It is well known that Random Projection (RP) is tightly linked to Locality Sensitive Hashing (LSH). My goal is to cluster a large number of points lying in a d-dimensional Euclidean space, where $d$ is very large.
Questions: Does it make sense to cluster the points via LSH after having reduced the dimensionality of their input space by using first RP? Why yes/no? Is there any redundancy in the combined use of RP as dimensionality reduction method before LSH as clustering method?