PolyMinHash: Efficient Area-Based MinHashing of Polygons for Approximate Nearest Neighbor Search

Abstract: Similarity searches are a critical task in data mining. As data sets grow larger, exact nearest neighbor searches quickly become unfeasible, leading to the adoption of approximate nearest neighbor (ANN) searches. ANN has been studied for text data, images, and trajectories. However, there has been little effort to develop ANN systems for polygons in spatial database systems and geographic information systems. We present PolyMinHash, a system for approximate polygon similarity search that adapts MinHashing into a novel 2D polygon-hashing scheme to generate short, similarity-preserving signatures of input polygons. Minhash is generated by counting the number of randomly sampled points needed before the sampled point lands within the polygon's interior area, yielding hash values that preserve area-based Jaccard similarity. We present the tradeoff between search accuracy and runtime of our PolyMinHash system. Our hashing mechanism reduces the number of candidates to be processed in the query refinement phase by up to 98% compared to the number of candidates processed by the brute-force algorithm.