Fast Spectral Ranking for Similarity Search
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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. Therefore, nearest neighbor search cannot be expected to be optimal for this task. Even if a nearest neighbor graph is computed offline, exploring the manifolds online remains expensive. This work introduces an explicit embedding reducing manifold search to Euclidean search followed by dot product similarity search. We show this is equivalent to linear graph filtering of a sparse signal in the frequency domain, and we introduce a scalable offline computation of an approximate Fourier basis of the graph. We improve the state of art on standard particular object retrieval datasets including a challenging one 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.
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