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How to force the topics to be different from the defined ones?

Suppose I have a collection of texts about cats and dogs.There should naturally be two topics: one about dogs and one about cats. But I'm not interested in such results, I'd like to get topics that are completely different (let's call them orthogonal). In other words I would like to use topic modeling to discover a different division of documents (but I don't know what). I thought about guided LDA, but in my opinion it is not applicable in this case (maybe I'm wrong?).

One idea is to remove from the corpus the words that make up the topic about cats and about dogs. I can imagine such a solution in such a way that I run the algorithm to model topics and in the obtained results I mark which topics are not interesting for me and run the algorithm again but already conditioned with this information.

Do you think this is a good idea? Or are there any methods designed for this?

I also found a paper Probabilistic Text Modeling with Orthogonalized Topics, in which the concept of orthogonal themes appears, but it is used in a different context than I want.

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