  Despite the success of deep learning on representing images for particular
object retrieval, recent studies show that the learned representations still
lie on manifolds in a high dimensional space. This makes the Euclidean nearest
neighbor search biased for this task. Exploring the manifolds online remains
expensive even if a nearest neighbor graph has been computed offline. This work
introduces an explicit embedding reducing manifold search to Euclidean search
followed by dot product similarity search. This is equivalent to linear graph
filtering of a sparse signal in the frequency domain. To speed up online
search, we compute an approximate Fourier basis of the graph offline. We
improve the state of art on particular object retrieval datasets including the
challenging Instre dataset containing small objects. At a scale of 10^5 images,
the offline cost is only a few hours, while query time is comparable to
standard similarity search.
