Fast spectral analysis for approximate nearest neighbor search

In large-scale machine learning, of central interest is the problem of approximate nearest neighbor (ANN) search, where the goal is to query particular points that are close to a given object under certain metric. In this paper, we develop a novel data-driven ANN search algorithm where the data structure is learned by fast spectral technique based on s landmarks selected by approximate ridge leverage scores. We show that with overwhelming probability, our algorithm returns the (1 + ϵ/ 4) -ANN for any approximation parameter ϵ∈ (0 , 1). A remarkable feature of our algorithm is that it is computationally efficient. Specifically, learning k-length hash codes requires O((s³+ ns²) log n) running time and O(d²) extra space, and returning the (1 + ϵ/ 4) -ANN of the query needs O(klog n) running time. The experimental results on computer vision and natural language understanding tasks demonstrate the significant advantage of our algorithm compared to state-of-the-art methods.