exercise 9.3.2 : In this exercise, we cluster items in the matrix of Fig. 9.8. Do the following steps. (a) Cluster the eight items hierarchically into four clusters. The following method should be used to cluster. Replace all 3’s, 4’s, and 5’s by 1 and replace 1’s, 2’s, and blanks by 0. use the Jaccard distance to measure the distance between the resulting column vectors. For clusters of more than one element, take the distance between clusters to be the minimum distance between pairs of elements, one from each cluster.

I am not able to understand how clustering is done?If I replace all 3,4,5 with 1 and 1,2, with 0 I am left with a matrix

  a b c d e f g h
A 1 1   1 0   1 0
B   1 1 1 0 0 0
C 0   0 1   1 1 1

What is meant by cluster formation here? How do I solve this exercise or any solution available online please give a link.


Replacing the non-zero values is meant to simplify the matrix, i.e. we only care whether the value is zero or not.

Then you're supposed to calculate the Jaccard distance between pairs of columns. For instance between the first two columns you have $|a\cap b|=1$, $|a\cup b|=2$ so the distance is 1/2.

After that you're supposed to apply hierarchical clustering using the distance. This means progressively grouping elements (here columns) which are close to each other according to the distance.


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