Compact distance histogram: a novel structure to boost k-nearest neighbor queries

The k-Nearest Neighbor query (k-NNq) is one of the most useful similarity queries. Elaborated k-NNq algorithms depend on an initial radius to prune regions of the search space that cannot contribute to the answer. Therefore, estimating a suitable starting radius is of major importance to accelerate k-NNq execution. This paper presents a new technique to estimate a tight initial radius. Our approach, named CDH-kNN, relies on Compact Distance Histograms (CDHs), which are pivot-based histograms defined as piecewise linear functions. Such structures approximate the distance distribution and are compressed according to a given constraint, which can be a desired number of buckets and/or a maximum allowed error. The covering radius of a k-NNq is estimated based on the relationship between the query element and the CDHs' joint frequencies. The paper presents a complete specification of CDH-kNN, including CDH's construction and radii estimation. Extensive experiments on both real and synthetic datasets highlighted the efficiency of our approach, showing that it was up to 72% faster than existing algorithms, outperforming every competitor in all the setups evaluated. In fact, the experiments showed that our proposal was just 20% slower than the theoretical lower bound.