How to put a single skill in multiple clusters?

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I have multiple skills and I want to find out the related skills to that skill.

For Example: If we have CSS, HTML, JAVASCRIPT, Angular.js

My usecase is to cluster skills together such that one skill lies in multiple clusters. I have already generated the word embeddings.

I have tried various algorithms like Dirichlet Process Mixtures, DBSCAN with Variable Epsilon, Hierarchical Clustering with Overlapping Merge but have not got my desired result. In all of them one skill is not belonging to multiple clusters.

What I got:

Cluster 1: HTML, CSS

Cluster 2: Javascript, Angular.js

But I am not getting mixed clusters.

Expected Result:

Cluster 1: CSS, HTML

Cluster 2: Javascript, Angular.js, CSS, HTML

Cluster 3: Javascript, Angular.js

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