LazyLSH: Approximate Nearest Neighbor Search for Multiple Distance Functions with a Single Index

Due to the "curse of dimensionality" problem, it is very expensive to process the nearest neighbor (NN) query in high-dimensional spaces; and hence, approximate approaches, such as Locality-Sensitive Hashing (LSH), are widely used for their theoretical guarantees and empirical performance. Current LSH-based approaches target at the L1 and L2 spaces, while as shown in previous work, the fractional distance metrics (Lp metrics with 0 < p < 1) can provide more insightful results than the usual L1 and L2 metrics for data mining and multimedia applications. However, none of the existing work can support multiple fractional distance metrics using one index. In this paper, we propose LazyLSH that answers approximate nearest neighbor queries for multiple Lp metrics with theoretical guarantees. Different from previous LSH approaches which need to build one dedicated index for every query space, LazyLSH uses a single base index to support the computations in multiple Lp spaces, significantly reducing the maintenance overhead. Extensive experiments show that LazyLSH provides more accurate results for approximate kNN search under fractional distance metrics.