sparsity means that while you may have large matrices and vectorsin principlemost of the values are zero (or so small that we can round them to zero as good approximationthereforeonly few things are relevant at any given time often problems that seem too big to solve are actually feasible because the data is sparse for exampleeven though one webpage can link to any other webpagethe graph of links is actually very sparse as each webpage will link to very tiny fraction of all other webpages in the previous graphwe can see that about documents have topicswhile the majority deal with around to of them no document talks about more than topics to large extentthis is function of the parameters usednamely the alpha parameter the exact meaning of alpha is bit abstractbut bigger values for alpha will result in more topics per document alpha needs to be positivebut is typically very smallusually smaller than one by defaultgensim will set alpha equal to len (corpus)but you can set it yourself as followsmodel models ldamodel ldamodelcorpusnum_topics= id word=corpus id wordalpha= in this casethis is larger alphawhich should lead to more topics per document we could also use smaller value as we can see in the combined histogram given nextgensim behaves as we expected