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I want to use a clustering algorithm which can catch the following within a multivariate binary dataset. In the sample below, since class 1 and 2 appear twice within column A and B they will form a cluster. The same will be for class 5 and 6. Class 3 and 4 will belong to a cluster which is located closer to class 1 and 2 since column B has class 1 to 4. Is hierarchical clustering an appropriate technique to display this kind of relationship?

The data are as follow:

A B C D
class1 1 1 0 0
class2 1 1 0 0
class3 0 1 0 0
class4 0 1 0 0
class5 0 0 1 1
class6 0 0 1 1
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Yes, hierarchical clustering will be appropriate for this. There are many different methods you can use (agglomerative etc.) which I won't go into.

The way to think about this is by looking at the distance between rows.

  • Class 1 and 2 get grouped together because the distance between their rows is zero. (They have the same elements).
  • Class 5 and 6 get grouped together for the same reason.
  • Class 3 and 4 get grouped together for the same reason.
  • Cluster 3&4 is closer to 1&2 than 5&6 because the distance between the rows is smaller.
  • For example, if our distance metric is just the sum of row-wise differences then the distance from 1&2 to 3&4 is 1 while the distance from 5&6 to 3&4 is 3.

So the two choices you need to make are:

  1. Which clustering algorithm to use.
  2. What distance metric to use.
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  • $\begingroup$ thank you, it helps. Do you know if it is possible to express the probability that a class will be selected with another class? FYI, I use Scipy with Pyhton to do this. $\endgroup$ Commented Oct 14, 2021 at 3:08

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