I have dim memories of using random k basis vectors to convert high dimensionality feature vectors to k dimensions, and doing m times to generate multiple projections as part of a an LSH schema. Min-hashing might have been involved.
IIRC, minhashing is used to approximate Jacquard similarity (a set-theoretic measure), while random hyperplanes (aka simhashing) is used to approximate cosine similarity (a geometric/algebraic measure). So they solve different problems, even though some problems can be cast in terms of either framework.
I have dim memories of using random k basis vectors to convert high dimensionality feature vectors to k dimensions, and doing m times to generate multiple projections as part of a an LSH schema. Min-hashing might have been involved.