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I tried topic modeling (LDA, NMF) to extract insights from the data.

I'm curious right now, are there other methods for unsupervised learning to cluster documents by the same or similar context?

(Aside) Are there any methods to show similarity of a topic or documents from topic?

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You could use doc2vec to create vector representations of each document. Once you have all the vector representations you can use standard unsupervised clustering techniques like k-means, hierarchical clustering, or K-SOM.

The doc2vec model you create will be able to compute cosine similarity between two documents and also find the n most similar documents to a given document and provide a similarity score for each.

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Generate TF-IDF scores and pass them to K-Means clustering to group similar documents together.

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