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Which of the following are correct? As a non-native English speaker they seem interchangeable to me, but I wonder if in the context of the sentence they have a different meaning to each other.

Explored different methods for topic modeling such as LSA and LDA.

Explored various methods for topic modeling such as LSA and LDA.

Explored several methods for topic modeling such as LSA and LDA.

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Any of your examples can be correct, but there are differences in meaning depending on which word you use.

Explored different methods....

Each method is unique and distinct from the other methods. This could include methods that are not specifically topic modeling methods (perhaps you're applying a technique from another discipline to propose a unique solution).

Explored various methods...

The methods are different, but share some commonality at a very high level. In this case, the commonality is that the methods are all topic modeling methods.

Explored several methods...

This only refers to the number of methods explored. It makes no assumptions about similarity or difference. It is often combined with different, for example:

We explored several different methods for topic modeling...

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