Scalable Approximate FRNN-OWA Classification

Fuzzy rough nearest neighbor classification with ordered weighted averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbor search. In practice, the query time complexity of exact nearest neighbor search algorithms in more than a handful of dimensions is near linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbors returned by hierarchical navigable small worlds (HNSW), a recent approximative nearest neighbor search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster.