Fast binary embeddings with Gaussian circulant matrices: improved bounds

Understand

We consider the problem of encoding a finite set of vectors into a small number of bits while approximately retaining information on the angular distances between the vectors.

• By deriving improved variance bounds related to binary Gaussian circulant embeddings, we largely fix a gap in the proof of the best known fast binary embedding method.
• Our bounds also show that well-spreadness assumptions on the data vectors, which were needed in earlier work on variance bounds, are unnecessary.
• In addition, we propose a new binary embedding with a faster running time on sparse data.