# Combine two sets of clusters

I have two sets of topics obtained from two different sets of news paper articles.

In other words, Cluster_1 = ${x_1, x_2, ..., x_n}$ includes the main topics of 'X' news paper set and Cluster_2 = ${y_1, y_2, ..., y_n}$ includes the main topics of 'Y' news paper set.

Now I want to find clusters in the two sets that are similar/related by considering the cluster attributes as given in the example below.

Example 1,
**X1 in Cluster_1** is mostly similar/related to **Y2 in Cluster_2**
**X2 in Cluster_1** is mostly similar/related to **Yn in cluster_2**
and so on.

Example 2:
News about Yet in Cluster_1 is mostly similar/related to News about Science in Cluster_2
News about Floods in Cluster_1 is mostly similar/related to News about Rains in Cluster_2


Since, I am dealing with two separate sets of clusters, what would be a suitable measurement/method I can use to connect the clusters in the two different sets?

• Are these two different groupings of the same observations? In the same space? Same dimensional space? What does "most similar/related" mean to you in this context? – Thomas Cleberg Aug 17 '17 at 2:31
• Thank you for the comment. I edited the question by including the missing information you have mentioned. – Volka Aug 17 '17 at 2:48
• Are your clusters the result of topic modeling with something like Latent dirichlet allocation over two newspapers, and you're wondering if you can compare the topics between the two newspapers? – Thomas Cleberg Aug 17 '17 at 3:26
• Yes, you are correct. – Volka Aug 17 '17 at 3:28
• Is it exactly latent dirichlet allocation, because that becomes important. – Thomas Cleberg Aug 17 '17 at 3:29

One such measure that's commonly used in these circumstances is the Hellinger Distance. To find the closest match for $x_1$ in the topics for $y$, you would calulate the Hellinger Distance between $x_1$ and each $y$ topic, then take the lowest one.