Academic way of saying "On the other hand"

"Conversely, various studies suggested that LDA may not work on short documents due to insufficient context."

There's nothing wrong with On the other hand in any context.

You could write

"By contrast, various studies suggested that LDA may not work on short documents due to insufficient context."

Both conversely, "with a reversed relationship", and on the contrary are ok if you are writing about parallel cases; by contrast (or in contrast) suggests a difference but not necessarily a paralled or directly opposite relation.

"However, various studies suggested that LDA may not work on short documents due to insufficient context"

Your text is ok, but since you are looking for a short version, here is my contribution :)

'On the contrary, various studies have suggested that LDA may not work on short documents due to insufficient context.'